Question Bank Directory

Which of the following statements is not correct?

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB = D$. The height $h$ is equal to

In a closed insulated container a liquid is stirred with a paddle to increase the temperature. The correct option regarding this among the following is:

Match the trophic levels with their correct species examples in grassland ecosystem. (a) Fourth trophic level (i) Crow (b) Second trophic level (ii) Vulture (c) First trophic level (iii) Rabbit (d) Third trophic level (iv) Grass Select the correct option

Match the following columns and select the correct option. Column-I: (a) Bt cotton, (b) Adenosine deaminase deficiency, (c) RNAi, (d) PCR. Column-II: (i) Gene therapy, (ii) Cellular defence, (iii) Detection of HIV infection, (iv) Bacillus thuringiensis.

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">Unpolarised light is incident from air on a</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">plane surface of a material of refractive index</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">'<span class="s1" style="font-width: normal; line-height: normal; font-family: Symbol; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;"></span>'. At a particular angle of incidence 'i', it is</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">found that the reflected and refracted rays are</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">perpendicular to each other. Which of the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">following options is correct for this situation?</p>

The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance

In the circuit shown in the figure, the input voltage $V_i$ is 20 V, $V_{BE} = 0$ and $V_{CE} = 0$. The values of $I_B$, $I_C$ and $\beta$ are given by

An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is

In a p-n junction diode, change in temperature due to heating

When the light of frequency $2\nu_0$ (where $\nu_0$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is $v_1$. When the frequency of the incident radiation is increased to $5\nu_0$, the maximum velocity of electrons emitted from the same plate is $v_2$. The ratio of $v_1$ to $v_2$ is

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">The refractive index of the material of a</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">prism is $\mu = \sqrt{2}$ and the angle of the prism is $A = 30^\circ$.</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">One of the two refracting surfaces of the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">prism is made a mirror inwards, by silver</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">coating. A beam of monochromatic light</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">entering the prism from the other face will</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">retrace its path (after reflection from the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">silvered surface) if its angle of incidence on</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">the prism is $i$.</p>

An inductor $20 \text{ mH}$, a capacitor $100 \text{ }\mu\text{F}$ and a resistor $50 \text{ }\Omega$ are connected in series across a source of emf, $V = 10 \sin 314 \text{ t}$. The power loss in the circuit is

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">A small sphere of radius 'r' falls from rest in a</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">viscous liquid. As a result, heat is produced</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">due to viscous force. The rate of production of</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">heat when the sphere attains its terminal</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">velocity, is proportional to</p>

A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity, $\vec{v} = v\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for: