1 The period of oscillation of a simple pendulam is $T= 2\pi \sqrt{\frac{L}{g}}$.Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillation of the pendulam is found to be 90 s using a wrist watch of 1 sresolution .The accurancy in the determination of g is A) 2 % B) 3 % C) 1 % D) 5 %
2 A train moving on a straight track with speed 20 ms-1. It is blowing its whistle at the frequency of 1000Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to (speed of sound =320 ms-1 ) A) 6% B) 12% C) 18% D) 24%
3 Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle θ with the vertical. If wires have mass λ per unit length then, the value of I is (g= gravitational acceleration) A) $\sin\theta\sqrt{\frac{\pi \lambda gL}{\mu_{0}\cos\theta}}$ B) $2\sin\theta\sqrt{\frac{\pi \lambda gL}{\mu_{0}\cos\theta}}$ C) $2\sqrt{\frac{\pi g L}{\mu_{0}}\tan\theta}$ D) $\sqrt{\frac{\pi \lambda g L}{\mu_{0}}\tan\theta}$
4 A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2MHz. The frequencies of the resultant signal is/are A) 2MHz only B) 2005 kHz and 1995 kHz C) 2005 kHz 2000 kHz and 1995 kHz D) 2000 kHz and 1995 kHz
5 Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided A) $\theta > \sin^{-1}\left[\mu\sin\left(A-\sin^{-1}\left(\frac{1}{\mu}\right)\right)\right]$ B) $\theta < \sin^{-1}\left[\mu\sin\left(A-\sin^{-1}\left(\frac{1}{\mu}\right)\right)\right]$ C) $\theta > \cos^{-1}\left[\mu\sin\left(A+\sin^{-1}\left(\frac{1}{\mu}\right)\right)\right]$ D) $\theta < \cos^{-1}\left[\mu\sin\left(A+\sin^{-1}\left(\frac{1}{\mu}\right)\right)\right]$
6 The synthesis of alkyl fluorides best accomplished by A) free radical fluorination B) Sandmeyer's reaction C) Finkelstein reaction D) Swarts reaction
7 Lat A and B be the two sets containing four and two elements respectively. Then, the number of subsets of the set A X B , each having at least three elements are, A) 219 B) 256 C) 275 D) 510
8 The number of integers greater than 6000 that can be formed. using the digits 3,5,6,7 and 8 without repetition , is A) 216 B) 192 C) 120 D) 72
9 The sum of first 9 terms of the series $\frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+...is$ A) 71 B) 96 C) 142 D) 192
10 If the function $g(x)=\begin{cases}k\sqrt{x+1}, & 0 \leq x \leq3\\mx+2, &3<x \leq 5\end{cases}$ differentiable , then value of k+m is A) 2 B) $\frac{16}{5}$ C) $\frac{10}{3}$ D) 4
11 Let f(x) be a polynomial of degree four having extreme values at x=1, amd x=2 . If $\lim_{x \rightarrow 0}\left[1+\frac{f(x)}{x^{2}}\right]=3$ , then f(2) is equal to A) -8 B) -4 C) 0 D) 4
12 The area (in sq units) of the region described by $(x,y:y^{2}\leq2x)$ and $(y\geq4x-1)$ is A) $\frac{7}{32}$ B) $\frac{5}{64}$ C) $\frac{15}{64}$ D) $\frac{9}{32}$
13 The area (in sq units) of the quadrilateral formed by the tangent at the endpoints of the latus rectum to the ellipse $\frac{x^{2}}{5}+\frac{y^{2}}{5}=1$ is A) $\frac{27}{4}$ B) 18 C) $\frac{27}{2}$ D) 27
14 The distance of the point (1,0,2) from the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane x-y+z=16 is A) $2\sqrt{14}$ B) 8 C) $3\sqrt{21}$ D) 13
15 If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30° , 45° and 60° respectively , then the ratio AB:BC is A) $\sqrt{3}:1$ B) $\sqrt{3}:\sqrt{2}$ C) $1:\sqrt{3}$ D) 2:3