Young's moduli of the material of wires A and B are in the ratio of 1:4, while its area of cross sections are in the ratio of 1:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of (Assume length of wires A and B are same):

• (a) 1:12
• (b) 12:1
• (c) 36:1
• (d) 1:36

A hollow glass stopper of relative density 2.5 just sinks in water. The ratio of volume of cavity to that of stopper is:

• (a) 1:2
• (b) 3:5
• (c) 1:5
• (d) 3:2

A gas undergoes a process in which the pressure and volume are related by \(VP^{n}=\) constant. The bulk modulus of the gas is:

• (a) nP
• (b) \(P^{1/n}\)
• (c) \(P/n\)
• (d) \(P^{n}\)

The initial pressure and volume of an ideal gas are \(P_{0}\) and \(V_{0}\). The final pressure of the gas when the gas is suddenly compressed to volume \(V_{0}/4\) will be: (Given \(\gamma=\) ratio of specific heats at constant pressure and at constant volume)

• (a) \(P_{0}\)
• (b) \(4P_{0}\)
• (c) \(P_{0}(4)^{\gamma}\)
• (d) \(P_{0}(4)^{1/\gamma}\)

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530 Å. The radius for the first excited state (n = 2) orbit is (in Å):

• (a) 0.13
• (b) 1.06
• (c) 4.77
• (d) 2.12

In \( PO_{4}^{3-} \) the formal charge on each oxygen atom and the P - O bond order respectively are:

• (a) -0.75, 0.6
• (b) -0.75, 1.0
• (c) -0.75, 1.25
• (d) -3, 1.25

The value of x is maximum for:

• (a) \( MgSO_{4} \cdot xH_{2}O \)
• (b) \( CaSO_{4} \cdot xH_{2}O \)
• (c) \( BaSO_{4} \cdot xH_{2}O \)
• (d) All have the same value of x.

Let P be a point on the parabola, \(x^{2}=4y\). If the distance of P from the centre of the circle, \(x^{2}+y^{2}+6x+8=0\) is minimum, then the equation of the tangent to the parabola at P, is:

• (a) \(x+4y-2=0\)
• (b) \(x+y+1=0\)
• (c) \(x-y+3=0\)
• (d) \(x+2y=0\)

If \(x=\sqrt{2^{cosec^{-1}t}}\) and \(y=\sqrt{2^{sec^{-1}t}}\) (\(|t|\ge1\)), then \(dy/dx\) is equal to:

• (a) \(y/x\)
• (b) \(-y/x\)
• (c) \(-x/y\)
• (d) \(x/y\)

If \(f(x)=\int_{0}^{x}t(\sin x-\sin t)dt\) then:

• (a) \(f'''(x)-f''(x)=\cos x-2x \sin x\)
• (b) \(f'''(x)+f'(x)=\cos x-2x \sin x\)
• (c) \(f'''(x)+f''(x)=\sin x\)
• (d) \(f'''(x)+f''(x)-f'(x)=\cos x\)