List of top Questions asked in MHT CET

A potentiometer wire of \(400\ \text{cm}\) length has a resistance of \(20\ \Omega\). It is connected in series with a resistance of \(15\ \Omega\) and a accumulator of EMF \(6\ \text{V}\) (negligible internal resistance). The potential gradient \(k=\frac{x}{7}\ \text{V/m}\). The value of \(x\) is
A hollow metal sphere of radius \(5\ \text{cm}\) is charged such that the potential on its surface is \(10\ \text{V}\). The electric field at its centre is
A closed loop consists of a \(15\ \text{V}\) battery, a \(5\ \text{V}\) battery (opposing the first), and a \(25\ \Omega\) resistor. The current through the loop is
Two SHM's \(x_{1}=a\sin \left(\omega t+\frac{3\pi }{2}\right)\) and \(x_{2}=a\sin (\omega t+\pi )\) are superimposed on each other. The resultant amplitude of motion is \((\sin \pi /2=1\) and \(\cos \pi /2=0)\)
A uniform electric field is given as \(\vec{E}=4\times 10^{4}\hat{j}\ \text{N/C}\). The flux of this field through a square of side \(10\ \text{cm}\) whose plane is parallel to the Y-Z plane is
A boy stands \(x\ \text{m}\) away from a high wall and claps his hands at a steady rate so that each clap coincides with the echo of the one before. If he makes \(60\) claps in \(2\) minutes and the velocity of sound is \(340\ \text{m/s}\), then the distance \(x\) from the wall is
A tuning fork produces \(6\) beats per second with both, \(60\ \text{cm}\) and \(40\ \text{cm}\) of the stretched wire of sonometer. The frequency of fork is
For the given wave equation \(y=10\,\cos \pi \left(\frac{x}{4}+\frac{t}{2}\right)\), the CORRECT statement is ( where x is in metre and time t is in second.)
A metal sphere cools at a rate of \(2^{\circ }\text{C/min}\) when the temperature is \(80^{\circ }\text{C}\). If the temperature of the surroundings is \(30^{\circ }\text{C}\), then the rate of cooling when its temperature is \(50^{\circ }\text{C}\) will be
Assuming the Sun to be a perfectly spherical black body of radius \(R\) and is at a temperature \(T\ \text{K}\), then the total radiant power incident on the Earth at a distance \(r\) from the sun is ( consider \(R_{o}\) is the radius of the Earth and \(\sigma\) is Stefan's constant).
Identify the INCORRECT statement for isobaric process.
The pressure at the surface of mercury in a barometer tube is \(P_{1}\) and the pressure at the surface of mercury filled in a conical flask is \(P_{2}\). The ratio of \(\frac{P_{1}}{P_{2}}\) is
If the ratio of specific heat of gas \(\gamma =\frac{C_{p}}{C_{v}}\), then the value of \(C_{p}\) in terms of \(\gamma\) and gas constant \(R\) is
Let \(\eta _{1}\) be the efficiency of a Carnot engine at \(T_{H}=547^{\circ }\text{C}\) and \(T_{C}=247^{\circ }\text{C}\) while \(\eta _{2}\) is the efficiency at \(T_{H}=847^{\circ }\text{C}\) and \(T_{C}=147^{\circ }\text{C}\). If \(\eta _{1}=\frac{x}{41}\eta _{2}\), the value of \(x\) is
Two small balls of same density \(\sigma\) and radii \(r\) and \(\frac{r}{3}\) are dropped into two different tubes of length \(L\), filled with liquids of densities \(\frac{\sigma }{2}\) and \(\frac{\sigma }{3}\) and coefficients of viscosity \(\eta _{1}\) and \(\eta _{2}\) respectively. If both balls reach the bottom of the tubes simultaneously, having moved at their respective terminal velocities, and the ratio \(\frac{\eta _{1}}{\eta _{2}}=\frac{x}{4}\), the value of \(x\) is
The radius of gyration of a thin hollow cylinder of radius \(R\) about a tangential axis passing perpendicular to the plane of the cylinder and parallel to the geometrical axis is
In a capillary tube of radius \(r\), water rises to a height \(10\ \text{cm}\) on Earth. If the apparatus is taken to the Moon \((g_{moon}=g/6)\) and the tube is replaced with one having double the radius \((2r)\), the water will rise to height
The periodic time \(T_{1}\) of a simple pendulum is \(4\ \text{s}\) at a place, at a height \(R\) above the earth's surface. If the pendulum is brought at a height \(\frac{2}{3}R\) above the earth surface, the periodic time decreases by \(xT_{1}\). The value of \(x\) is
A solid disc of radius \(40\ \text{cm}\) and the mass of \(20\ \text{kg}\) is rotating with an angular velocity of \(300\ \text{rpm}\), about an axis passing through its centre of mass and perpendicular to its plane. The magnitude of retarding torque required to bring the disc at rest in \(20\ \text{s}\) is \(x\pi \ \text{Nm}\). The value of \(x\) is
A planet of mass \(m\) moves in an elliptical orbit around the Sun of mass \(M\). Let \(r_{1}\) be the distance at aphelion and \(r_{2}\) be the distance at perihelion. If \(v_{1}\) and \(v_{2}\) are the velocities of the planet at these points, then ratio of kinetic energy at aphelion to kinetic energy at perihelion is
Two cars, P and Q move toward each other, getting \(8\ \text{m}\) closer every second. If they move in the same direction, they get \(0.6\ \text{m}\) closer every second. If car P is faster than car Q then, the ratio of speeds of car P to car Q is
The ratio of the weight of the man in stationary lift and in a lift accelerating upwards with uniform acceleration is \(2:3\). The acceleration of lift is
The heat generated in a circuit is given by \(Q=I^{2}Rt\). If the percentage error in the measurement of \(Q\) is \(1\%\), \(R\) is \(2\%\), and \(t\) is \(1\%\), then the percentage error in the measurement of current \(I\) is
A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the particle is \(\sqrt{ngr}\) when the string makes an angle of \(60^{\circ }\) with the lower vertical. The tension \(T\) in the string at an angle of \(60^{\circ }\) is \(\left(\cos 60^{\circ }=\frac{1}{2}\right)\)
A gas molecule of mass \(m\), moving with velocity \(\vec{v}=a\hat{i}+b\hat{j}+c\hat{k}\) hits a container wall that is parallel to the \(xz\)-plane. Assuming a perfectly elastic collision, what is the change in momentum of the molecule?