The ratio of wavelengths of proton and deuteron accelerated by potential \(V_{p}\) and \(V_{d}\) is 1: \(\sqrt{2}\). Then, the ratio of \(V_{p}\) to \(V_{d}\) will be

An electric field, \(\overrightarrow{\mathrm{E}}=\frac{2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^2\) area having unit vector \(\hat{\mathrm{n}}=\left(\frac{2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{6}}\right)\). The electric flux for that surface is _______ \(\mathrm{Vm}\)

A shell is fired from a fixed artillery gun with an initial speed \(u\) such that it hits the target on the ground at a distance \(R\) from it. If \(t_1\) and \(t_2\) are the values of the time taken by it to hit the target in two possible ways, the product \(t_1t_2\) is

In a Young's double slit experiment \(15\) fringes are observed on a small portion of the screen when light of wavelength \(500 \;\mathrm{nm}\) is used. Ten fringes are observed on the same section of the screen when another light source of wavelength \(\lambda\) is used. Then the value of \(\lambda\) is (in \(\mathrm{nm})\)

A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)

A \(0.5\) kg mass is in contact against the inner wall of a cylindrical drum of radius \(4\) m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is \(5\) rad/s. The coefficient of friction between the drum's inner wall surface and mass is _______. (Take \(g = 10\) m/s\(^2\))

A convex lens (of focal length \(20\, cm\)) and a concave mirror, having their principal axes along the same lines, are kept \(80\, cm\) apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of \(30\, cm\) to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be.....\(cm\)

A particle moves along the \(x\)-axis and has its displacement \(x\) varying with time \(t\) according to the equation \(\mathrm{x}=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2\) where \(c_0\) and \(c\) are constants of appropriate dimensions. Then, which of the following statements is correct?

The velocity \((v)\) and time \((t)\) graph of a body in a straight line motion is shown in the figure. The point \(S\) is at \(4.333\) seconds. The total distance covered by the body in \(6 \;s\) is\(.......m\)

Given below are two statements. One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion A :Two identical balls \(A\) and \(B\) thrown with same velocity '\(u\) ' at two different angles with horizontal attained the same range \(R\). If \(A\) and \(B\) reached the maximum height \(h_{1}\) and \(h_{2}\) respectively, then \(R =4 \sqrt{ h _{1} h _{2}}\) Reason R: Product of said heights. \(h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)\) Choose the \(CORRECT\) answer 

Two trains ' \(A\) ' and ' \(B\) ' of length ' \(l\) ' and ' \(4 l\) ' are travelling into a tunnel of length ' \(L\) ' in parallel tracks from opposite directions with velocities \(108\,km / h\) and \(72\,km / h\), respectively. If train '\(A\)' takes \(35\,s\) less time than train ' \(B\) ' to cross the tunnel then, length ' \(L\) ' of tunnel is \(...........\,m\) \(\text { (Given } L=60 l \text { ) }\)

If \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \(\lambda_{1}: \lambda_{2}\) is

An astronaut of mass \(m\) is working on a satellite or biting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_G\) on the astronaut is