Online Test - NextGen Physics

1. Given that $\vec A+\vec B+\vec C=0$. Out of three vectors, two are equal in magnitude and the magnitude of the third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between the vectors are:

A. $30^\circ,60^\circ,90^\circ$ B. $45^\circ,45^\circ,90^\circ$ C. $45^\circ,60^\circ,90^\circ$ D. $90^\circ,135^\circ,135^\circ$

2. The escape velocity for a body projected vertically upwards from the surface of Earth is $11\ km/s$. If the body is projected at an angle of $45^\circ$ with the vertical, the escape velocity will be:

A. $22$ B. $11$ C. $\frac{11}{\sqrt2}$ D. $11\sqrt2$

3. Find the mechanical advantage for pulling mass $M$ by the person as shown in the figure.

A. $2$ B. $4$ C. $8$ D. $16$

4. A torque of $30\ Nm$ is applied for $15\ s$ on a stationary wheel. The moment of inertia is $2\ kg,m^2$. The angular displacement in $10\ s$ is:

A. $750$ B. $1500$ C. $3000$ D. $6000$

5. A bomb explodes into two fragments of masses $1g$ and $3g$. Total kinetic energy is $6.4\times10^4J$. Find the K.E. of the smaller fragment.

A. $2.5\times10^4J$ B. $2.5\times10^4J$ C. $3.5\times10^4J$ D. $5.2\times10^4J$

6. A solid cylinder of radius $R$ and conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ having conductivity $K_2$. The effective thermal conductivity is:

A. $K_1+K_2$ B. $\frac{K_1K_2}{K_1+K_2}$ C. $\frac{2K_1+K_2}{4}$ D. $\frac{K_1+3K_2}{4}$

7. Find the quantity of heat required to convert $40g$ of ice at $-20^\circ C$ into water at $20^\circ C$. Given $L=0.336\times10^6J/kg$, $c_{ice}=2100J/kgK$, $c_{water}=4200J/kgK$.

A. $18480$ B. $17580$ C. $18685$ D. $17412$

8. Young's modulus of a wire is $6\times10^{12}N/m^2$ and there is no transverse strain. Modulus of rigidity is:

A. $3\times10^{12}$ B. $2\times10^{12}$ C. $10^{12}$ D. None of these

9. In a screw gauge having 100 divisions, pitch = $0.5mm$. Zero lies 6 divisions below reference line. With a wire inserted, 4 main scale divisions and 46th circular scale division are visible. Diameter of wire is ______ $\times10^{-2}mm$.

A. $23$ B. $20$ C. $21$ D. $22$

10. Water is filled in a tank up to a height of $3m$. Base of the tank is $1m$ above ground. At what height should a hole be made for maximum horizontal range?

A. $3m$ from ground B. $1.5m$ from ground C. $1.5m$ from base D. $2m$ from ground

11. A wheel initially at rest begins to rotate about its axis with constant angular acceleration. If it rotates through an angle θ₁ in first 2 s and a further angle θ₂ in the next 2 s, then the ratio θ₁ : θ₂ is:

A. 1 : 6 B. 6 : 1 C. 3 : 1 D. 1 : 3

12. A galvanometer having a coil resistance of 60 Ω shows full-scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read currents up to 5.0 A by:

A. Putting in series a resistance of 15 Ω B. Putting in series a resistance of 240 Ω C. Putting in parallel a resistance of 15 Ω D. Putting in parallel a resistance of 240 Ω

13. The graph shows the variation of velocity of a rocket with time. The maximum height attained by the rocket is:

A. 1.1 km B. 5 km C. 55 km D. None of these

14. A beam of light both reflects and refracts at the surface between air and glass. The refractive index of glass is 1.4. If the refracted and reflected rays are perpendicular to each other, then the angle of incidence in air is:

A. tan⁻¹(1.4) B. sin⁻¹(1/1.4) C. tan⁻¹(1/1.4) D. sin⁻¹(1.4)

15. A galvanometer having a coil resistance of 60 Ω shows full-scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read currents up to 5.0 A by:

A. Putting in series a resistance of 15 Ω B. Putting in series a resistance of 240 Ω C. Putting in parallel a resistance of 15 Ω D. Putting in parallel a resistance of 240 Ω

16. When a photosensitive surface is irradiated by light of wavelengths $ \lambda_1 $ and $ \lambda_2 $, the maximum kinetic energies of the emitted photoelectrons are $ E_1 $ and $ E_2 $ respectively. The work function of the photosensitive surface is:

A. $\frac{\lambda_1 E_1-\lambda_2 E_2}{\lambda_2-\lambda_1}$ B. $\frac{\lambda_1 E_1+\lambda_2 E_2}{\lambda_2-\lambda_1}$ C. $\frac{\lambda_1 E_2-\lambda_2 E_1}{\lambda_2-\lambda_1}$ D. $\frac{\lambda_1 E_2+\lambda_2 E_1}{\lambda_2-\lambda_1}$

17. A radioactive decay can form an isotope of the original nucleus with the emission of which particles?

A. $1\alpha$ and $4\beta$ B. $1\alpha$ and $2\beta$ C. $1\alpha$ and $1\beta$ D. $4\alpha$ and $1\beta$

18. The relative permittivity of distilled water is $81$. The velocity of light in it will be: (Given $\mu_r = 1$ and $c = 3\times10^8\ \text{m/s}$)

A. $5\times10^7$ m/s B. $4\times10^7$ m/s C. $3\times10^7$ m/s D. $2\times10^7$ m/s

19. Two small conducting balls of identical mass $20\,g$ and identical charge $10^{-10}\,C$ hang from non-conducting threads of length $L=300\,cm$. If the equilibrium separation of the balls is $x$ and $x \ll L$, then the magnitude of $x$ is: Given $\frac{1}{4\pi\varepsilon_0}=9\times10^9$ and $g=10\ \mathrm{m/s^2}$

A. $\left(\frac{2}{5}\right)^{1/3}$ mm B. $\left(\frac{3}{10}\right)^{1/3}$ mm C. $\left(\frac{10}{3}\right)^{1/3}$ mm D. $\left(\frac{5}{2}\right)^{2/3}$ mm

20. An LR circuit with a battery is connected at $t=0$. Which of the following quantities is not zero just after the circuit is closed?

A. Current in the circuit B. Magnetic field energy in the inductor C. Power delivered by the battery D. Induced emf in the inductor

21. If $B_V$ and $B_H$ are respectively the vertical and horizontal components of the earth's magnetic field at a place where the angle of dip is $60^\circ$, then the total magnetic field at that place is:

A. $\sqrt{3}\,B_H$ B. $\sqrt{3}\,B_V$ C. $\frac{2B_V}{\sqrt{3}}$ D. $\frac{\sqrt{3}}{2}B_H$

22. If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of the $n=\infty$ state is:

A. $3.4\,eV$ B. $6.8\,eV$ C. $0$ D. $\infty$

23. The power factor of the circuit shown in the figure is:

A. $0.5$ B. $1$ C. $\frac{1}{\sqrt{2}}$ D. $\sqrt{2}$

24. The value of current through the $20\,\Omega$ resistor is:

A. $1.2$ A B. $0.3$ A C. $0.6$ A D. $1.8$ A

25. A point source of light is placed at $2f$ from a converging lens of focal length $f$. A plane mirror is placed on the other side of the lens at a distance $d$ such that rays reflected from the mirror are parallel after passing through the lens again. If $f=30\ \text{cm}$, then $d$ is equal to:

A. $15$ cm B. $30$ cm C. $45$ cm D. $75$ cm

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