1 The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is $I$. What is the ratio l/R such that the moment of inertia is minimum? A) $\frac{\sqrt{3}}{2}$ B) 1 C) $\frac{3}{\sqrt{2}}$ D) $\sqrt{\frac{3}{2}}$
2 A capacitance of 2µF is required in an electrical circuit across a potential difference of 1kV. A large number of 1 µ F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is A) 16 B) 24 C) 32 D) 2
3 In amplitude modulation. sinusoidal carrier frequency used is denoted by ωc and the signal frequency is denoted by ωm . The bandwidth (Δωm) of the signal is such that Δωm << ωc . Which of the following frequencies is not contained in the modulated wave ? A) $\omega_{c}$ B) $\omega_{m}+\omega_{c}$ C) $\omega_{c}-\omega_{m}$ D) $\omega_{m}$
4 A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is A) $\frac{2g}{3l}\sin\theta$ B) $\frac{3g}{2l}\cos\theta$ C) $\frac{2g}{3l}\cos\theta$ D) $\frac{3g}{2l}\sin\theta$
5 A diverging lens with a magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of the magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is A) virtual and at a distance of 40cm from convergent lens B) real and at a distance of 40cm from the divergent lens C) rea; and at a distance of 6 cm from the convergent lens D) real and at a distance of 40 cm from the convergent lens
6 A magnetic needle of magnetic moment 6.7 × 10-2 Am2 and moment of inertia 7.5 × 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is A) 8.89 s B) 6.98 s C) 8.76 s D) 6.65 s
7 A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that this density remains the same, the stress in the leg will change by a factor of A) $\frac{1}{9}$ B) 81 C) $\frac{1}{81}$ D) 9
9 The most abundant elements by mass in the body of a healthy human adult are Oxygen (61.4%); Carbon (22.9%); Hydrogen (10.0%); and Nitrogen (2.6%). The weight which 75 kg person would gain if all 1H atoms are replaced by 2H atoms is A) 15 kg B) 37.5 kg C) 7.5 kg D) 10 kg
10 Two reactions R1 and R2 have identical pre-exponential factors. The activation energy of R1 exceeds that of R2 by 10 kj mol-1 . If k1 and k2 are rate constants for reactions R1 and R2, respectively at 300 K. then ln $(\frac{k_{2}}{k_{1}})$ is equal to (R=8.314 J mol-1 K-1) A) 8 B) 12 C) 6 D) 4
11 1 g of a carbonate (M2CO3) on treatment with excess HCl produces 0.01186 mole of CO2 . The molar mass M2CO3 in g mol-1 is A) 1186 B) 84.3 C) 118.6 D) 11.86
12 For three events A. B and C. If P ( exactly one of A or B occurs)= P (exactly one of B or C occurs)= $\frac{1}{4}$ and P (all the three events occurs simultaneously )= $\frac{1}{16}$ , then the probability that atleast one of the events occurs, is A) $\frac{7}{32}$ B) $\frac{7}{16}$ C) $\frac{7}{64}$ D) $\frac{3}{16}$
13 The area ( in sq units) of the region {(x,y):x ≥ 0, x +y ≤ 3, x2 ≤ 4y and y ≤ 1+√x } is A) $ \frac{59}{12}$ B) $ \frac{3}{2}$ C) $ \frac{7}{3}$ D) $ \frac{5}{2}$
14 If the image of the point P(1,-2,3) in the plane 2x+3y-4z+22=0 measured parallel to the line $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q, then PQ is equal to A) $3\sqrt{5}$ B) $2\sqrt{42}$ C) $\sqrt{42}$ D) $6\sqrt{5}$
15 If a hyperbola passes through the point $P(\sqrt{2},\sqrt{3})$ and has foci at (± 2,0), then the tangent to this hyperbola at P also passes through the point A) $(3\sqrt{2},2\sqrt{3})$ B) $(2\sqrt{2},3\sqrt{3})$ C) $(-\sqrt{3},\sqrt{2})$ D) $(-\sqrt{2},-\sqrt{3})$