A curved in a level road has a radius \(75\, m\). The maximum speed of a car turning this curved road can be \(30 \,m / s\) without skidding. If radius of curved road is changed to \(48\, m\) and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........\(m / s\).

A paralle plate capacitor is made up of stair like structure with a palte area \(A\) of each stair and that is connected with a wire of length \(b\), as shown in the figure. The capacitance of the arrangement is \(\frac{ x }{15} \frac{\varepsilon_{0} A }{ b }\). The value of \(x\) is ............

An object is projected in the air with initial velocity \(u\) at an angle \(\theta\). The projectile motion is such that the horizontal range \(R\), is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be \(.......\) degree.

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

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

Two identical thin metal plates has charge \(q _{1}\) and \(q _{2}\) respectively such that \(q _{1}> q _{2}\). The plates were brought close to each other to form a parallel plate capacitor of capacitance \(C\). The potential difference between them is.

In the given figure, the \(emf\) of the cell is \(2.2\, {V}\) and if internal resistance is \(0.6\, \Omega\). Calculate the power dissipated in the whole circuit: (in \(W\))

The typical transfer characteristic of a transistor in \(CE\) configuration is shown in figure. A load resistor of \(2\,k\Omega\) is connected in the collector branch of the circuit used. The input resistance of the transistor is \(0.50\,k \Omega\). The voltage gain of the transistor is.

At a certain place the angle of dip is \(30^{\circ}\) and the horizontal component of earth's magnetic field is \(0.5 G\). The earth's total magnetic field (in \(G\) ), at that certain place, is ................

Binding energy of a certain nucleus is \(18 \times 10^8 J\). How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus?

A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

Three capacitors, each of \(3\,\mu F\), are provided. These cannot be combined to provide the resultant capacitance of.........\(\mu F\)

A logic gate circuit has two inputs \(A\) and \(B\) and output \(Y\). The voltage waveforms of \(A, B\) and \(Y\) are shown below The logic gate circuit is.