Give me question paper for IIT JEE entrance examination for admission in IIT colleges situated in India ?

Here I am giving you question paper for IIT JEE entrance examination for admission in IIT colleges situated in India below ..

5. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale
divisions. The diameter of the cylinder is
(A) 5.112 cm (B) 5.124 cm
(C) 5.136 cm (D) 5.148 cm

Sol. (B)
Main scale division (s) = .05 cm
Vernier scale division (v) = 49
100
= .049
Least count = .05 – .049 = .001 cm
Diameter: 5.10 + 24 × .001
= 5.124 cm

6. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is
(A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9
Sol. (D)

8. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the size of the object. The wavelength of light inside the lens is 2
3
times the wavelength in free
space. The radius of the curved surface of the lens is
(A) 1 m (B) 2 m (C) 3 m (D) 4 m
Sol. (C)

10. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the
pulse is 30 mW and the speed of light is 3  108 m/s. The final momentum of the object is
(A) 0.3  1017 kg ms1 (B) 1.0  1017 kg ms1
(C) 3.0  1017 kg ms1 (B) 9.0  1017 kg ms1
Sol. (B)

13. A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation
y(x, t) = 0.01m sin [(62.8m1)x] cos[(628s1)t]. Assuming  = 3.14, the correct statement(s) is (are)
(A) The number of nodes is 5.
(B) the length of the string is 0.25 m.
(C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01m.
(D) The fundamental frequency is 100 Hz.
Sol. (B, C)

16. A bob of mass m , suspended by a string of length l1 is given a minimum velocity required to complete a
full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m
suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible.
If the second bob, after collision acquires the minimum speed required to complete a full circle in the
vertical plane, the ratio l1/l2 is
Sol. (5)

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