List of practice Questions

For three low density gases $A , B , C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ' $K$ ' is :

If the vectors $\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}$, $\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}$ are coplanar and the projection of $\overrightarrow{a}$ on the vector $\overrightarrow{b}$ is $\sqrt{54}$ units, then the sum of all possible values of $\lambda + \mu$ is equal to

Let [x] denote the greatest integer ≤ x. Consider the function $f(x)=max \{x^2,1+[x] \}$. Then the value of the integral $∫_0^2 f(x)dx$ is

$\displaystyle\lim _{t \rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots+n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

Let the tangents at the points A(4, –11) and B(8, –5) on the circle $x^2+y^2-3x+10y-15=0$, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

If a radioactive element with a half-life of 30 min undergoes beta decay. The fraction of the radioactive element that remains undecayed after 90 min is:

A block of mass m slides down the plane inclined at angle $30\degree$ with an acceleration $\frac{g}{4}$. The value of the coefficient of kinetic friction will be:

The surface tension of a soap bubble is $2 \times 10^{-2} \, \text{N/m}$. Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be:

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of $\hat{j}$ component of magnetic field ($B_y$) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:

A stone is projected at an angle of $30\degree$ to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

A bicycle tyre is filled with air having pressure of 270 kPa at $27\degree C$. The approximate pressure of the air in the tyre when the temperature increases to $36\degree C$ is:

Assertion A: If $ dQ $ and $ dW $ represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: \[ dQ = dU - dW. \]
Reason R: First law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

In a cuboid of dimension $2L \times 2L \times L$, a charge q is placed at the center of the surface ‘S’ having area of 4 L². The flux through the opposite surface to ‘S’ is:

Which of the following statements is not correct in the case of light emitting diodes (LEDs)?
A. It is a heavily doped p-n junction.
B. It emits light only when it is forward-biased.
C. It emits light only when it is reverse-biased.
D. The energy of the light emitted is equal to or slightly less then the energy gap of the semiconductor used.
Choose the correct answer from the options given below:

Match List I with List II:

List-I (Physical Quantity)		List-II (Dimensional Formula)
(A)	Pressure Gradient	(I)	$[M^0L^2T^{–2}]$
(B)	Energy density	(II)	$[M^1L^{–1}T^{–2}]$
(C)	Electric field	(III)	$[M^1L^{–2}T^{–2}]$
(D)	Latent heat	(IV)	$[M^1L^1T^{–3}A^{–1}]$

Choose the correct answer from the options given below:

Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation.
B. Speed of light in a medium is independent of the wavelength of light.
C. The speed of light is independent of the motion of the source.
D. The speed of light in a medium is independent of intensity.
Choose the correct answer from the options given below:

In a Young’s double slit experiment, two slits are illuminated with light of wavelength $800 \, \text{nm}$. The first minimum is detected at $P$. The value of slit separation $a$ is:

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given: Earth’s radius = $6.4 \times 106\text{ m}$

Find the mutual inductance in the arrangement, when a small circular loop of radius R is placed inside a large square loop of side $L$ ($L \gg R$). The loops are coplanar and their centers coincide:

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

The threshold wavelength for photoelectric emission from a material is $5500Å$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. 75 W infra-red lamp
B. 10 W infra-red lamp
C. 75 W ultra-violet lamp
D. 10 W ultra-violet lamp
Choose the correct answer from the options given below: