1 Distance of centre of mass of a solid uniform cone from its vertex is z0.If the radius of its base is R and its height is h, then z0 is equal to A) $\frac{h^{2}}{4R}$ B) $\frac{3h}{4}$ C) $\frac{h^{2}}{R}$ D) $\frac{h}{4}$
2 In the circuit shown below, the current in the 1Ω resistor is A) 1.3 A, from P to Q B) 0 A C) 0.13 A , from Q to P D) 0.13 A , from P to Q
3 A red LED emits light at 0.1 W uniformly around it. The amplitude of the electric field of the light at a distance of 1m from the diode is A) 1.73 V/m B) 2.45 V/m C) 5.48 V/m D) 7.75 V/m
4 On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens principle leads us to conclude that as it travels, the light beam A) becomes narrower B) goes horizontally without any deflection C) bends downwards D) bends upwards
5 The vapour pressure of acetone at 20° C is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20° C, its vapour pressure was 183 torr. The molar mass (gmol-1) of the substance is A) 32 B) 64 C) 128 D) 488
6 The standard Gibbs energy change at 300K for the reaction, $2A\rightleftharpoons B+C$ is 2494.2 J. At a given time , the composition of the reaction mixture is $[A]=\frac{1}{2}$ , [B]=2 and $[C]=\frac{1}{2}$ . The reaction proceeds in the [ R=8.314 JK/mol, e=2.718] A) forward direction because Q > $K_{c}$ B) reverse direction because Q >$K_{c}$ C) forward direction because Q < $K_{c}$ D) reverse direction because Q < $K_{c}$
7 Two Faraday of electricity is passed through a solution of CuSO4. The mass of copper deposited at the cathode is [at .mass of Cu=63.5 u] A) 0 g B) 63.5 g C) 2 g D) 127 g
8 3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06 N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal ) is A) 18 mg B) 36 mg C) 42 mg D) 54 mg
9 The ionic radii (in Å ) of N3-,O2- and F- respectively are A) 1.36,1.40 and 1.71 B) 1.36 , 1.71 and 1.40 C) 1.71 , 1.40 and 1.36 D) 1.71 ,1.36 and 1.40
10 The colour of $KMnO_{4}$ is due to A) $M \rightarrow L$ charge transfer transition B) d - d transition C) $L \rightarrow M$ charge transfer transition D) $\sigma $ - $\sigma $ transition
11 In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is [ at. mass Ag=108, Br=80] A) 24 B) 36 C) 48 D) 60
12 In the following sequence of reaction, Toluene $\underrightarrow{KmnO_{4}} $ A $\underrightarrow{SOCl_{2}} $ B $\xrightarrow [ {BasO_{4}}]{{H_{2}/Pd}}$ C The product C is A) $C_{6}H_{5}COOH$ B) $C_{6}H_{5}CH_{3}$ C) $C_{6}H_{5}CH_{2}OH$ D) $C_{6}H_{5}CHO$
13 A complex number z is said to be unimodular, if |z| =1, suppose z1 and z2 are complex numbers such that $\frac{z_{1}-2z_{2}}{z-z_{1}z_{2}}$ is unimodular and z2 is not unimodular. Then , the point z1 lies on a A) straight line parallel to X-axis B) Straight line parallel to Y- axis C) circle of radius 2 D) circle of radius $\sqrt{2}$
14 Let $\alpha$ and $\beta$ be thr roots of equation $x^{2}-6x-2=0$ . If $a_{n}=\alpha^{n}-\beta^{n}$ , for $n\geq 1$ , then the value of $\frac{a_{10}-2a_{8}}{2a_{9}}$ is equal to A) 6 B) -6 C) 3 D) -3
15 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