1 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
2 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) $\omega_{m}$
3 In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be A) $90^{0}$ B) $135^{0}$ C) $180^{0}$ D) $45^{0}$
4 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
5 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
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
8 The sodium salt of an organic acid 'X' produces effervescence with conc. H2SO4 . 'X' reacts with the acidified aqueous CaCl2 solution to give a white precipitate which decolorises acidic solution of KMnO4. 'X' is A) $C_{6}H_{5}COONa$ B) $HCOONa$ C) $C_{}H_{3}COONa$ D) $Na_{2}C_{2}O_{4}$
10 Given ,$E^{0}_{Cl_{2}/Cl^{-}}$=1.36 V $E^{0}_{Cr^{3+}/Cr}=-0.74 V$ $E^{0}_{Cr_{2}O^{2-}_{7}/Cr^{3+}}=1.33 V$ $E^{0}_{MnO^{-}_{4}/Mn^{2+}}=1.51 V$ Among the following , the strongest reducing agent is A) Cr B) $Mn^{2+}$ C) $Cr^{3+}$ D) $Cl^{-}$
11 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) $\frac{3}{16}$
12 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
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 The normal to the curve y(x-2) (x-3)=x+6 at the point, where the curve intersects the Y-axis passes through the point A) $(-\frac{1}{2},-\frac{1}{2})$ B) $(\frac{1}{2},\frac{1}{2})$ C) $(\frac{1}{2},-\frac{1}{3})$ D) $(\frac{1}{2},\frac{1}{3})$
15 The value of $(^{21}C_{1}-^{10}C_{1})+(^{21}C_{2}-^{10}C_{2})+(^{21}C_{3}-^{10}C_{3})+.....+(^{21}C_{10}-^{10}C_{10})$ is A) $2^{21}-2^{11}$ B) $2^{21}-2^{10}$ C) $2^{20}-2^{9}$ D) $2^{20}-2^{10}$
