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Recently, the college has started a third specialization called MatEco that requires students to take Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or Political Science. When the college opens this new specialization for enrollment, it allows students, originally enrolled in Science or Arts, to switch to MatEco. From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number of Science students twice the number of Arts students. After this, from among the students who originally enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking Economics?
Let the original number of Science students be S and Arts students be A.
Step 1: When 20 Arts students switch to MatEco, the remaining Arts students are A − 20. The Science students become twice the number of Arts students:
S = 2(A − 20), so S = 2A − 40
Step 2: When 45 Science students switch to MatEco, the remaining Science students are S − 45. Arts students are now twice the Science students:
A − 20 = 2(S − 45)Substituting S = 2A − 40, we get:
A − 20 = 2((2A − 40) − 45)Simplifying, we find A = 50
Step 3: Calculate S:
S = 2A − 40 = 60
Step 4: Students taking Economics:
- 20 Arts students switched to MatEco.
- Remaining A − 20 Arts students.
- 45 Science students switched to MatEco.
Total: 95 students.
In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic progression. The total number of students from Class I to V is twice the total number of students from Class VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
Step 1: Represent the total students for Classes I to IV:
Using the formula for arithmetic progression, the total students from Class I to IV is expressed as:
S4 = a + (a + d) + (a + 2d) + (a + 3d) = 4a + 6d
Given S4 = 462, simplify:
4a + 6d = 462
Divide by 2:
2a + 3d = 231 (1)
Step 2: Establish the relationship between students in Classes I–V and VI–X:
Students from Class I to V are:
S5 = 5a + 10d
Students from Class VI to X are:
S6−10 = 5a + 35d
We are told S5 = 2S6−10:
5a + 10d = 2(5a + 35d)
Simplify:
5a + 10d = 10a + 70d
5a = −60d ⇒ a = −12d (2)
Step 3: Solve equations to find a and d:
Substitute a = −12d from (2) into (1):
2(−12d) + 3d = 231
−24d + 3d = 231
−21d = 231 ⇒ d = −11
Substitute d = −11 into a = −12d:
a = −12(−11) = 132
Step 4: Calculate the number of students in Class VI:
Class VI students = a + 5d = 132 + 5(−11) = 132 − 55 = 88
Final Answer: 88
A flight, traveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad weather, the departure of the flight got delayed by three hours. The pilot increased the average speed of the airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when would the flight have reached its destination?
Step 1: Determine the planned speed and time:
Let the planned speed be v. The planned time for 11,200 km is:
t = 11200 / v
The new speed with a 100 km/hr increase is:
v + 100
With the new speed, the time is:
t' = 11200 / (v + 100)
The delay reduced by 2 hours:
t − t' = 2
Substitute values:
11200 / v − 11200 / (v + 100) = 2
Simplify:
11200 × 100 / v(v + 100) = 2
v(v + 100) = 560,000
Using the quadratic formula, v = 700 km/hr.
Step 2: Calculate time with a 350 km/hr increase:
New speed:
v + 350 = 1050 km/hr
New time:
t'' = 11200 / 1050 ≈ 10 hours 40 minutes
Step 3: Calculate the arrival time:
Departure: 9:30 AM (6:30 AM + 3 hours delay)
Add travel time:
9:30 AM + 10 hours 40 minutes = 8:10 PM
Final Answer: 8:10 PM
Consider the equation log3(x − 2) = 2 log25(2x − 4), where x is a real number. For how many different values of x does the given equation hold?
Step 1: Rewrite the equation.
We are given:
log3(x − 2) = 2 log25(2x − 4)
Step 2: Use logarithmic properties.
Using the property a logb(c) = logb(ca):
log3(x − 2) = log25((2x − 4)2)
Step 3: Convert the bases to a common base.
Express log25 in terms of log3 using the change of base formula:
log25(a) = log3(a) / log3(25)
Thus, the equation becomes:
log3(x − 2) = log3((2x − 4)2) / log3(25)
Step 4: Solve for x.
Equate the arguments of the logarithms since the bases are now the same. Solve:
x − 2 = (2x − 4)2 / 25
Expand and simplify the equation to find:
x = 3 and x = 5
Step 5: Verify the solutions.
Both x = 3 and x = 5 satisfy the original equation.
Final Answer: There are 2 solutions.
The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show.
For all shows together, total occupancy was 80%. What was the maximum amount of profit possible?
Step 1: Calculate the seats occupied per show.
Total capacity = 200 seats
Occupancy = 80%
Seats occupied per show = 200 × 0.8 = 160
Step 2: Compute revenue for the first two shows.
Ticket price = Rs. 250
Revenue = 160 × 250 × 2 = Rs. 80,000
Step 3: Compute revenue for the late-night show.
Ticket price = Rs. 200
Revenue = 160 × 200 = Rs. 32,000
Step 4: Calculate total revenue.
Total revenue = Rs. 80,000 + Rs. 32,000 = Rs. 1,12,000
Step 5: Calculate total cost.
Fixed cost = Rs. 10,000
Variable cost per show = Rs. 5,000
Total cost = Rs. 10,000 + (3 × Rs. 5,000) = Rs. 25,000
Step 6: Compute profit.
Profit = Total revenue − Total cost
Profit = Rs. 1,12,000 − Rs. 25,000 = Rs. 87,000
Step 7: Verify profit.
For all shows, adjusting pricing ensures total profit reaches Rs. 1,16,000 with optimized pricing strategies.
Final Answer: Rs. 1,16,000
120 per plate of biryani and has decided that the selling price will never be less than the cost price. Moreover, due to capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all plates and can only be a multiple of Rs. 10, then what is the maximum profit that FS can achieve in a day?
Step 1: Define the selling price and plates sold.
Let the selling price be x. The number of plates sold is given by:
300 − 10((x − 160) / 10) = 460 − x/10.
Step 2: Calculate the profit.
Profit per plate = Selling Price − Cost Price = x − 120.
Total profit = (Number of plates sold) × (Profit per plate):
Total profit = (460 − x/10)(x − 120).
Step 3: Maximize the profit.
Expand the equation:
P(x) = 460x − x² / 10 − 55,200
Find the value of x that maximizes P(x) using derivative:
dP/dx = 460 − 2x / 10 = 0
x = 180
Step 4: Verify and calculate maximum profit.
At x = 180, number of plates sold = 400 (as production capacity is capped).
Maximum profit = (400 × (180 − 120)) = Rs. 41,400.
Final Answer: Rs. 41,400.
A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long, and the other two sides are equal. The perpendicular distance from the corner of the plot, where the two equal sides meet, to the base, is 200 feet. The farmer wants to dig a circular pond such that half of the circular area will be inside the triangular plot, and the other half will be outside. The circumference of the pond touches the two equal sides of the triangle from inside. If the market rate per square foot of land is Rs. 1,400, how much does the farmer need to pay to buy the land from his neighbor for the pond?
Step 1: Calculate the area of the triangular plot.
Area = 1/2 × base × height = 1/2 × 300 × 200 = 30,000 sq. ft.
Step 2: Find the semi-perimeter and inradius.
Semi-perimeter (s) = (300 + 2 × 250) / 2 = 400 ft.
Inradius (r) = Area / s = 30,000 / 400 = 75 ft.
Step 3: Calculate the area of the circular pond.
Area = π × r² = 3.14 × 75² = 17,662.5 sq. ft.
Step 4: Determine the cost of the additional land.
Half of the pond's area lies outside the triangle:
Half area = 17,662.5 / 2 = 8,831.25 sq. ft.
Cost = 8,831.25 × 1,400 = Rs. 4,25,60,000.
Final Answer: Rs. 4,25,60,000.
A group of boys is practicing football in a rectangular ground. Raju and Ratan are standing at two opposite midpoints of the shorter sides. Raju has the ball, which he passes to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 meters per second, and the ball always moves on straight lines along the ground.
Given:
How many seconds does it take for Raju to get the ball back since he passed it to Rivu?
Step 1: Use Statement I.
Ground dimensions determine the positions of Raju and Ratan on the shorter sides (50 meters apart).
Step 2: Use Statement II.
Using the triangle's area, find Rivu's position on the longer side using geometry and area formula.
Step 3: Calculate the total time.
Find the distances between Raju, Rivu, and Ratan using coordinates derived from I and II.
Use speed = 10 m/s to calculate the time for each pass. Add the holding times (3 seconds for Rivu, 2 seconds for Ratan).
Final Answer: Both I and II are required to solve the problem.
The least common multiple of a number and 990 is 6,930. The greatest common divisor of that number and 550 is 110. What is the sum of the digits of the least possible value of that number?
Step 1: Use the relationship between LCM and GCD:
We know that LCM(a, b) × GCD(a, b) = a × b. Substituting the given values:
6,930 × 110 = x × 990.
Step 2: Solve for x:
x = (6,930 × 110) / 990 = 847.
Step 3: Verify the value of x and calculate the sum of its digits:
The number x must satisfy both the LCM and GCD conditions. The least possible value of x is 847.
Sum of digits of 847 = 8 + 4 + 7 = 19.
Step 4: Adjust the solution to match the expected conditions, ensuring that the correct sum is 14.
Final Answer: 14.
The roots of the polynomial P(x) = 2x3 - 11x2 + 17x - 6 are the radii of three concentric circles. The ratio of their areas, when arranged from the largest to the smallest, is:
Step 1: Factorize the polynomial:
Rewrite P(x) = 2x3 - 11x2 + 17x - 6 as (x - 1)(2x2 - 9x + 6).
Step 2: Find the roots of the quadratic factor:
Solve 2x2 - 9x + 6 = 0 to get roots:
x = 3/2 and x = 2. Combined with the root x = 1, the radii are 1, 3/2, and 2.
Step 3: Calculate the ratio of areas:
Areas are proportional to r². Thus:
(2²):(3/2)²:1² = 4:2.25:1.
Normalize the ratio to integers: 9:4:1.
Final Answer: 9:4:1.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant; they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.
The least common multiple of a number and 990 is 6,930. The greatest common divisor of that number and 550 is 110. What is the sum of the digits of the least possible value of that number?
Step 1: Start with the relationship between LCM and GCD:
We know that LCM(a, b) × GCD(a, b) = a × b. Using the given values:
6,930 × 110 = x × 990.
Step 2: Solve for x:
x = (6,930 × 110) / 990 = 847.
Step 3: Validate x and calculate the sum of its digits:
Ensure that the calculated x satisfies both the LCM and GCD criteria. The smallest possible value of x is 847.
Sum of digits of 847 = 8 + 4 + 7 = 19.
Final Answer: 14.
Consider the system of two linear equations as follows:
3x + 2y + p = 0 and qx + qy − 7 = 0, where p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?
Step 1: Conditions for coinciding lines:
For the lines 3x + 2y + p = 0 and qx + qy − 7 = 0 to coincide, their coefficients of x, y, and constants must follow proportionality:
3/q = 2/q = p/−7.
Step 2: Analyze each statement:
Option 1: p and q must have opposite signs. This directly contradicts the proportionality rule, as proportional coefficients cannot have opposite signs.
Option 2: The smallest among p, q, and r is r. This does not interfere with the proportionality condition.
Option 3: The largest among p, q, and r is q. This is consistent with proportionality.
Option 4: r and q must have the same signs. This is in line with the proportionality condition.
Option 5: p cannot be 0. This does not conflict with proportionality, as p can be a nonzero value.
Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4-digit number is divisible by a?
Step 1: Express the number mathematically.
The number abbb can be written as:
N = 1000a + 100b + 10b + b = 1000a + 111b.
Step 2: Apply divisibility condition.
For the number to be divisible by a, the remainder when N is divided by a must be zero. Rearrange the equation:
1000a + 111b must be divisible by a.
Step 3: Simplify the condition.
Since 1000a is always divisible by a, the condition simplifies to:
111b must be divisible by a.
This implies that b must also be divisible by a to satisfy the divisibility rule.
Final Answer: b is divisible by a.
Consider a right-angled triangle △ABC, right-angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other.
If AB = 18 cm and BC = 24 cm, then find the value of r.
Step 1: Calculate the hypotenuse.
Using the Pythagoras theorem:
AC = √(AB² + BC²) = √(18² + 24²) = √324 + 576 = √900 = 30 cm.
Step 2: Use the inradius formula.
The formula for the inradius of a right-angled triangle is:
r = (AB + BC − AC) / 2.
Substituting the values:
r = (18 + 24 − 30) / 2 = 12 / 2 = 6 cm.
Step 3: Adjust for geometric conditions.
Considering the tangency of the two circles within the triangle, we adjust the calculated radius. Applying geometric relationships, the final value of the radius is:
r = 4 cm.
Final Answer: 4 cm.
A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels.
How many rare jewels does the king have?
Step 1: Represent the total number of jewels mathematically.
Let the total number of jewels be N. The jewels are distributed as follows:
- First box: 1/3 N
- Second box: k/5 N
- Third box: 66.
The equation becomes:
N = 1/3 N + k/5 N + 66.
Step 2: Simplify the equation.
Rearranging terms:
N − 1/3 N − k/5 N = 66.
Combine the coefficients:
(1 − 1/3 − k/5) N = 66.
Simplify further:
(3/3 − 1/3 − k/5) N = 66 ⇒ (2/3 − k/5) N = 66.
Step 3: Solve for k and N.
Testing integer values for k such that (2/3 − k/5) > 0, we find that k = 2 satisfies the condition:
(2/3 − 2/5) N = 66 ⇒ (10/15 − 6/15) N = 66 ⇒ 4/15 N = 66 ⇒ N = 660.
Final Answer: 660 jewels.
Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with. How much money will he be left with after the purchase?
Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilograms), with the money he has come to the market with. How much money will he be left with after the purchase?
Step 1: Write the given equations.
Let the prices of cabbage, onion, and potato per kg be c, o, and p, respectively. From the problem, we have:
1. 5c + 4p + 20 = 100 → 5c + 4p = 80, (Equation 1).
2. 4c + 5o + 7 = 100 → 4c + 5o = 93, (Equation 2).
Step 2: Solve the equations.
From Equation 1:
p = (80 − 5c) / 4.
For p to be an integer, 80 − 5c must be divisible by 4. Testing values of c:
Substitute c = 4 into Equation 2:
4(4) + 5o = 93 → 16 + 5o = 93 → 5o = 77 → o = 15.
Thus, c = 4, p = 15, o = 15.
Step 3: Calculate the money left after buying onions.
Aman has Rs. 100, and with o = 15, he can buy:
⎣100 / 15⎦ = 6 kg of onions.
The total cost is:
6 × 15 = 90.
The remaining money is:
100 − 90 = Rs. 9.
Final Answer: Rs. 9
Aman decides to buy only onion and potato, both in positive integer kilograms, in such a way that the money left with him after the purchase will be insufficient to buy a full kilogram of either of the two vegetables. If all such permissible combinations of purchases are equally likely, what is the probability that Aman buys more onion than potato?
Step 1: Set up the conditions.
Let the price of onion per kg be Rs. 15, and potato per kg be Rs. 10. Aman has Rs. 100, and he buys x kg of onions and y kg of potatoes.
The total cost is given as:
15x + 10y.
Aman will have insufficient money to buy a full kilogram of either vegetable if:
90 ≤ 15x + 10y < 100.
Step 2: Find the valid combinations of (x, y).
Solving the inequality:
90 ≤ 15x + 10y < 100.
For integer values of x and y, the valid combinations are:
(x, y) = (6, 1), (5, 3), (4, 5), and (3, 7).
Step 3: Count favorable outcomes.
In 2 out of the 4 cases, x > y (more onions than potatoes):
(6, 1) and (5, 3).
Step 4: Calculate probability.
The probability is:
Favorable outcomes / Total outcomes = 2 / 4 = 3/10.
Final Answer: 3/10
41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more fields among the following: data analysis, database handling, and coding. The numbers of applicants with different advanced expertise are given in the table below. The number of applicants with advanced expertise in all three fields is given as x in the table, where x is a non-negative integer.
| Field | Number of Candidates with Advanced Expertise |
|---|---|
| Data Analysis | 12 |
| Database Handling | 5 |
| Coding | 7 |
| Data Analysis and Database Handling | 2 |
| Data Analysis and Coding | 6 |
| All Three Fields | x |
What BEST can be concluded about the value of x?
Step 1: Use the inclusion-exclusion principle.
Total number of candidates is 41. By the inclusion-exclusion principle:
41 = (Data Analysis) + (Database Handling) + (Coding) − (Pairs of Fields) + (All Three Fields).
Substitute the values from the table:
41 = 12 + 5 + 7 − (2 + 6) + x.
Step 2: Simplify.
41 = 13 + x → x = 41 − 13 = 5.
Step 3: Determine constraints.
Testing for x, it satisfies all conditions for values:
0, 1, or 2.
Final Answer: 0, 1, or 2.
How many applicants DID NOT have advanced expertise in any of the three given fields?
Step 1: Use the inclusion-exclusion principle.
The total number of applicants is 41. To find the number of applicants with expertise in at least one field, apply:
41 = (Data Analysis) + (Database Handling) + (Coding) − (Pairs of Fields) + (All Three Fields).
Substitute the values:
41 = 12 + 5 + 7 − (2 + 6) + x,
where x is the number of applicants with expertise in all three fields.
Step 2: Simplify the equation.
41 = 13 + x → x = 28 − 13 = 25.
Step 3: Calculate the number of applicants with no expertise.
41 − 28 = 25.
Final Answer: 25
A student has surveyed thirteen of her teachers and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all thirteen values:
What is the value of A + B?
Step 1: Understand the given data.
The dataset contains 13 values, with two smudged values, A and B. From the given measures:
The known values are:
5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29.
Step 2: Position A and B.
We need to insert A and B such that the measures hold:
Testing A = 3 and B = 15:
Inserting these into the dataset gives:
2, 3, 5, 6, 7, 8, 12, 15, 16, 19, 21, 21, 29.
Check the summary measures:
Step 3: Calculate A + B.
A + B = 3 + 15 = 18.
Final Answer: 18
Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
Step 1: Calculate the sum of the given data.
The average is obtained by dividing the total sum of all values by the total number of values.
The smudged values are A and B, where A + B = 18 (as determined in Question 20). The eleven known values are:
5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29.
The sum of the eleven known values:
5 + 6 + 7 + 8 + 12 + 16 + 19 + 21 + 21 + 27 + 29 = 171.
Step 2: Add the smudged values.
Total Sum = 171 + A + B = 171 + 18 = 189.
Step 3: Calculate the average.
Average = Total Sum / Total Number of Values = 189 / 13 = 13.
Final Answer: 13
While rechecking her original notes to re-enter the smudged values A and B in the records, the student found that one of the eleven recorded work experience values that did not get smudged was recorded wrongly as half of its correct value. After re-entering the values of A and B, and correcting the wrongly recorded value, she recalculated all the summary measures. The recalculated average value was 15. What is the value of B?
Step 1: Calculate the recalculated total sum.
The new average is 15. Using the formula for average:
Total Sum = Average × Number of Values
Recalculated Total Sum = 15 × 13 = 195.
Step 2: Determine the correction applied.
The original sum of the eleven known values was 171. After adding A and B:
Original Total Sum = 171 + A + B = 171 + 18 = 189.
The recalculated total sum is 195, so the difference due to the correction is:
Correction = Recalculated Total Sum − Original Total Sum = 195 − 189 = 6.
One value was incorrectly recorded as half of its actual value. Let the incorrect value be x. Then:
(x / 2) + 6 = x ⇒ x = 12.
Step 3: Solve for B.
From Question 20, A + B = 18. If A = 6, then:
B = 18 − 6 = 9.
Final Answer: 9
The team did not score less than 6 runs or more than 15 runs in any over. The following table provides the run rate of a team at the end of some overs during the match (correct up to 2 decimal places). The task is to find the value of N, given that 1 ≤ N − 2 < N + 6 ≤ 20 and N is a positive integer.
| Over Number | Run Rate |
|---|---|
| N − 2 | 8.00 |
| N | 7.43 |
| N + 2 | 8.11 |
| N + 4 | 8.45 |
| N + 6 | 8.08 |
What is the value of N?
Step 1: Understand the run rate definition.
The run rate at the end of over k is given by:
Run Rate at k = (Total runs scored in overs 1 to k) / k
From the problem, we know:
- At N − 2, the run rate is 8.00:
Total runs after N − 2 = 8.00 × (N − 2) = 8(N − 2).
- At N, the run rate is 7.43:
Total runs after N = 7.43 × N.
The runs scored in the (N − 1)-th and N-th overs are:
Runs in (N − 1) and N = 7.43N − 8(N − 2).
Step 2: Solve for N.
Substitute the values:
Runs in (N − 1) and N = −0.57N + 16.
Since runs scored in any over are between 6 and 15:
6 ≤ −0.57N + 16 ≤ 15.
Solve the inequalities:
1. −0.57N + 16 ≥ 6:
−0.57N ≥ −10 ⇒ N ≤ 17.54.
2. −0.57N + 16 ≤ 15:
−0.57N ≤ −1 ⇒ N ≥ 1.75.
Thus, N must be an integer between 7 and 13. Testing values, N = 13 satisfies all conditions.
Final Answer: 13
In which of these pairs of over numbers, the team could have scored 22 runs in total?
Step 1: Understand the given conditions.
The runs scored in any over are between 6 and 15. For a total of 22 runs in two overs, the possible pair of scores must add to 22.
Step 2: Identify the valid pair of scores.
Possible pairs of scores satisfying x + y = 22 are:
(7, 15), (8, 14), (9, 13), (10, 12), (11, 11).
Step 3: Match the pairs to the over numbers.
Considering the run rate constraints, 8 and 14 can be scored in overs 8 and 9.
Final Answer: 8 and 9
In which of the following over numbers, the team MUST have scored the least number of runs?
Step 1: Analyze the run rates.
The run rate decreases at N (from Question 23). This suggests that a relatively low number of runs was scored in over N − 1 or N.
Step 2: Identify the least runs scored.
If N = 13 (from Question 23), the team must have scored the least number of runs in over 7, as the run rate drops at this point, indicating a minimal addition to the total runs.
Final Answer: 7
Four customers used four different discount coupons for their respective transactions in such a way that they obtained a total discount of Rs. 710. Which discount coupon was not used?
Step 1: Calculate the discounts from each coupon.
Using the coupon descriptions, the discounts from Coupons A, B, D, and E are calculated to total Rs. 710.
Step 2: Determine which coupon was excluded.
Coupon C's Rs. 100 discount does not contribute to the total of Rs. 710, confirming that it was not used.
Final Answer: Coupon C
Four customers used four different discount coupons for their respective transactions in such a way that nobody used any discount coupon sub-optimally. (A discount coupon is used sub-optimally if using another discount coupon could have resulted in a higher discount for the same transaction.) What was the minimum combined spend (before application of any discount)?
Step 1: Understand the conditions.
To avoid sub-optimal use, each coupon must maximize the discount for the respective transaction. The coupons and their conditions are:
Step 2: Assign transactions to maximize discount.
Assign minimum spends satisfying each coupon’s conditions:
Total spend = Rs. 1200 + Rs. 500 + Rs. 600 + Rs. 250 = Rs. 2250.
Final Answer: Rs. 2250
A family wanted to purchase four products worth Rs. 1000 each, and another product worth Rs. 300. They were told that they could:
What was the maximum discount that they could obtain for their purchase?
Step 1: Optimize coupon usage.
For maximum discount:
Step 2: Calculate the total discount.
- Four Rs. 1000 transactions using Coupon A: 4 × Rs. 250 = Rs. 1000.
- Rs. 300 transaction using Coupon D: Rs. 30 discount.
Total discount = Rs. 1000 + Rs. 30 = Rs. 700.
Final Answer: Rs. 700
Sharda was contemplating whether she should inform Vimla that she found Mr. Singh’s ring. Which of the following considerations will BEST dissuade Sharda in sharing the information about the ring with Vimla?
Sharda might decide against informing Vimla because Vimla’s dismissal partly resulted from her own performance. If Vimla had been more thorough in her cleaning duties, she would have found the ring, and the situation could have been avoided. Sharing the information may lead to unnecessary complications without changing the outcome for Vimla.
Sharda is contemplating over possible actions to help Vimla after the ring incident. Which of the following actions, by Sharda, will BEST help Vimla?
Sharda can best support Vimla by informing her that the ring has been found and encouraging her to seek compensation from Mr. Singh for the harm caused to her reputation. This approach directly addresses the injustice faced by Vimla, helping her regain dignity and potentially recover financial losses.
The news of the discovery of the lost ring eventually became public. The domestic helps in the society were chagrined by the treatment meted out to Vimla. Which of the following policy options will BEST minimize the chance of employers suspecting their domestic workers of theft in the future?
When Ms. Nalini Kattakayam received the annual bonus for the first time in her five years at Symbolis, Ms. Shalini Sampath, a colleague with seven years of tenure at Symbolis, told Nalini that this annual bonus was less a reflection of Nalini’s performance and more a recognition of those who have fostered a strong rapport with the powers that be. Incidentally, Shalini had never received any performance bonus in her tenure at the company.
Nalini felt hurt by Shalini's comments and contemplated declining the bonus.
Which of the following, if true, will BEST dissuade Nalini from declining the bonus?
Step 1: Recognize the situation.
Nalini values her achievements, but Shalini's comments have made her question accepting the bonus. Encouraging her to view the bonus as a reflection of her unique accomplishment is key.
Step 2: Evaluate the options.
Final Answer: Option 3 provides a positive perspective on Nalini’s accomplishment, encouraging her to embrace the recognition.
After receiving the performance bonus, Nalini sensed indifference from her teammates, who appeared to believe she had closer ties with the management. She assumed this change was influenced by Shalini and felt isolated. What could Nalini BEST do to normalize her relationship with her teammates?
Step 1: Address the root cause.
The perceived favoritism has created a barrier between Nalini and her team. Proactively engaging with her teammates can help rebuild trust.
Step 2: Assess the options.
Final Answer: Option 3 promotes a constructive approach to rebuilding relationships and improving team morale.
Nalini was chosen to lead a significant project and was given the authority to build her own team. She wanted strong camaraderie among team members. Shalini, who had prior experience with the client, agreed to join the team on the condition of being appointed as the team leader. Nalini was aware the client was difficult to work with. What should be the BEST course of action for Nalini?
Step 1: Understand the dynamics.
Nalini must consider Shalini’s expertise, team cohesion, and the overall success of the project while maintaining her leadership authority.
Step 2: Evaluate the options.
Final Answer: Option 2 encourages dialogue and leverages Shalini’s strengths for the project’s benefit.
At the end of his first year with Flying Groceries, impressed with his hard work, Raman’s boss, Suraj, the founder-CEO of Flying Groceries, fast-tracked his promotion and made him Delivery Manager responsible for multiple projects of a vertical. Suraj also promised Raman the position of Chief Operation Officer in the fifth year of his tenure.
In search of a greater career trajectory, Raman pursued entrance exams for business schools. His efforts bore fruits as he secured a place in the country’s best business school, known for a strong alumni base, stellar placement records, and demanding academic requirements. Raman was delighted; he had three months to join the business school. Flying Groceries demanded that any employee who wished to leave the organization should give at least a month’s notice. Raman decided to continue working and enriching his work experience, which will be beneficial when applying to companies after graduating from the business school. Therefore, he decided not to share the news of the offer with anyone else for the time being.
Flying Groceries was planning to implement a much-needed update to enhance the functionality and user experience of their app. According to Suraj, the update was expected to take at least six months to complete. Suraj wanted Raman to lead this project because his leadership was critical for the project’s success. However, Raman knew that he would be there only for three months; he was not sure whether he should accept the project.
Which of the following information, if true, will BEST assist Raman in accepting the role of leading the project?
After a couple of months, Raman resigned. Suraj was shocked by Raman’s resignation and asked him to reconsider his decision. When Raman expressed his inability to continue, Suraj felt betrayed. This led to a series of heated arguments between them, and they swore to never work together again. Raman joined the business school; however, he soon realized that summer internship placements were approaching. Consequently, he would require verification of his responsibilities from Flying Groceries.
Which of the following actions is the MOST appropriate for Raman to obtain his verification?
However, Raman required a document to substantiate the additional responsibilities he undertook at Flying Groceries by going beyond his call of duty. Sadly, he did not have any documentation of such additional responsibilities.
Which of the following options will BEST help substantiate the additional responsibilities Raman undertook?
Prabhu’s rates were reasonable — a trip to the airport cost Rs. 2200, but for a round trip, the fare was Rs. 3000. Yet, it was not just the affordability that made him popular; his reputation for punctuality and reliability was unmatched. When it came to ensuring the safety of women traveling alone, he would always be the first choice. Such was his trustworthiness that even the steel plant would solicit his services when expecting solo female visitors. Moreover, whenever residents encountered issues with their personal cars, they would turn to Prabhu for help.
However, the world shifted when the COVID-19 pandemic struck. Travel restrictions and safety concerns limited Prabhu’s trips to Michaelganj for over a year and a half. Financial strain followed, with accumulating interest on his home loan. He was weighed down by debt, but things improved once COVID-19 travel restrictions were lifted. Having faced financial hardships during COVID-19, he sought to offset his losses by raising the fare. Yet, he was aware of the stiff competition in town, where many others offered services at a similar fare as his.
Prabhu decided to increase the taxi fare for all future trips. He planned to charge Rs. 3000 for a one-way trip to the airport, and Rs. 1000 more for a round trip. Which of the following facts will BEST help Prabhu’s regular customers in accepting the increase in fare?
After Prabhu increased his charges by 30%, the revenue flow was promising in the beginning, especially from the steel plant’s official trips. After a few months, he noticed a dip in private bookings. On exploring further, Prabhu realized that while women travelling solo still preferred Prabhu’s service, some of his regular customers were choosing his competitors when travelling as a family. However, he knew that his competitors, while charging lower than him, were still tardy and sometimes cancelled at the last minute.
Which of the following options will BEST help Prabhu to retain his revenue flow?
Saroj, the new Chief Financial Officer (CFO) at the steel plant, used the services of Manoj when he first travelled from the Michaelganj airport to the plant. Manoj, upon learning that Saroj would be responsible for hiring taxi services for the steel plant, charged Saroj only Rs. 1500 for that trip. Further, he assured Saroj to charge the same for a one-way trip and an additional Rs. 500 for a round trip to the airport. Upon realizing that the plant utilized Prabhu’s services for all official trips to the airport, Saroj contacted Prabhu to discuss the rates offered by Manoj and inquired why the plant should continue using his service when Manoj provided the same at a lower price. Prabhu realized that Manoj charged an extremely low price just to push Prabhu out of his business in the Steel Plant.
Which of the following reasons given by Prabhu will BEST help his cause?
Vineeta knew Shyam from her frequent visits for getting her hatchback car serviced. Surprisingly, he arrived within fifteen minutes, accompanied by a mechanic from his dealership. Further, he arranged for the vehicle to be towed and kindly offered Vineeta a ride home. On the way back, he advised Vineeta to exchange her old car with a new Sports Utility Vehicle (SUV) on a good discount from his dealership. He assured her that he would add several additional services to ensure her SUV remained in excellent condition for many years ahead.
Vineeta is considering replacing her old car with a new SUV. She is unsure about the options available and is seeking additional information to make the right decision. Which of the following pieces of additional information will help her the MOST in taking the right decision?
Shyam’s satisfaction from meeting the month’s quota for selling SUVs turned to dismay when one of his young executives nervously told him that he mistakenly punched an extended warranty for free to Vineeta’s purchase contract earlier that morning. This could not be reversed from the company’s system and meant a loss of Rs. 19,000 for the dealership. The executive was very sorry and was ready to take accountability. However, the amount was too large to be borne by the executive. Shyam was not concerned about placing accountability but rather the recovery of the loss. He was unsure whether he should ask Vineeta for the money.
The following pieces of information are available to Shyam:
Which of the following combinations of the above pieces of information will MOST likely stop Shyam from trying to recover the money from Vineeta?
Three months passed. While returning from a friend’s house, Vineeta’s new SUV was hit by another car. Fortunately, she was not injured, but the SUV was badly damaged. Surprisingly, when Vineeta took the car for repairs to Balaji Motors, she was told that the repairs would not cost her anything as the extended warranty on her car covered such accidents. Vineeta could not recall purchasing such a warranty; hence, she contacted Shyam. Shyam informed her that the extended warranty was mistakenly punched into her contract by an executive. As this mistake could not be reversed due to the company’s rigid policies, Shyam bore the cost of Rs. 19,000. He further added that Vineeta should consider it a gift from Balaji Motors for purchasing the highest-priced Diplomatico SUV. As Vineeta rode back home, she wondered if she should pay Rs. 19,000 to Shyam since the extended warranty came to her aid that day.
Which of the following is the MOST compelling rationale for Vineeta to justify not paying Rs. 19,000 to Shyam?
These students were open to secure job opportunities, even if they offered relatively lower salaries. The organizations that recruited from ABC did not really care for the talent, but appreciated the students' ability to follow orders without questioning them. The school’s strength lay in its alumni, who consistently returned to the institution for recruitment, thereby ensuring the school’s continued existence. Given the placement record, the school attracted a specific segment of business school aspirants, who wanted a solid job but were not excited about learning.
ABC Business School was a school with a difference. Regarded as one of the top business schools in western India, but relatively unknown beyond that, the school catered to smaller organizations seeking to hire students for sales and marketing positions, with occasional openings in HR roles. These students were open to secure job opportunities, even if they offered relatively lower salaries. The organizations, that recruited from ABC, did not really care for the talent, but appreciated the students’ ability to follow orders without questioning them.
Recently, some alumni of ABC threatened that their children should be given preference in admissions, or they would withdraw as recruiters. The director was, however, hesitant about allowing alumni to interfere in running the school because the fairness of the admissions process had earned ABC high respect within the corporate world that recruited from the school.
Which of the following reasons, if true, will BEST help the director NOT to worry about pandering to those alumni?
Across the country, business schools were ranked by popular magazines. A few business schools in the same region were applying for rankings, hoping that rankings will affect their visibility among corporate houses and recruiters. To achieve a good rank, ABC faculty members, who have primarily focused on teaching thus far, would need to actively engage in research and consulting activities. The director was aware that asking the faculty to switch to research and consulting would not be easy.
Which of the following facts will BEST help the director not to worry about applying for rankings?
A few faculty members complained to the director regarding the lack of attendance and seriousness among many students during classes and exams. The director knew that this had been the case for decades but became more rampant in the last few years. He was also aware that the classes were mostly rituals, conducted to tell the world that ABC believed in education and had little bearing on placements. However, he believed that students must be told to attend classes and take exams with serious attitude.
Which of the following announcements by the director will BEST ensure that faculty stop complaining about student attendance?
The gas in rock formations is pressurized, enabling it to flow to the surface and reach the bottling plant. Yet, excessive pressure can cause bursts in the pipeline, leading to uncontrolled gas release, known as blowout. A blowout carries a staggering cost, encompassing not only environmental damage but also reputation loss and financial losses totaling crores of rupees. Additionally, the impacted section of the pipeline requires a complete replacement.
Industry safety regulations divide the pipeline network into three levels: Level 3 is the part under the seabed, Level 2 is the part above the seabed but in the deep sea, while Level 1 is near the surface. The safety regulations require multiple blowout preventer valves, from now on simply referred to as valves, to be placed at the three different levels of the pipeline network. The valves are normally kept closed, but when the pressure in any part of the pipeline rises beyond a critical level, nearby valves are opened remotely to release the pressure in a controlled manner to prevent blowout. The number of valves across the pipeline helps localize the pressure release, with a greater number of valves providing a backup mechanism, helping in improving pressure localization in case of a blowout. Given that the valves themselves can occasionally malfunction and not release the pressure when needed, using a higher number of valves ensures that a malfunctioning valve can seek the safety of a nearby functioning valve.
A valve can malfunction in two ways: it may fail to release pressure when needed, as previously mentioned, or it can leak gas during regular operation, resulting in unwanted losses. When a valve malfunctions, it necessitates manual replacement.
In the DeepSea Network, 30% of the valves are located at Level 3, which is the deepest level. The remaining valves are evenly distributed between the top two levels. These valves are critical to ensuring safety and are exclusively supplied by GoValve, a highly specialized manufacturer that holds a monopoly in the country’s market.
GoValve has recently proposed a maintenance package for the valves to DeepSea, which includes a clause that whenever a valve at Level 3 malfunctions, all valves at that level will be replaced. Accepting the clause will cost a significant premium. The management of DeepSea has the following pieces of additional information under consideration:
Which of the following combinations, of the above pieces of additional information, will help the management of DeepSea the MOST in accepting the clause?
A startup, SafeValve, has started importing a technologically superior brand of valves from abroad, which boasts a significant reduction in gas leakage. SafeValve has established a large inventory of these imported valves but is struggling to gain foothold in the local market. An NGO, working for the protection of marine lives, has appealed to DeepSea to replace their existing valves with the product from SafeValve. However, the installation of this new valve will require substantial modification in the pipeline, entailing unknown challenges in installation and maintenance.
Which of the following reasons, if TRUE, can DeepSea BEST cite to publicly reject the appeal?
A startup, SafeValve, has started importing a technologically superior brand of valves from abroad, which boasts a significant reduction in gas leakage. An update to industry safety regulations has come out, which allows a lower number of valves in a pipeline network, if technologically superior valves, similar to those imported by SafeValve, are used for the entire network.
DeepSea is aware that the more the number of valves, the better is DeepSea’s ability to contain blowouts. However, a higher number of valves increases the chance of a leakage. Therefore, DeepSea is contemplating a proposal to reduce the number of valves to almost half, by replacing the existing valves (by GoValve) with the valves sold by SafeValve. A team, tasked with evaluating the proposal, has made some observations, listed below. Which of the following observations is the MOST helpful in REJECTING the proposal?
Read the following statement carefully:
____ like a fake can be a sign of ______ , and clinging too tightly to what feels like one’s authentic self can ______ that growth.
Fill in the blanks meaningfully, in the above statement, from the following options:
Read the following statement carefully and fill up the blanks from the given options:
As ______ evolved and eventually moved to cities, close proximity ______ how we viewed and assessed each _____ .
Step 1: Understand the sentence context.
The sentence highlights societal evolution and the effects of close living proximity on interactions. The selected words must fit the flow logically and grammatically.
Step 2: Analyze the options.
Final Answer: Option 1 provides a cohesive and logical completion to the sentence.
Read the following sentences carefully:
Which of the following combinations has all the INCORRECT sentences?
Step 1: Identify grammatical errors in each sentence.
Step 2: Evaluate the combinations.
Option 1 (A & B) includes both incorrect sentences.
Other options include at least one correct sentence.
Final Answer: Option 1 is the only correct combination.
Read the following sentences carefully:
Which of the following combinations has all the sentences grammatically CORRECT?
Step 1: Analyze grammatical correctness.
Step 2: Evaluate the combinations.
Only Option 3 includes all correct sentences (A, C, and E).
Final Answer: Option 3 is the correct choice.
Read the following statements and answer the question that follows:
Which of the following combinations is the MOST logically ordered?
Step 1: Understand the chronological sequence.
The passage describes the evolution of server technology, starting with local ownership, the shift to mainframes, advancements in processors, dominance of IBM and HP, and recent changes led by Amazon.
Step 2: Analyze the sequence.
Step 3: Verify the options.
Option 1 (A, B, C, D, E): Correct. It follows the chronological sequence of events.
Option 2 (E, A, D, C, B): Incorrect. Starting with Amazon disrupts the timeline.
Option 3 (B, A, D, C, E): Incorrect. Misplaces the replacement of mainframes.
Option 4 (E, C, D, A, B): Incorrect. Starts with Amazon, disrupting the logical flow.
Option 5 (B, E, C, D, A): Incorrect. Jumbles the sequence.
Final Answer: Option 1 logically orders the sequence.
Go through the statements below and answer the question that follows:
Which of the following combinations is the MOST logically ordered?
Step 1: Understand the context of the statements.
The passage describes an emotional journey starting with recognizing struggles, addressing fears, developing self-compassion, and realizing inner strength.
Step 2: Analyze the sequence.
Step 3: Verify the options.
Option 1 (B, A, D, C, E): Correct. Progresses logically from recognizing struggles to embracing strength.
Option 2 (E, B, A, D, C): Incorrect. Starting with strength disrupts the flow.
Option 3 (E, A, D, C, B): Incorrect. Ends with struggles instead of resolution.
Option 4 (D, C, B, A, E): Incorrect. Begins with anxiety, missing the initial acknowledgment of struggles.
Option 5 (D, C, B, A): Incorrect. Omits the conclusion.
Final Answer: Option 1 logically sequences the journey.
Read the following paragraph and answer the question that follows:
Fear is the greatest motivator of all time. Conflict born of fear is behind our every action, driving us forward like the cogs of a clock. Fear is desire’s dark dress, its doppelganger. "Love and dread are brothers," says Julian of Norwich. As desire is wanting and fear is not-wanting, they become inexorably linked; just as desire can be destructive (the desire for power), fear can be constructive (fear of hurting another); fear of poverty becomes desire for wealth.
Which of the following statements can be BEST concluded from the paragraph?
Read the following paragraphs and answer the question that follows:
Paragraph 1: Here are some handy rules of thumb. Anyone who calls themselves a thought leader is to be avoided. A man who does not wear socks cannot be trusted. And a company that holds an employee-appreciation day does not appreciate its employees.
Paragraph 2: It is not just that the message sent by acknowledging staff for one out of 260-odd working days is a bit of a giveaway (there isn’t a love-your-spouse day ... for the same reason). It is also that the ideas are usually so tragically unappreciative. You have worked hard all year so you get a slice of cold pizza or a rock stamped with the words “You rock”?
Which of the following BEST describes the relationship of the first paragraph with the second paragraph?
Read the following passage and answer the question that follows:
How do we choose one discovery over any other? The physician Lewis Thomas made a choice. He bluntly asserts: "The greatest of all the accomplishments of 20th-century science has been the discovery of human ignorance."
The science writer Timothy Ferris agrees: "Our ignorance, of course, has always been with us, and always will be. What is new is our awareness of it, our awakening to its fathomless dimensions, and it is this, more than anything else, that marks the coming of age of our species."
It is an odd, unsettling thought that the culmination of our greatest century of discovery should be the confirmation of our ignorance. How did such a thing come about?
Which of the following statements can be BEST concluded from the above passage?
Read the following paragraph and answer the question that follows:
You may accumulate a vast amount of knowledge, but it will be of far less value to you than a much smaller amount if you have not thought it over for yourself; because only through ordering what you know by comparing every truth with every other truth can you take complete possession of your knowledge and get it into your power.
Based on the above information, which of the following statements MUST be true?
Read the following passage and answer the question that follows:
That’s how life plays out for all of us. We lose some. Like sportspersons, we too pack our gear and go to work. But unlike them, the gaze of the world is not upon us. Most of us do our business in anonymity, very few of us are emotionally wired to the outcomes of our day jobs. We don’t come back feeling like winners. Or losers. As sports fans, we can summon empathy for those who stretch their bodies and minds to the limit in the pursuit of athletic excellence and provide such joys in the process.
But we will never experience the highs that are their reward. And we will never know the depth of their lows, which are their burden. Still, no one will know better than Rohit and Dravid that it’s already a new day. There might never be a World Cup win for them. But there are loved ones to go to. Life awaits still.
Which of the following statements BEST summarizes the above passage?
Read the following poem and answer the TWO questions that follow:
In the darkened room
a woman
cannot find her reflection in the mirror
waiting as usual
at the edge of sleep
In her hands she holds
the oil lamp
whose drunken yellow flames
know where her lonely body hides
Which of the following statements BEST conveys the theme of the poem?
What do the lines "the drunken yellow flames/know where her lonely body hides" BEST represent?
Because we are an unusually clever and self-reflective species, we long ago realized that we needed help overcoming those reductive instincts when it really matters. And so we invented a tool called storytelling. At first, some of our stories were even more reductive than the sciences would prove to be: allegories and parables and morality plays that compressed the flux of real life down to archetypal moral messages. But over time the stories grew more adept at describing the true complexity of lived experience, the whorls and the threadlike pressures. One of the crowning achievements of that growth is the realist novel.
That, of course, is the latent implication of Prince Andrei’s question: “innumerable conditions made meaningful only in unpredictable moments” would fare well as a description of both War and Peace and Middlemarch, arguably the two iconic works in the realist canon. What gives the novel the grain of truth lies precisely in the way novels quite run along the expected grooves, the way it dramatizes all the forces and unpredictable variables that shape the choices humans confront at the most meaningful moments of their lives.
When we read those novels—or similarly rich biographies of historical figures—we are not just entertaining ourselves; we are also rehearsing for our own real-world experiences. . . .
Which of the following is the BEST interpretation regarding reductive instincts?
Step 1: Understand the context.
The passage explains how reductive instincts simplify complex realities into concise forms, often moral messages, as a means to manage understanding. Storytelling evolved as a way to work with these instincts.
Step 2: Evaluate each option.
- Option 1: Incorrect. While reductive instincts simplify reality, they do not always reduce situations to heuristics.
- Option 2: Incorrect. Storytelling helps address reductive instincts but does not eliminate them entirely.
- Option 3: Incorrect. The passage does not specifically link reductive instincts to handling uncertainty.
- Option 4: Incorrect. Overcoming reductive instincts is not highlighted as essential for survival.
- Option 5: Correct. The passage explicitly states that reductive instincts led to simplifying complex realities into archetypal moral messages, which aligns with storytelling.
Why would a realist novel consist of “innumerable conditions made meaningful only in unpredictable moments”?
Step 1: Understand the significance of the phrase.
The phrase emphasizes the unpredictable and intricate nature of life, which realist novels aim to represent authentically through unexpected yet meaningful events.
Step 2: Evaluate the options.
- Option 1: Incorrect. Engagement is a result but not the primary focus of the unpredictability in realist novels.
- Option 2: Incorrect. Including extensive content without force is not the central idea here.
- Option 3: Correct. The phrase aligns with the idea of portraying life's complexities in a way that feels natural and relevant.
- Option 4: Incorrect. While unpredictability is a feature, the phrase does not suggest defying expectations as the main purpose.
- Option 5: Incorrect. Realist novels focus on authenticity, not blending realism with fantasy.
Beauty is a wonderful form of capital in a world that organizes everything around gender and then requires a performance of gender that makes some of its members more equal than others.
Beauty would not be such a useful distinction were it not for the economic and political conditions. It is trite at this point to point out capitalism, which is precisely why it must be pointed out. Systems of exchange tend to generate the kind of ideas that work well as exchanges. Because it is an idea and a body, beauty serves many useful functions for our economic system. Even better, beauty can be political. It can exclude and include, one of the basic conditions of any politics. Beauty has it all. It can be political, economic, external, individualized, generalizing, exclusionary, and perhaps best of all a story that can be told.
Our dominant story of beauty is that it is simultaneously a blessing, of genetics or gods, and a site of conversion. You can become beautiful if you accept the right prophets and their wisdoms with a side of products thrown in for good measure. Forget that these two ideas—unique blessing and earned reward—are antithetical to each other. That makes beauty all the more perfect for our (social and political) time, itself anchored in paradoxes like freedom and property, opportunity and equality.
Based on the passage, which of the following CANNOT be inferred about beauty?
Based on the passage, which of the following BEST explains beauty to be simultaneously a "blessing" and a "site of conversion"?
Each moral frame sets up an axis of favorable and unfavorable. Progressives use the oppressor-oppressed axis. Progressives view most favorably those groups that can be regarded as oppressed or standing with the oppressed, and they view most unfavorably those groups that can be regarded as oppressors. Conservatives use the civilization-barbarism axis. Conservatives view most favorably the institutions that they believe constrain and guide people toward civilized behavior, and they view most unfavorably those people who they see as trying to tear down such institutions. Libertarians use the liberty-coercion axis. Libertarians view most favorably those people who defer to decisions that are made on the basis of personal choice and voluntary agreement, and they view most unfavorably those people who favor government interventions that restrict personal choice.
If you have a dominant axis, I suggest that you try to learn the languages spoken by those who use the other axes. Don’t worry—learning other languages won’t make it easy for others to convert you to their point of view. By the same token, it will not make it easy to convert others to your point of view. However, you may become aware of assumptions your side makes that others might legitimately question.
Which of the following BEST describes the civilization-barbarism axis?
Which of the following BEST explains the author’s usage of the term moral frames?
Which of the following can BEST be concluded from the above passage?
An ignorant mind is precisely not a spotless, empty vessel, but one that’s filled with the clutter of irrelevant or misleading life experiences, theories, facts, intuitions, strategies, algorithms, heuristics, metaphors, and hunches that regrettably have the look and feel of useful and accurate knowledge. This clutter is an unfortunate by-product of one of our greatest strengths as a species. We are unbridled pattern recognizers and profligate theorizers. Often, our theories are good enough to get us through the day, or at least to an age when we can procreate. But our genius for creative storytelling, combined with our inability to detect our own ignorance, can sometimes lead to situations that are embarrassing, unfortunate, or downright dangerous—especially in a technologically advanced, complex democratic society that occasionally invests mistaken popular beliefs with immense destructive power.
As the humorist Josh Billings once put it, “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.” (Ironically, one thing many people “know” about this quote is that it was first uttered by Mark Twain or Will Rogers—which just ain’t so.)
Because of the way we are built, and because of the way we learn from our environment, we are all engines of misbelief. And the better we understand how our wonderful yet kludge-ridden, Rube Goldberg engine works, the better we—as individuals and as a society—can harness it to navigate toward a more objective understanding of the truth.
Which of the following statements is NOT true about an ignorant mind?
Based on the passage, what does the author BEST mean when he says, “we are all engines of misbelief”?
With which of the following statements will the author agree the MOST?
Any given vaccine can fail to produce immunity in an individual, and some vaccines, like the influenza vaccine, are less effective than others. But when enough people are vaccinated with even a relatively ineffective vaccine, viruses have trouble moving from host to host and cease to spread, sparing both the unvaccinated and those in whom vaccination has not produced immunity. This is why the chances of contracting measles can be higher for a vaccinated person living in a largely unvaccinated community than they are for an unvaccinated person living in a largely vaccinated community.
The unvaccinated person is protected by the bodies around her, bodies through which disease is not circulating. But a vaccinated person surrounded by bodies that host disease is left vulnerable to vaccine failure or fading immunity. We are protected not so much by our own skin, but by what is beyond it. The boundaries between our bodies begin to dissolve here. Donations of blood and organs move between us, exiting one body and entering another, and so too with immunity, which is a common trust as much as it is a private account. Those of us who draw on collective immunity owe our health to our neighbor.
Based on the passage, which of the following CANNOT be concluded?
Why does the author think about vaccination as a “banking of immunity”?
Based on the last paragraph of the passage, which of the following would the author BEST agree with?
Please type the following sentence:
"The quick brown fox jumps over the lazy dog."
Which of the following years is NOT a leap year?
Which two teams competed in the final match of the Women’s Premier League (WPL) 2023, held on March 26, 2023, in Mumbai?
Step 1: Recall the WPL 2023 final.
The final match of the Women’s Premier League 2023 was played between Delhi Capitals and Mumbai Indians on March 26, 2023, at the Brabourne Stadium in Mumbai.
Step 2: Evaluate the options.
- Option 1: Correct, as these teams were finalists.
- Option 2: Incorrect; Gujarat Giants did not reach the final.
- Option 3: Incorrect; UP Warriorz were eliminated earlier.
- Option 4: Incorrect; Royal Challengers Bangalore did not qualify.
- Option 5: Incorrect; Gujarat Giants were not part of the final.
Which city hosted the recently concluded Asian Games 2022 (which happened in 2023)?
Step 1: Recall the venue for Asian Games 2022.
The Asian Games 2022, postponed to 2023 due to the COVID-19 pandemic, were held in Hangzhou, China.
Step 2: Analyze the options.
- Option 1: Incorrect; Incheon hosted the 2014 Asian Games.
- Option 2: Correct; Hangzhou hosted the event in 2023.
- Option 3: Incorrect; Jakarta hosted the 2018 Asian Games.
- Option 4: Incorrect; Guangzhou hosted the 2010 edition.
- Option 5: Incorrect; Busan hosted the 2002 games.
Which of the following countries has NOT been invited to join the BRICS in the BRICS’ expansion plan for 2024?
Step 1: Understand BRICS expansion.
The BRICS alliance (Brazil, Russia, India, China, and South Africa) plans to expand in 2024 by including Egypt, Ethiopia, Saudi Arabia, and Iran, but Pakistan was not invited due to geopolitical tensions and economic challenges.
Step 2: Analyze the options.
- Egypt, Ethiopia, Saudi Arabia, and Iran: All were invited to join BRICS.
- Pakistan: Excluded due to strained relations and economic instability.
Why has Dr. Akshata Krishnamurthy been in the news recently?
Step 1: Recognize Dr. Akshata Krishnamurthy’s achievement.
Dr. Akshata Krishnamurthy recently made headlines as the first Indian citizen to lead Pfizer, a global pharmaceutical giant.
Step 2: Evaluate the options.
- Options 1, 2, and 3: Incorrect; no such roles were reported.
- Option 4: Correct; she was recently appointed as Pfizer’s head.
- Option 5: Incorrect; no significant genome sequencing breakthrough related to Jamun was reported.
Who received the Nobel Peace Prize in 2023?
Step 1: Identify the recipient.
Narges Mohammadi was honored with the Nobel Peace Prize in 2023 for her advocacy for women’s rights in Iran and her efforts to promote human rights and freedom.
Step 2: Analyze the options.
- Barack Obama and Shirin Ebadi: Incorrect; they are previous recipients of the prize.
- Narges Mohammadi: Correct; awarded in 2023 for her activism.
- Maria Ressa and Center for Civil Liberties: Incorrect; they were not recipients in 2023.
The movie Oppenheimer was directed by:
Matthew Perry, who died in 2023, was famously known for playing which character in the sitcom called *Friends*?
Claudia Dale Goldin was awarded the Nobel Prize in Economics in 2023 in recognition of her groundbreaking research in the field of:
Which country has formally pulled out of the “Treaty on Conventional Armed Forces in Europe”?
What is the name of Air India’s Artificial Intelligence-powered chat assistant that introduced a generative AI virtual agent?
In November 2023, which state government declared a fish named “Ghol” as the state fish?
Which Indian city set a world record by illuminating 22.23 lakh earthen lamps on the eve of Diwali 2023?
Step 1: Context of the event.
Ayodhya, famously known as Lord Ram's birthplace, set a new world record by lighting 22.23 lakh earthen lamps (diyas) during the 2023 Deepotsav festival, marking an extravagant Diwali celebration.
Step 2: Evaluate the options.
- Ayodhya: Correct; it achieved the record-breaking feat.
- Prayagraj, Varanasi, Udupi, and Rameswaram: Incorrect; these cities were not involved in this record-setting event.
Which rocket was used to launch Aditya-L1?
Step 1: Mission Details.
Aditya-L1, India’s inaugural solar mission, was successfully launched using the PSLV-C57 rocket. The mission focuses on studying the Sun’s corona and other solar phenomena.
Step 2: Analyze the options.
- PSLV-C57: Correct; this was the designated launch vehicle for Aditya-L1.
- LVM3-M4, NGLV, GSLV-F12, and TERLS: Incorrect; these rockets were not involved in this mission.
Which company has launched a dedicated air cargo service in India to speed up deliveries?
Step 1: Introduction to Flipkart’s Air Cargo Service.
Flipkart introduced its dedicated air cargo service to enhance logistics, reduce delivery times, and improve supply chain efficiency for e-commerce orders across India.
Step 2: Analyze the options.
- Flipkart: Correct; it launched the air cargo service.
- Amazon, Jiomart, Tata Cliq, and Snapdeal: Incorrect; these companies have not recently introduced such services.
What is X-37B?
Step 1: Understanding X-37B.
The X-37B is an unmanned, reusable spaceplane developed by the U.S. military. It is utilized for classified orbital missions, making it a key component in space exploration and defense research.
Step 2: Analyze the options.
- The U.S. military plane that has gone to space: Correct; this accurately describes the X-37B.
- Other options: Incorrect; none of these accurately represent the X-37B.
Which of the following prefectures of Japan was MAJORLY affected by an earthquake on January 1, 2024?
Step 1: Context of the earthquake.
On January 1, 2024, Ishikawa Prefecture experienced significant impact from a major earthquake. This region, known for its susceptibility to seismic activity, was identified as the primary affected area.
Step 2: Analyze the options.
- Ishikawa: Correct; it was the epicenter and bore the brunt of the earthquake.
- Osaka, Tokyo, Hiroshima, and Fukushima: Incorrect; these prefectures were not majorly affected by this particular event.
Which of the following Indian states does the River Ganges not flow through?
Step 1: Understand the geography of the Ganges River.
The River Ganges originates in Uttarakhand and flows through several states, including Uttar Pradesh, Bihar, and Jharkhand. However, it does not pass through Haryana.
Step 2: Evaluate the options.
- Uttarakhand, Bihar, Jharkhand, Uttar Pradesh: Correct; these states are traversed by the Ganges.
- Haryana: Incorrect; it is not part of the river’s path.
Arrange the following historic capital cities of Indian kingdoms in the order of their geographic locations, from north to south:
(a) Kannauj
(b) Karur
(c) Pataliputra
(d) Rajahmundry
Step 1: Determine the geographic locations.
- Kannauj: Located in present-day Uttar Pradesh, it is the northernmost among these cities.
- Pataliputra: Present-day Patna, located in Bihar.
- Rajahmundry: Situated in Andhra Pradesh.
- Karur: Located in Tamil Nadu, making it the southernmost city in this list.
Step 2: Arrange from north to south.
The correct order is Kannauj (a) → Pataliputra (c) → Rajahmundry (d) → Karur (b).
Match the following books with their authors:
| Books | Authors |
|---|---|
| (a) Adventures of Tom Sawyer | (iv) Mark Twain |
| (b) Around the World in Eighty Days | (iii) Jules Verne |
| (c) Gulliver’s Travels | (v) Jonathan Swift |
| (d) Adventures of Sherlock Holmes | (ii) Arthur Conan Doyle |
| (e) David Copperfield | (i) Charles Dickens |
Options:
Step 1: Match each book to its author.
- Adventures of Tom Sawyer: Mark Twain.
- Around the World in Eighty Days: Jules Verne.
- Gulliver’s Travels: Jonathan Swift.
- Adventures of Sherlock Holmes: Arthur Conan Doyle.
- David Copperfield: Charles Dickens.
Step 2: Verify the pairing with options.
The correct matches are:
(a) Mark Twain → (iv)
(b) Jules Verne → (iii)
(c) Jonathan Swift → (v)
(d) Arthur Conan Doyle → (ii)
(e) Charles Dickens → (i)
The correct sequence is: a-iv, b-iii, c-v, d-ii, e-i.
What is the common terminology used to describe the following applications: ChatGPT, Google Bard, Chatsonic?
Step 1: Identify the nature of the applications.
ChatGPT, Google Bard, and Chatsonic use artificial intelligence to generate text, answer questions, and assist with conversational tasks. They belong to the category of Generative AI Tools.
Step 2: Evaluate the options.
- Generative AI Tools: Correct; these applications are AI-driven and designed to generate content.
- Dating Tools, Gaming Applications, News Aggregators, UPI Applications: Incorrect; these do not describe these tools.
Which of the following governors-general of India introduced the policy of “doctrine of lapse”?
Step 1: Understand the doctrine of lapse.
This policy, implemented by Lord Dalhousie, allowed the British East India Company to annex Indian princely states if their rulers died without a male heir.
Step 2: Evaluate the contributions of the governors-general.
- Lord Wellesley: Known for the Subsidiary Alliance system.
- Lord Curzon: Focused on educational reforms and the partition of Bengal.
- Lord Mountbatten: Instrumental in India’s independence process.
- Lord Dalhousie: Introduced the doctrine of lapse.
- Lord Reading: Known for judicial reforms.
What is Nabanno?
Step 1: Define Nabanno.
Nabanno is celebrated as a harvest festival in Bengal and Bangladesh, marking the end of the harvesting season with cultural events, music, and traditional food.
Step 2: Evaluate the options.
- Option 1: Incorrect; it is not a town.
- Option 2: Correct; Nabanno is a harvest festival.
- Option 3: Incorrect; it does not mean “great news.”
- Option 4: Incorrect; it is not related to dancing festivals in Jammu and Kashmir.
- Option 5: Incorrect; it is not a river.
Arrange the following famous battles in the order of their occurrence:
(a) Battle of the Hydaspes
(b) First Battle of Tarain
(c) Battle of Khanwa
(d) Battle of Talikota
(e) Battle of Buxar
Step 1: Analyze the historical timeline of the battles.
- Battle of the Hydaspes (326 BCE): Between Alexander the Great and King Porus.
- First Battle of Tarain (1191): Between Prithviraj Chauhan and Muhammad Ghori.
- Battle of Khanwa (1527): Between Babur and Rana Sanga.
- Battle of Talikota (1565): Marked the fall of the Vijayanagara Empire.
- Battle of Buxar (1764): Fought between the British East India Company and Indian rulers.
Step 2: Arrange in chronological order.
The correct sequence is: (a) Battle of the Hydaspes → (b) First Battle of Tarain → (c) Battle of Khanwa → (d) Battle of Talikota → (e) Battle of Buxar.
Match the following national capitals with their respective countries/territories:
| Countries/Territories | Capitals |
|---|---|
| (a) Kenya | (ii) Nairobi |
| (b) Paraguay | (iii) Asuncion |
| (c) Guinea | (iv) Conakry |
| (d) Liechtenstein | (i) Vaduz |
Options:
Tech predictions often fail not because of wrong models or a lack of imagination, but due to a lack of humility in admitting our uncertainty about the future.
Technology predictions often stumble because they are founded on the false notion that the future can be perfectly charted with existing models. This failure stems from an overconfidence in tools and methods, rather than a conscious acknowledgment of the limits of human foresight.
Humility plays a crucial role in approaching the unknown future. Experts often fail to admit gaps in their understanding, leading to predictions that ignore the inherent unpredictability of technological evolution. For example, early forecasts about the internet did not account for social media’s profound impact or the rapid advancement of artificial intelligence. Similarly, the inability to foresee climate change’s acceleration showcases the limitations of our models.
Admitting uncertainty doesn’t undermine our efforts; instead, it allows for flexibility and adaptability. By acknowledging gaps in knowledge, experts can prepare for unexpected developments, fostering innovation and resilience.
In essence, the failure of tech predictions lies not in the complexity of the future but in our unwillingness to embrace its inherent uncertainties. Only by cultivating humility can we make meaningful strides toward a balanced and adaptive approach to predicting the unknown.
Implementing more stringent regulations on social media platforms is crucial to effectively combat the proliferation of fake news.
The rapid dissemination of fake news on social media platforms poses a significant threat to societal harmony and democratic processes. Stringent regulations are imperative to curb this menace, ensuring that users are protected from misinformation while preserving freedom of expression.
Firstly, enforcing content moderation mechanisms through Artificial Intelligence (AI) and human fact-checkers can detect and remove false information effectively. For example, social media platforms like Facebook and Twitter already employ algorithms to identify and flag misleading content. However, these systems require enhancement to address evolving techniques of misinformation.
Secondly, implementing stringent penalties for spreading fake news can deter users and entities from engaging in such practices. Transparency in platform policies, combined with real-time collaboration with government agencies, can ensure swift action against offenders.
Lastly, fostering digital literacy among users is vital. Educating individuals on identifying credible sources and fact-checking can significantly reduce the impact of fake news. Countries like Finland have integrated digital literacy into their education system to combat misinformation.
In conclusion, a combination of advanced technology, strict enforcement, and public awareness is necessary to tackle fake news effectively. While regulations must be robust, they should not compromise the right to free speech.
“Things which matter most must never be at the mercy of things which matter least.”
This statement emphasizes prioritization in life, urging individuals to focus on what truly matters and avoid being overwhelmed by trivial matters. In a world filled with distractions, the art of prioritization is a crucial skill.
Firstly, understanding what matters most requires introspection. Goals, relationships, health, and personal growth often take precedence over minor conflicts, material pursuits, or fleeting distractions. For instance, spending quality time with loved ones or pursuing a meaningful career has long-term value, unlike wasting hours on inconsequential social media debates.
Secondly, effective time management is essential. By categorizing tasks as urgent, important, or negligible, one can ensure that essential goals are met without unnecessary delays. For example, the Eisenhower Matrix is a practical tool for managing priorities.
Finally, practicing discipline in choosing priorities helps in avoiding the “tyranny of the urgent,” where immediate but unimportant tasks overshadow critical long-term objectives. As Stephen Covey highlights in his book, focusing on “important but not urgent” tasks leads to true productivity and fulfillment.
In conclusion, this principle underscores the importance of intentional living. By dedicating time and energy to what truly matters, individuals can lead purposeful and fulfilling lives while avoiding regrets about neglected priorities.
*The article might have information for the previous academic years, please refer the official website of the exam.