The acceleration of a moving body is found from the:

• (A) area under velocity-time graph
• (B) area under displacement-time graph
• (C) slope of distance-time graph
• (D) slope of velocity-time graph
• (E) area under acceleration-time graph

The time period of an earth’s satellite revolving at a height of 35,800 km is

• (A) 24 hours
• (B) 100 minutes
• (C) 12 hours
• (D) 48 hours
• (E) 52 hours

For most of the materials, Young’s modulus (Y) and rigidity modulus (G) are related as

• (A) \(G = 3Y\)
• (B) \(G = \frac{Y}{3}\)
• (C) \(G = \frac{3}{2} Y\)
• (D) \(G = \frac{Y}{8}\)
• (E) \(10G = 3Y\)

The pressure on an object of bulk modulus \(B\) undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain \(\frac{\Delta V}{V}\) is:

• (A) \(B^2\left(\frac{\Delta V}{V}\right)\)
• (B) \(B\left(\frac{\Delta V}{V}\right)^2\)
• (C) \(\frac{1}{B}\left(\frac{\Delta V}{V}\right)\)
• (D) \(\frac{1}{B^2}\left(\frac{\Delta V}{V}\right)\)
• (E) \(B\left(\frac{\Delta V}{V}\right)\)

When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is:

• (A) 1 : 3
• (B) 2 : 1
• (C) 3 : 1
• (D) 1 : 2
• (E) 2 : 3

When a magnetic field is applied on a stationary electron, it

• (A) remains stationary
• (B) spins about its own axis
• (C) moves in the direction of the field
• (D) moves perpendicular to the direction of the field
• (E) moves opposite to the direction of the field

The resistors \(R_1 = 3\Omega\) and \(R_2 = 1\Omega\) are connected in parallel to a 20 V battery. Find the heat developed in the resistor \(R_1\) in one minute.

• (A) 600 J
• (B) 800 J
• (C) 6000 J
• (D) 8000 J
• (E) 7000 J

Among the following, the molecule that will have the highest dipole moment is:

• (A) H\(_2\)
• (B) HI
• (C) HBr
• (D) HCl
• (E) HF

An odd electron molecule among the following is (2015)

• (A) CO
• (B) SO\(_2\)
• (C) CO\(_2\)
• (D) NO
• (E) O\(_2\)

Which one of the following is the correct relation between \(C_p\) and \(C_V\) for one mole of an ideal gas? (R is molar gas constant)

• (A) \(C_p = C_V - R\)
• (B) \(C_p = C_V + R\)
• (C) \(C_p = R - C_V\)
• (D) \(C_p = C_V \times R\)
• (E) \(C_p = C_V / R\)

Which of the following is a Lewis acid?

• (A) HCl
• (B) HO\(^-\)
• (C) H\(_2\)O
• (D) Co\(^{3+}\)
• (E) NH\(_3\)

The average oxidation state of sulphur in the tetrathionate ion is:

• (A) +3
• (B) +2.5
• (C) +5
• (D) +3.5
• (E) +1.5

Which of the following is an electron donating group?

• (A) NO\(_2\)
• (B) -CH\(_3\)
• (C) -COOH\(_4\)
• (D) -CN
• (E) -OC\(_6\)H\(_5\)

If \(a y = x + b\) is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of \(2a + b\) is equal to:

• (A) 1
• (B) 3
• (C) 5
• (D) -3
• (E) -1

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

• (A) \(5x + 2y = 21\)
• (B) \(5x + 2y = 0\)
• (C) \(2x - 5y = 21\)
• (D) \(5x - 2y = 21\)
• (E) \(2x + 3y = 21\)

The end-points of a diameter of a circle are (−1,4) and (5,4). Then the equation of the circle is

• (A) \((x − 3)^2 + y^2 = 9\)
• (B) \((x − 3)^2 + (y + 4)^2 = 3\)
• (C) \((x − 2)^2 + (y − 4)^2 = 9\)
• (D) \((x + 3)^2 + (y + 4)^2 = 9\)
• (E) \((x − 3)^2 + (y − 4)^2 = 4\)

The foci of a hyperbola are (8,3) and (0,3) and eccentricity is \(4/3\). Then the length of the transverse axis is:

• (A) \(32/3\)
• (B) 4
• (C) 8
• (D) \(8/3\)
• (E) 6

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 elements is:

• (A) 32
• (B) 64
• (C) 128
• (D) 256
• (E) 512

If \(x^{22}\) is in the \((r + 1)^{th}\) term of the binomial expansion of \((3x^3 - x^2)^9\), then the value of \(r\) is equal to

• (A) 3
• (B) 4
• (C) 5
• (D) 6
• (E) 7