1 An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz . What is the frequency of the microwave measured by the observer ? [ speed of ight = 3 x 108 ms-1 ] A) 12.1 GHz B) 17.3 GHz C) 15.3 GHz D) 10.1 GHz
2 The following observations were taken for determining surface tension T of water by capillary method. Diameter of capillary, d=1.25 × 10-2 m rise of water, h=1.45 × 10-2 m. Using g=9.80 m/s2 and the simplified relation $T= \frac{rhg}{2}\times 10^{3} N/m.$ The possible error in surface tension is closest to A) 1.5% B) 2.4% C) 10% D) 0.15%
3 In the given circuit diagram, when the current reaches a steady state in the circuit, the charge on the capacitor of capacitance C will be A) $CE \frac{r_{1}}{(r_{2}+r)}$ B) $CE \frac{r_{2}}{(r_{}+r_{2})}$ C) $CE \frac{r_{1}}{(r_{1}+r_{})}$ D) CE
4 An electric dipole has a fixed dipole moment p, which makes angle θ with respect to X-axis. When subjected to an electric field $E_{1}=E\hat{i}$ , it experiences a torque $T_{1}=\tau\hat{k}$ . When subjected to another electric field $E_{2}=\sqrt{3}E_{1}\hat{j}$ , it experiences a torque T2 = -T1 . The angle θ is A) $45^{0}$ B) $60^{0}$ C) $90^{0}$ D) $30^{0}$
5 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) $\frac{3g}{2l}\sin\theta$
7 pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4 respectively. The pH of their salt (AB) solution is A) 7.2 B) 6.9 C) 7.0 D) 1.0
8 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
9 Both lithium and magnesium display several similar properties due to the diagonal relationship:however the one which is incorrect is A) Both form basic carbonates. B) Both form soluble bicarbonates C) Both form nitrides D) nitrates of both Li and Mg yield $NO_{2}$ and $O_{2}$ on heating
10 The major products obtained in the following reaction is A) $(\pm)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$ B) $C_{6}H_{5}CH= CHC_{6}H_{5}$ C) $(+)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$ D) $(-)C_{6}H_{5}CH(O^{t}Bu)CH_{2}C_{6}H_{5}$
11 If 20 m of wire is available for fencing off a flower -bed in the form of a circular sector, then the maximum area ( in sq m) of the flower-bed is A) 12.5 B) 10 C) 25 D) 30
12 Let $I_{n}=\int_{}^{} tan^{n}x dx (n>1), If $ $I_{4}+I_{6}=a\tan^{5}x+bx^{5}+C,$ , where C is a constant of integration, then orderd pair (a,b) is equal to A) $(-\frac{1}{5},1)$ B) $(\frac{1}{5},0)$ C) $(\frac{1}{5},-1)$ D) $(-\frac{1}{5},0)$
13 The eccentricity of an ellipse whose centre is at the orgin is 1/2 . If one of its directrices is x=-4, then the equation of the normal to it at (1, $\frac{3}{2}$) is A) 2y-x=2 B) 4x-2y=1 C) 4x+2y=7 D) x+2y=4
14 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) $(-\sqrt{2},-\sqrt{3})$
15 $\lim_{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2x)^{3}}$ equals A) $\frac{1}{24}$ B) $\frac{1}{16}$ C) $\frac{1}{8}$ D) $\frac{1}{4}$