1 Match the following fundamental forces of nature with their relative strength . A) A:II,B:IV,C:I,D:III B) A:III ,B:II,C:IV, D:I C) A:II,B:III,C:IV,D:I D) A:IV,B:II,C:I,D:II
2 A vertical spring mass system has the same line period as simple pendulum undergoing small oscillations .Now , both of them are put in an elevator going downwards with an acceleration 5 m/s2 . The ratio of time period of the spring mass system to the time period of the pendulum is (Assume, acceleration due to gravity , g= 10 m/s2) A) $\sqrt{\frac{3}{2}}$ B) $\sqrt{\frac{2}{3}}$ C) $\frac{1}{\sqrt{2}}$ D) $\sqrt{2}$
3 How much pressure (in atm) is needed to compress a sample for water by 0.4 % ? (Assume , Bulk modulus of water = $2.0 \times 10^{9}$ Pa) A) 60atm B) 70 atm C) 80 atm D) 90 atm
4 One mole of nitrogen gas being initially at a temperature of T0 =300K is adiabatically compressed to increase its pressure 10 times .The final gas temperature after compression is (Assume , nitrogen gas molecules as rigid diatomic and $100^{1/7}$= 1.9) A) 120K B) 750 K C) 650 K D) 570K
5 In Young's double slit experiment, mth order and n th order of bright fringes are formed at point P on a distant screen if monochromatic source of wavelength 400 nm and 600 nm are used respectively . The minimum vale of m and n are respectively , A) 4.6 B) 3.2 C) 2.3 D) 4.2
6 The space between the two large parallel plates is filled with a material of uniform charge density $\rho$ . Assume that one of the plate is kept at x=0 . The potential at any point x between these plates is given by (A and B are constants) A) $-\frac{\rho x^{3}}{2\epsilon_{0}}$ B) $-\left(\frac{\rho x^{2}}{2\epsilon_{0}}+Ax\right)$ C) $-\left(\frac{\rho x^{2}}{2\epsilon_{0}}+Ax+B\right)$ D) $-\left(\frac{\rho x^{3}}{4\epsilon_{0}}+Ax^{2}+Bx\right)$
7 A ball is projected vertically up from ground. Boy A standing at the window of first floor of a nearby building observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is 2s . Another boy B standing on the second floor notices that time interval between the ball passing him twice, during up motion and down motion is 1s . Calculate the difference between the vertical positions of boy B and boy A (Assume , acceleration due to gravity ,g=10 m/s2) A) 8.45 m B) 3.75 m C) 4.25 m D) 2.50 m
8 An ideal gas is placed in a tank at $27^{0} C$. The pressure is initially 600 kPa. One-fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is $327^{0}$ C? A) 900 kPa B) 1000 kPa C) 1050 kPa D) 1250 kPa
9 A capacitor of capacitance 4$\mu$ F is charged to a potential difference of 6 V with a battery. The battery is removed and in its place another capacitor of capacitance is 8$\mu$ F introduced and the circuit is closed. The potential difference attained by each of the capacitors in V is A) 2 B) 4 C) 6 D) 8
10 In a transistor circuit, the collector current is changed by 8.9 mA, if the emitter current is changed to 9.0 mA . The value of current amplification factor $\beta$ is A) 89 B) 92 C) 84 D) 96
11 A metal plate of thickness 2mm and area $36 \pi cm^{2}$ is slide into a parallel plate capacitor of plate spacing 6 mm and are $36 \pi cm^{2}$ . The metal plate is at a distance 3 mm from one of the plates. What is the capacitance of this arrangement? $\left( Let\frac{1}{4 \pi \in_{0}}=9 \times 10^{9} Nm^{2}C^{-2}\right)$ A) 8 pF B) 15 pF C) 25pF D) 20pF
12 Assertion (A) Si and GaAs are the preferred materials for solar cells Reason (R) Both these materials have energy band gaps much below the energy level corresponding to the maximum solar irradiance in the solar spectrum The correct answer is A) (A) is correct but (R) is incorrect B) Both (A) and (R) are correct and (R0 is the correct explanation of (A) C) Both (A) and (R) are correct. but (R0 is not the correct explanation of (A) D) Both (A) and (R) are incorrect
13 Identify the correct option A) The rang of the gravitonal force is large but not infinite B) The range of electromagnetic force is large but lesser than the range of gravitational force C) The range of weak nuclear force is smaller than the range of strong nuclear force, gravitation force and electromagnetic force D) The range of the weak as well as strong nuclear force is of the the order of $10^{-10}$ m
14 A boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved 100 m. if the truck is moving horizontally along a straight line with a constant speed 30 m/s, at what speed (relative to the truck) must the projectile is thrown.(Assume, g=10 m/s2) A) $\frac{55}{3} m/s$ B) $\frac{43}{2} m/s$ C) $\frac{50}{3} m/s$ D) $\frac{23}{3} m/s$
15 A message signal is used to modulate a carrier signal of frequency 5 MHz and peak voltage of 40 V . In the process, two side-bands are produced separated by 40 kHz. If the modulation index is 0.75, then the peak voltage and frequency of the messages signal, respectively are A) 60 V, 10 kHz B) 60 V, 20 kHz C) 30 V, 10 kHz D) 30V, 20 kHz
