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A heat engine is involved with exchange of heat of $1915J,-40J,+125J\text{and}-QJ$, during one cycle achieving an efficiency of $50.0$%. The value of $Q$ is

Consider two masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that they complete circular motion in the same time t. The ratio of their untripetal acceleration is,

An iron made, regular shaped body moves with an initial velocity of “v” on an inclined plane. It reaches to a maximum height of 7 v ²/10 g.What is the geometrical shape of the body?

In the arrangement shown, the block is released from rest from $x=0$ (when the spring was in its natural length), on a rough incline surface having $\mu =0.5x.$ The maximum elongation in the spring will be,

A body of mass $m$ rests on a horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between the body and surface will be

A battery is connected to a potentiometer and the balance point is obtained at $84\text{cm}$ along the wire. When its terminals are connected by a $5\Omega$ resistor, the balance point changes to $70\text{cm}$.



$\left(i\right)$ Calculate the internal resistance of the cell.



​​​​​​​$[$1 Mark$]$

A rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased then the stress force developed in it is proportional to

An ideal heat engine exhausting heat at ${42}^{\circ }C$ is to have 25% efficiency. It must take heat at

What is

i) dimension less constant and dimension less variable.

ii)dimension full constant and dimension full variable.

Explain with example .

What is the difference between all these four?

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction, the magnitude of the minimum additional force needed is

1. 3850.51

A projectile's launch speed is 2 times its speed at maximum height. Find launch angle ${\theta }_0$.

A disc of mass $m$ and radius $R$ is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass $m/2$ each, are placed in it on either side of the centre of the disc as shown in the figure. The disc is given an initial angular velocity ${\omega }_0$ and released.



The angular speed of the disc when the balls reach the end of the disc is

1. 500

Three particles are projected vertically upward from a point on the surface of the earth with velocities $\sqrt{2gR/3}$, $\sqrt{gR}$, $\sqrt{4gR/3}$ respectively where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the surface of the earth. The maximum heights attained are respectively $h_1,h_2,h_3$​.

Two vectors have magnitudes $3$ units and $6$ units respectively. What should be the angle between these two vectors if the resultant vector is perpendicular to the smaller one?

Find the molar specific heat (in $\text{J mol}{}^{-1}\text{K}{}^{-1}$) for a process where $P=\frac{a}{T}$, for one mole of a monatomic gas, ${}^{\prime }{a}^{\prime }$ being constant.

A biconvex thick lens is constructed with glass $(\mu =1.50)$. Each of the surfaces has a radius of 10 cm and the thickness at the middle is 5 cm. Locate the image of an object placed far away from the lens.

A block of mass $1.9\text{kg}$ is at rest at the edge of a table, of height $1\text{m}$. A bullet of mass $0.1\text{kg}$ collides with the block and sticks to it. If the velocity of the bullet is $20{\text{ms}}^{-1}$ in the horizontal direction just before the collision then the kinetic energy, just before the combined system strikes the floor, is [Take $g=10{\text{ms}}^{-2}$]. Assume there is no rotational motion and losses of energy after the collision is negligible.

A thin rod $\text{MN}$, free to rotate in the vertical plane about the fixed end $\text{N}$, is held in a horizontal position. If the rod is released from this position, speed of end $\text{M}$ when the rod makes an angle $\alpha$ with the horizontal will be proportional to

The work function of sodium is 2.46eV and its threshold wavelength is $5040A^{\circ }$. Then the value of universal plank’s constant is (given $c=3\times {10}^{8}m/s$ )

An electron gun ‘G’ emits electrons of energy 2 keV travelling in the positive X direction. The electrons are required to hit the spot ‘S’ where GS = 0.1 m and the line GS makes an angle of ${60}^{\circ }$ with the x-axis. A uniform magnetic field ‘B’ parallel to GS exists in the region outside the gun. The minimum value of B needed to make the electron hit ‘S’ is

The magnitude of x & y components of vector( A) are 7 & 6 respectively. Also the magnitude of x &y components of vector(A+B) are 11 & 9 respectively. The magnitude of vector (B) is?

A ball is thrown vertically upwards. Which of the given graphs are correct? v, h and t represent velocity, height from ground, and time respectively.

Average power in an A.C circuit is 50 watt. Resistance of circuit is $32\Omega$, and source voltage is 50V. Power factor of this circuit is

A container holds $50.0mL$ of nitrogen at $25°C$ and a pressure of $736mmHg$. What will be its volume if the temperature increases by $35°C$ and pressure remains constant ?