An inclined plane making an angle of \(30^{\circ}\) with the horizontal is placed in a uniform horizontal electric field \(200 \, \frac{ N }{ C }\) as shown in the figure. A body of mass \(1\, kg\) and charge \(5\, mC\) is allowed to slide down from rest at a height of \(1\, m\). If the coefficient of friction is \(0.2,\) find the time (in \(s\) )taken by the body to reach the bottom. \(\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.\); \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)

A block of mass \(M\) slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is \(\theta\). The magnitude of the contact force will be.

A particle starts from the origin at time \(t = 0\) and moves along the positive \(x-\) axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(t = 5\,s\) ?.........\(m\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

Which one of the following forces cannot be expressed in terms of potential energy?

A block of mass \(M\) placed inside a box descends vertically with acceleration \('a'\). The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of \('a'\) will be .............

In an \(LC\) oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes \(x\) times its initial resonant frequency \(\omega_0\). The value of \(x\) is:

Let \(P(4, -4)\) and \(Q(9, 6)\) be two points on the parabola, \(y^2 = 4x\) and let \(X\) be any point on the arc \(POQ\) of this parabola, where \(O\) is the vertex of this parabola, such that the area of \(\Delta PXQ\) is maximum. Then this maximum Area (in sq. units) is

If the minimum value of \(f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0\), is 14 , then the value of \(\alpha\) is equal to.

If \(m\) is a non-zero number and \(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c\) , then \(f(x)\) is

For three events \(A,B \) and \(C\)  ,\(P (\) Exactly one of \(A\) or \(B\) occurs\()\, =\, P (\) Exactly one of \(C\) or \(A\) occurs \() =\) \(\frac{1}{4}\) and \(P (\) All the three events occur simultaneously \() =\) \(\frac{1}{16}\) Then the probability that at least one of the events occurs is :

In a bombing attack, there is \(50 \%\) chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least \(99 \%\) chance of completely destroying the target, is