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 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) $\sqrt{\frac{3}{2}}$
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 A copper ball of mass 100 g is at a temperature T. It is dropped in a copper calorimeter of mass 100g, filled with 170 g of water at room temperature. Subsequently, the temperature of the system is found to be 75° C . T is (Given, room temperature = 30° C, the specific heat of copper =0.1 cal/ g° C ) A) $885^{0}C$ B) $1250^{0}C$ C) $825^{0}C$ D) $800^{0}C$
5 In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is A) 225 Wb B) 250 Wb C) 275 Wb D) 200 Wb
6 When a current of 5 mA is passed through a galvanometer having a coil of resistance 15Ω, it shows full-scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0-10 V is A) $2.045 \times 10^{3}$O B) $2.535 \times 10^{3}$O C) $4.005 \times 10^{3}$O D) $1985 \times 10^{3}$O
7 A time-dependent force F =6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 s will be A) 22J B) 9 J C) 18 J D) 4.5 J
8 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 On the treatment of 100 mL of 0.1 M solution of CoCl3. 6H2O with an excess of AgNO3: 1.2× 1022 ions are precipitated. The complex is A) $[Co(H_{2}O)_{4}Cl_{2}]Cl.2H_{2}O$ B) $[Co(H_{2}O)_{3}Cl_{3}].3H_{2}O$ C) $[Co(H_{2}O)_{6}]Cl_{3}$ D) $[Co(H_{2}O)_{5}Cl_{}]Cl_{2}.H_{2}O$
10 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) $6\sqrt{5}$
11 Let a vertical tower AB have its end A on the level ground. Let C be the mid-pont of AB and P be a point on the ground such that AP=2AB. If $\angle$ BPC= β , then tanβ is equal to A) $\frac{6}{7}$ B) $\frac{1}{4}$ C) $\frac{2}{9}$ D) $\frac{4}{9}$
12 For any three positive real numbers a,b and c. If 9(25a2+b2)+25(c2-3ac) =15b (3a+c), then A) b,c and a are in GP B) b,c and a are in AP C) a,b and c are in AP D) a, b and c are in GP
13 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) $(-\frac{1}{5},0)$
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 The radius of a circle having minimum area, which touches the curve y=4-x2 and the line y=|x| , is A) $2(\sqrt{2}+1)$ B) $2(\sqrt{2}-1)$ C) $4(\sqrt{2}-1)$ D) $4(\sqrt{2}+1)$