A particle executes simple harmonic motion between \(x =- A\) and \(x =+ A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is \(2 s\); then time taken by particle in going from \(x =\frac{ A }{2}\) to \(A\) is \(.........\,s\)

A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)

A beam of protons with speed \(4 \times 10^{5}\, ms ^{-1}\) enters a uniform magnetic field of \(0.3\, T\) at an angle of \(60^{\circ}\) to the magnetic field. The pitch of the resulting helical path of protons is close to....\(cm\) (Mass of the proton \(=1.67 \times 10^{-27}\, kg\), charge of the proton \(=1.69 \times 10^{-19}\,C\))

If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be

A current \(i\) is flowing in a straight conductor of length \(L.\) The magnetic induction at a point on its axis at a distance \(\frac {L}{4}\) from its centre will be

A boy thrown a ball into air at \(45^{\circ}\) from the horizontal to land it on a roof of a building of height H . If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is _________ m .
\(\left( g =10 m / s ^2\right)\)

Two identical conducting spheres \(A\)  and \(B,\)  carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is \(F\) . A third identical conducting sphere, \(C,\)  is uncharged. Sphere \(C\)  is first touched to \(A,\) then to \(B,\)  and then removed. As a result, the force between \(A\)  and \(B\)  would be equal to

In the given circuit all resistances are of value \(R\,ohm\) each. The equivalent resistance between \(A\) and \(B\) is 

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is __________ cm.

An electron is moving along the positive \(x\)-axis. If the uniform magnetic field is applied parallel to the negative \(z\)-axis. then \(A.\) The electron will experience magnetic force along positive \(y\)-axis \(B.\) The electron will experience magnetic force along negative \(y\)-axis \(C.\) The electron will not experience any force in magnetic field \(D.\) The electron will continue to move along the positive \(x\)-axis \(E.\) The electron will move along circular path in magnetic field Choose the correct answer from the options given below:

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into \(a\) square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

A proton and an \(\alpha\) -particle, having kinetic energies \(K _{ p }\) and \(K _{\alpha},\) respectively, enter into \(a\) magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \(\alpha\) -particle is \(2: 1 .\) The ratio of \(K _{ p }: K _{\alpha}\) is :

A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is