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(#M40026997) KVPY QUESTION General Ability Test Keep an EYE

A parent nucleus X is decaying into daughter nucleus Y which in turn decays to Z. The half lives of X and Y are
40000 years and 20 years respectively. In a certain sample, it is found that the number of Y nuclei hardly changes
with time. If the number of X nuclei in the sample is 4 × 1020, the number of Y nuclei present in its is

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(#M40026996) KVPY QUESTION General Ability Test Keep an EYE

A cylindrical steel rod of length 0.10 m and thermal conductivity 50 W.m–1 K–1 is welded end to end to copper
rod of thermal conductivity 400 W.m–1. K–1 and of the same area of cross section but 0.20 m long. The free end of
the steel rod is maintained at 100º C and that of the copper and at 0º C. Assuming that the rods are perfectly
insulated from the surrounding, the temperature at the junction of the two rods

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(#M40026995) KVPY QUESTION General Ability Test Keep an EYE

A ball of mass m suspended from a rigid support by an inextensible massless string is released from a height h
above its lowest point. At its lowest point it collides elastically with a block of mass 2m at rest on a frictionless
surface. Neglect the dimensions of the ball and the block. After the collision the ball rises to a maximum height
of–

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(#M40026994) KVPY QUESTION General Ability Test Keep an EYE

The potential energy of a point particle is given by the expression V (x) = –αx + β sin (x/γ). A dimensionless
combination of the constant α, β and γ is

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(#M40026993) KVPY QUESTION General Ability Test Keep an EYE

A particle is acted upon by a force given by F = – αx3 – βx4 where α and β are positive constants. At the point
x = 0, the particle is

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(#M40026992) KVPY QUESTION General Ability Test Keep an EYE

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is
held at a temperature of 100ºC while the other one is kept 0º C. If the two are brought into contact, then, assuming
no heat loss to the environment, the final temperature that they will reach is

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(#M40026991) KVPY QUESTION General Ability Test Keep an EYE

A body is executing simple harmonic motion of amplitude a and period T about the equilibrium position x = 0.
large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in
a very small interval x to x + |dx| is highest at

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(#M40026990) KVPY QUESTION General Ability Test Keep an EYE

The ratio of the speed of sound to the average speed of an air molecule at 300 K and 1 atmospheric pressure is
close to

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(#M40026989) KVPY QUESTION General Ability Test Keep an EYE

A steady current I flows through a wire of radius r, length L and resistivity ρ. The current produced heat in the
wire. The rate of heat loss in a wire is proportional to its surface area. The steady temperature of the wire is
independent of–
(A) L (B) r (C) I (D) ρ

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(#M40026988) KVPY QUESTION General Ability Test Keep an EYE

A loop carrying current I has the shape of a regular polygon of n sides. If R is the distance from the centre to any
vertex, then the magnitude of the magnetic induction vector B
􀁇
at the centre of the loop is

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