The projectile motion of a particle of mass \(5\, g\) is shown in the figure. The initial velocity of the particle is \(5 \sqrt{2}\, ms ^{-1}\) and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points \(A\) and \(B\) is \(x \times 10^{-2}\, kgms ^{-1} .\) The value of \(x ,\) to the nearest integer, is ...... .

The magnetic field of a plane electromagnetic wave is given by \(\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T\) The amplitude of the electric field would be.

A long solenoid is formed by winding \(70\) turns \(cm ^{-1}\). If \(2.0\,A\) current flows, then the magnetic field produced inside the solenoid is \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______.

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity \(B\), the magnetic field \(B_s\) inside the superconductor will be such that

A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius \(\mathrm{R} / 2\) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

Three identical coils \(C _1, C _2\) and \(C _3\) are closely placed such that they share a common axis.\(C _2\) is exactly midway.\(C _1\) carries current I in anti-clockwise direction while \(C _3\) carries current I in clockwise direction. An induced current flows through \(C _2\), will be in clockwise direction when

A body of mass \(M\) thrown horizontally with velocity \(v\) from the top of the tower of height \(\mathrm{H}\) touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{M}\) thrown at a velocity \(\frac{v}{2}\) from the top of the tower of height \(4 \mathrm{H}\) will touch the ground at a distance of _______.

Let \(I(x)=\int \frac{(x+1)}{x\left(1+x e^x\right)^2} d x, x > 0\), If \(\lim _{x \rightarrow \infty} I(x)=0\), then \(I(1)\) is equal to

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature \(50^{\circ} C\). The gas is now heated to double its temperature. The modified pressure is _________ Pa .

A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to: