Two new and different cells having emf v₁ and v₂ have their balance points P₁ and P₂ respectively, then

(a)   v₁ > v₂ 

(b)  v₁ < v₂ 

(c)  v₁ = v₂ 

(d)  insufficient data

Which one of the following statements is not a tautology ?

(1)  P → (p ∨ q)

(2)   (p ∧ q) → (~p) ∨ q

(3)  (p  ∧ q) → p 

(4)   (p ∨ q) → (p) ∨ (~q) 

Two identical thin metal strips, one of aluminum and the other of iron are riveted together to form a bimetallic strip. The temperature is raised by 50°C. If the central planes of the two strips are separated by 2 mm and the coefficients of thermal expansion for aluminum and iron are respectively 30 x 10^-6 / °C and 10 x 10^-6 / °C, the average radius of curvature of the bimetallic strip is about 

(a) 50 cm (b) 100 cm (c) 150 cm (d) 200 cm 

Let a body be placed at a point on the earth’s surface at a latitude λ where the radius of the earth is R. Then, the body experiences an effective acceleration

(a)  g – Rω² cos λ

(b)  g + Rω² sin λ

(c)  g – Rω² cos² λ

(d)  g – Rω²/ cos²λ

A vertical narrow wire is illuminated with laser. Alternate dark and bright bands are formed on a graph paper pasted on a distant wall. Indicate the correct statement/s. 

(a)  making appropriate measurements, it is possible to determine the diameter of the wire 

(b)  this phenomenon exhibits that light does not follow rectilinear paths 

(c)  this is a case of Fraunhoffer diffraction 

(d)  this is a case of interference of an infinitely large number of Huygens’s secondary waves leading to a diffraction pattern

A thin annular metal disc of inner and outer radii R₁ and R₂  respectively, is freely suspended from a point on its outer circumference. The length of the corresponding equivalent simple pendulum is

A particle moves in a plane with a constant speed along a path y = 2x² + 3x – 4. When the particle is at (0, – 4) the direction along which it is moving is inclined to the X axis at an angle 

(a) 63⁰ (b) 72⁰ (c) 27⁰ (d) 0⁰

In and atom an electron excites to the fourth orbit. When it jumps back to the energy levels a spectrum is formed. Total number of spectral lines in this spectrum would be 

(A)   3

(B)   4

(C)   5

 (D)   6 

A large cylindrical vessel contains water to a height of 10 m. It is found that the thrust acting on the curved surface is equal to that at the bottom. If atmospheric pressure can support a water column of 10 m, the radius of the vessel is

(a) 10 m (b) 15 m (c) 5 m (d) 25 m 

Consider two point masses m₁ and m₂ connected by alight rigid rod of length r₀. The moment of inertia of the system about an axis passing through their centre of mass and perpendicular to the rigid rod is given by