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If $P,Q,R$ are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

If I place a dielectric of thickness 2cm and relative permittivity 2 in between the plates of a parallel plate capacitor, with area $3c{m}^2$ and plate spacing 4 cm, what is the new capacitance?

A bar of mass $m$ and length $l$ is hanging from point $\text{A}$ as shown in figure. Find the increase in its length due to its own weight. The Young's modulus of elasticity of the wire is $Y$ and area of cross-section of the wires is $A$.

A boy, standing inside a box sliding on a smooth inclined plane, throws a ball and catches it back at the same level. The unit vector along the velocity of the ball with respect to the box velocity will be

A body is rotated in the vertical plane by means of a thread of length $l$ with minimum possible velocity. When the body goes up and reaches at the highest point B of its path, the thread breaks and the body moves on a parabolic path under the influence the gravitational field as shown in the diagram. The horizontal range AC would be

A cylinder of ideal gas is closed by an $8kg$ movable piston (area $60c{m}^2$). Atmospheric pressure is ${10}^{5}Pa$. When the gas is heated from $30°C$ to $100°C$, the piston rises by $20cm$. The piston is then fixed in its place and the gas is cooled back to $30°C$. Let $\Delta Q_1$ be the heat added to the gas in the heating process and $\left|\Delta Q_2\right|$ the heat lost during cooling. Then the value of $\Delta Q_1-\left|\Delta Q_2\right|$ will be

What is the resistance of this $4$ strip resistor ?



Colour are in order- Yellow, violet, red, golden.

Find component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$ i.e. A||B and in perpendicular direction of $\overrightarrow{B}$ that is $A_{{\perp }_B}$.

Consider the cyclic process $ABCA$ as shown in the figure, performed on a sample of $2.0$ mole of an ideal gas. A total of $1200\text{J}$ of heat is withdrawn from the sample in the process. Find the magnitude of the work done (in joules) by the gas during the part $BC$. $(R=8.3{\text{JK}}^{-1}{\text{mol}}^{-1})$

An ascending gradient of 1 in 45 meets a descending gradient of 1 in 60. A summit curve has to be designed gradient for design speed of 80 km/h so as to provide a safe overtaking sight distance of 230 m. Estimate the length of the summit curve.

1. 213.143

The correct $I-H$ curve for paramagnetic materials is,

In the figure shown, the forces are acting simultaneously on the body of mass $10\text{kg}$ which is initially at rest. Find its velocity after $10\text{s}$.

Two Polaroids as oriented with their planes perpendicular to incident light and transmission axis, making an angle of ${30}^{\circ }$ with each other. What fraction of incident unpolarised light is transmitted ?

A person of mass $60\text{kg}$ is inside a lift of mass $940\text{kg}$ and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

Two charges $q_1$ and $q_2$ are placed 30 cm apart as shown in the figure. A third charge $q_3$is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{q_3}{4\pi {ϵ}_0}k$, where k is

A particle slides on the surface of a fixed smooth sphere starting from the topmost point. Find the angle subtended by the motion of particle from top to the point when it leaves contact with the sphere.

The value of current $I$ in the given circuit is -

The difference between the incident energy and threshold energy for an electron in a photoelectric effect experiment is 5eV. The de Broglie wavelength of the electron is -

For the shown arrangement of potentiometer, Find the value of $x$ , if $\text{P}$ is a null point. Resistance of portion $\text{OB}$ is $20\Omega$

In an AC circuit, the impedance is $\sqrt{3}$ times the reactance, then the phase angle is -

A cement concrete pavement has thickness of $25\text{cm}$ and of two lanes with a longitudinal joint along the centre. if the coefficient of friction (f) is 1.5 then the area of steel required per meter is $c{m}^2$ [Take ${\gamma }_{concrete}=2400kg/m^3$ and ${\sigma }_s=1400kg/c{m}^2$, width of pavement, w = 3.5 m]

1. 2.25

An ideal voltmeter is connected in the figure. The current in circuit is

During a current change from $2\text{A to}4\text{A in}0.05\text{sec},8\text{V}$ of emf is developed in a coil. The coefficient of self-induction is



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A conducting rod $\text{PQ}$ of length $l=2\text{m}$ is moving at a speed of $2{\text{ms}}^{-1}$ making an angle of ${60}^{\circ }$ with its length. A uniform magnetic field $B=\sqrt{3}\text{T}$ exists in a direction perpendicular to the plane of motion. Then

A clinical thermometer cannot show _______ as its reading.

A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

Speedometer of a car measures ______ velocity.

The unit vector which is perpendicular to the vectors $\overrightarrow{A}=\hat{i}+2\hat{j}-\hat{k}$ and $\overrightarrow{B}=3\hat{i}-2\hat{j}+\hat{k}$ is

Find the current through $2\text{V}$ battery.

A boat moves relative to water with a velocity which is $\frac{1}{n}$ times the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting ?