In a coil of resistance \(100\ \Omega\) , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is......\(Wb\)

A particle of mass \(m\) with an initial velocity \(u\hat i\) collides perfectly elastically with a mass \(3m\) at rest. It moves with a velocity \(v\hat j\) after collision, then, \(v\) is given by

A particle of mass \(\mathrm{m}\) is dropped from a height \(h\) above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2 \mathrm{gh}} .\) If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\) is

A capacitor C is first charged fully with potential difference of \( V_{0} \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In time t, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field \(B_1,\) at its centre when a current \(I\) passes through it.The second wire is bent into a coil with  three identical loops adjacent to each other and produces magnetic field \(B_2\) at the centre of the loops when current \(I/3\) passes through it. The ratio \(B_1 : B_2\) is

An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) )

Identify the correct statements from the following: \((A)\) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. \((B)\) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. \((C)\) Work done by friction on a body sliding down an inclined plane is positive. \((D)\) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero. \((E)\) Work done by the air resistance on an oscillating pendulum in negative. Choose the correct answer from the options given below:

The integral \(\int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x\) is equal to

If \(\alpha\) and \(\beta\) are the roots of the equation, \(7 x^{2}-3 x-2=0,\) then the value of \(\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}\) is equal to

A line is a common tangent to the circle \((x-3)^{2}+y^{2}=9\) and the parabola \(y^{2}=4 x.\) If the two points of contact \(( a , b )\) and \(( c , d )\) are distinct and lie in the first quadrant, then \(2(a+c)\) is equal to ........ .

The electric field intensity produced by the radiation coming from a \(100\, W\) bulb at a distance of \(3\, m\) is \(E\). The electric field intensity produced by the radiation coming from \(60\, W\) at the same distance is \(\sqrt{\frac{x}{5}} E\). Where the value of \(x=......... .\)

An electric bulb rated \(50 \mathrm{~W}-200 \mathrm{~V}\) is connected across a \(100 \mathrm{~V}\) supply. The power dissipation of the bulb is _______.

In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of \(40\,cm\) from \(A\). If a \(10\,\Omega \) resistor is connected in series with \(R_1\), the null point shifts by \(10\,cm\). The resistance that should be connected in parallel with \(\left( {{R_1} + 10} \right)\,\Omega \) such that the null point shifts back to its initial position is .............. \(\Omega\)