The correct truth table for the following logic circuit is _______.

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to gas is different from change in its internal energy.
C. The volume of the gas is increased.
D. The internal energy of the gas is increased.
E. The process is isochoric (constant volume process)
Choose the correct answer from the options given below:

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height \(h\) is \(....\,S.\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :


Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities \(v_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}\). If we wait sufficiently long for elastic collision to happen, then \(v_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}\), \(v_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s}\) will be the final velocities.

Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below :

Identify the correct truth table of the given logical circuit.

The resistance \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\) where \(\mathrm{V}=(200 \pm 5) \mathrm{V}\) and \(I=(20 \pm 0.2) A\), the percentage error in the measurement of \(R\) is _______.

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

Let \( A=\{-2,-1,0,1,2,3,4\} \). Let R be a relation on A defined by xRy if and only if \( 2x+y \le 2 \). Let \(l\) be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \( l+m+n \) is equal to:

If \(b _{ n }=\int \limits_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} nx }{\sin x } dx , n \in N\), then

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area \(A\). Then \(A ^{4}\) is equal to ............

Surface of certain metal is first illuminated with light of wavelength \({\lambda _1} = 350\,nm\) and then, the light of wavelength \({\lambda _2} = 540\,nm\). It is found that the maximum speed of the photo electrons in the two cases differ by a factor of \(2\). The work function of the metal (in \(eV\)) is close to: (Energy of photon \( = \frac{{1240}}{{\lambda {\rm{(in\, nm)}}}}\,eV\))

The foot of the perpendicular drawn from the origin, on the line, \(3x + y = \lambda \,\left( {\lambda  \ne 0} \right)\) is \(P\). If the line meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\), then the ratio \(BP : PA\) is

Let \(\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) If \(8 x^{2}+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to: