LCM of the numbers 12 and 20 will be :

• (a) 30
• (b) 60
• (c) 120
• (d) 140

The sum of zeroes of the quadratic polynomial \(x^2 + 2x + 5\) will be :

• (a) 2
• (b) -2
• (c) 5
• (d) -5

In linear equation \(\frac{x}{3} + \frac{y}{2} = 6\) if \(x = 9\) then the value of \(y\) will be :

• (a) 2
• (b) 4
• (c) 6
• (d) 8

The roots of the quadratic equation \(x^2 + 5x + 6 = 0\) will be :

• (a) -3, -2
• (b) 3, 2
• (c) -3, 2
• (d) 3, -2

The seventeenth term of the A. P. : 3, 8, 13, ... will be :

• (a) 83
• (b) 88
• (c) 98
• (d) 105

If the points A (6, 1), B (8, 2), C (9, 4) and D (7, 3) are the vertices of a parallelogram, taken in order, the point of intersection of diagonals will be :

• (a) (15/2, 5/2)
• (b) (15/2, 5)
• (c) (7/2, 5)
• (d) (5, 15/2)

In the following statements, the true statement is :

• (a) All circles are congruent.
• (b) All rectangles are similar.
• (c) All equilateral triangles are similar.
• (d) All polygons are similar.

In the above figure, if \(AD = 2.0\) cm, \(AE = 1.8\) cm, \(EC = 3.6\) cm and \(DE \parallel BC\) the measure of \(BD\) will be :

• (a) 3.6 cm
• (b) 4.0 cm
• (c) 5.4 cm
• (d) 6.0 cm

In triangle \(ABC\) if \(\angle B = 90^\circ\), \(AB = 5\) cm and \(BC = 12\) cm, the value of \(\sin A\) will be :

• (a) 5/13
• (b) 5/12
• (c) 12/13
• (d) 13/17

The value of \(4 \sin 30^\circ \cos 60^\circ\) will be :

• (a) 1
• (b) 1/2
• (c) 1/4
• (d) 1/8

The value of Tan A + Cot A will be :

• (a) Sin² A + Cot² A
• (b) Sec A Cosec A
• (c) Sin A Cos A
• (d) 1

If tan A = √3, then the value of Sec A will be :

• (a) 4
• (b) 3
• (c) 2
• (d) 1/2

HCF of the numbers 49 and 91 will be :

• (a) 7
• (b) 9
• (c) 11
• (d) 13

LCM and HCF of two numbers are 182 and 13 respectively. If one number is 26, then other number will be :

• (a) 13
• (b) 39
• (c) 78
• (d) 91

Two coins are tossed simultaneously. The probability of getting at least one head is :

• (a) 1/4
• (b) 1/2
• (c) 3/4
• (d) 1

If the mode of some observations is 20 and mean is 26. The value of their median will be :

• (a) 26
• (b) 24
• (c) 20
• (d) 30

The angle of a sector of a circle with radius 4 cm is 30°. The area of the sector will be :

• (a) \(\pi/3\) cm²
• (b) \(3/4\) cm²
• (c) \(\pi/4\) cm²
• (d) \(4/9\) cm²

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 2 cm and the height of the cone is equal to its radius. The volume of the solid will be :

• (a) \(2\pi\) cm³
• (b) \(4\pi\) cm³
• (c) \(6\pi\) cm³
• (d) \(8\pi\) cm³

The median class of the following frequency distribution will be :


 

• (a) 5-10
• (b) 10-15
• (c) 15-20
• (d) 25-30

The modal class of the following frequency table will be :


 

• (a) 10-20
• (b) 40-50
• (c) 0-10
• (d) 30-40

Prove that \(2\sqrt{2}\) is an irrational number.

Find the distance between the points (-4, 5) and (2, -3).

In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8)?

Prove that : \(\frac{2 \cos^3 \theta - \cos \theta}{\sin \theta - 2 \sin^3 \theta} = \cot \theta\)

If an arc of a circle of radius 10.5 cm, subtends an angle of 60° at the centre, then find the length of the arc.

Find the mode of the following frequency table :


 

The two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that \(\angle PTQ = 2 \angle OPQ\).

In the figure ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Prove that \(\frac{AE}{ED} = \frac{BF}{FC}\).

A dice is thrown twice. What is the probability that: i) 6 will not come up either time? ii) 6 will come up at least once?

Find the median of the following data :


 

The first term and the last term of an A.P. are 8 and 341 respectively. If the common difference is 9, then find the number of terms in it and their sum.

Solve the following pairs of linear equations : \(3x - 5y = 4\), \(9x = 2y + 7\)

The sum of a two-digit number and the number obtained by reversing the digits is 110. If the tens digit of the number is 6 more than the units digit, then find the number.

The altitude of a right triangle is 35 cm less than its base. If the hypotenuse is 65 cm, find the other two sides.

The angles of depression of the top and the bottom of a 6 m high building from the top of a multi-storeyed building are 30° and 60° respectively. Find the height of the multi-storeyed building and the distance between the two buildings.



OR



Two poles of equal heights are standing opposite each other on either side of the road, which is 60 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60°, respectively. Find the height of the poles and the distances of the point from the poles.

A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.



OR



A solid is in the shape of a cone standing on a right circular cylinder with both their radii being equal to 7.5 cm and the height of the cone is equal to its radius. If the total height of the solid is 22.5 cm, find the volume of the solid. (Use \(\pi = 3.14\), \(\sqrt{3} = 1.732\))