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 For the circuits A and B as shown in the figure, identify the correct option A) Circuit A is for accurate measurement of high resistance and B is for low resistance B) Circuit A is for accurate measurement of low resistance and B is for high resistance C) Both circuits can accurately measured high resistance only D) Both circuits can accurately measured low resistance only
3 The magnitude of the force vector acting on a unit length of a thin wire carrying a current I= 8A at a point O, if the wire is bent as shown in the figure with a radius , $R=10 \pi$ cm is A) 64 $\mu N/m $ B) 32 $\mu N/m $ C) 20 $\mu N/m $ D) 100 $\mu N/m $
4 The collision of an electron with kinetic energy 5.5 eV and a hydrogen atom in its ground state can be described as A) completely inelastic B) may be completely inelastic C) may be partially elastic D) elastic
5 The logic circuit below has the truth table same as that of A) NOR gate B) NAND gate C) AND gate D) OR gate
6 Which of the following represents fundamental force of nature ? A) Gravitational force, Coulomb's force : strong surface tension force; weak van der Waal's force B) Gravitational force; electromagnetic force; strong viscous force; weak nuclear force C) Gravitational force; magnetostatic force; strong nuclear force; weak frictional force D) Gravitational force; electromagnetic force; strong nuclear force; Weak nuclear force
7 A particle of mass m is moving along a circle of radius R such that its tangential acceleration at varies with distance covered x as at =ax2 where $\alpha$ is a constant. The kinetic energy,K of the particle varies with the distance as K= $\beta x^{c}$, where $\beta$ and c are constants. The values of $\beta$ and c are A) $\beta=\frac{m\alpha}{3};c=3$ B) $\beta=\frac{m\alpha}{4};c=3$ C) $\beta=\frac{m\alpha}{2};c=3$ D) $\beta=\frac{m\alpha}{2};c=3$
8 A particle A moves along the line, y=30m with a constant velocity, v parallel to the x-axis. At the momemt particle A passes the y-axis, particle B starts from the origin witrh zero initial speed and a constant acceleration .$a=0.40 m/sec^{2}$ . The angle between a and y-axis is $60^{0}$. If the particles A and B collide after sometimes , then the value of |v| will be A) 2 m/s B) 3 m/s C) 4 m/s D) 5 m/s
9 A body of mass 0.3 kg hangs by a spring with a force constant of 50N/m . The amplitude of oscillations is damped and reaches $\frac{1}{e}$ of its original value in about 100 oscillations. If $\omega$ and $\omega'$ are the angular frequencies of undamped and damped oscillations respectively , then percentage of $\left(\frac{\omega-\omega'}{\omega}\right)$ is A) $\left(\frac{1}{800 \pi}\right)$ B) $\left(\frac{\pi^{2}}{600 }\right)$ C) $\left(\frac{1}{800\pi^{2} }\right)$ D) $\left(\frac{\pi}{400 }\right)$
10 A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? [ Assume g=10 m/s2, $\rho_{water}$= 103 kg/m3, viscosity =1 centi-poise] A) 3 cm B) 4 cm C) 6 cm D) 2 cm
11 A carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_{1}$ and $T_{2}$ , where $T_{1} >T_{2}$ . If only $T_{1}$ is changed by 0.4% , the change in efficiency is $\triangle\eta_{1}$ , whereas if only $T_{2}$ is changed by 0.2% , the efficiency is changed by $\triangle\eta_{2}$ . The ratio $\frac{\triangle\eta_{1}}{\triangle\eta_{2}}$ is approximately A) -2 B) -4 C) +3 D) +4
12 The limit of resolution of a telescope is $2.5 \times 10^{-7}$ rad. If the telescope is used to detect light of wavelength 500 nm coming from a star, the diameter of the objective lens used by the telescope is A) 244 cm B) 258 cm C) 228 cm D) 264 cm
13 For the circuit shown in the figure, calculate the resistance between points A and B A) 0.5 R B) R C) 15 R D) $\frac{6}{5}R$
14 Four identical metal plates are located in the air at equal distance d from each other . The area of each plate in S. If the outermost plates are connected by a conducting wire as shown in the figure the capacitance between points A and B will be A) $\frac{\epsilon_{0}S}{d}$ B) $\frac{3}{2}\frac{\epsilon_{0}S}{d}$ C) $\frac{1}{2}\frac{\epsilon_{0}S}{d}$ D) $\frac{2}{3}\frac{\epsilon_{0}S}{d}$
15 A person applies a sine wave and square wave to an AND gate as shown in the figure (i) and (ii) . Assuming that both the voltages are applied in phase , the person observers the output at E and F on (i) and (ii) , respectively. [Assume minimum voltage of 5V is equivalent to logic (i)] A) Sqaure wave at 50 Hz and square wave at 100 Hz B) Sine wave at 50 Hz and square wave at 100 Hz C) No output and sine wave at 100 Hz D) No output and pulsed wave at 100 Hz