A light wave is propagating with plane wave fronts of the type \(x+y+z=\) constant. The angle made by the direction of wave propagation with the \(x\)-axis is:

An object of mass 1000 g experiences a time dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N\). The power generated by the force at time \(t\) is :

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment \(1\) is filled with an ideal gas and Compartment \(3\) is filled with a real gas. Compartments \(2\) and \(4\) are vacuum . A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum Statement \(-1\) : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum Statement \(-2\) : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential

Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\)  as the semimajor axis, and  \(ca\) as the semiminor axis. If \(t_1\)  is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then

Which of the following pair of nuclei are isobars of the element?

A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

A particle of charge \(q\) and mass \(m\) is projected from origin with an initial velocity \(\vec{v} = \left(\dfrac{v_0}{\sqrt{2}}\hat{x} + \dfrac{v_0}{\sqrt{2}}\hat{y}\right)\). There exists a uniform magnetic field \(\vec{B} = B_0 \hat{z}\) and a space varying electric field \(\vec{E} = E_0 e^{-\lambda x}\hat{x}\) within the region \(0 \leq x \leq L\). After travelling a distance such that \(x\)-coordinate has changed from \(x=0\) to \(x=L\), the change in the kinetic energy is _______.

During an adiabatic compression, \(830\, J\) of work is done on \(2\, moles\) of a diatomic ideal gas to reduce its volume by \(50\%\). The change in its temperahture is nearly..... \(K\) \((R\, = 8.3\, J\,K^{-1}\, mol^{-1} )\)

Consider a curve \(y=y(x)\) in the first quadrant as shown in the figure. Let the area \(A_{1}\) is twice the area \(A _{2}\). Then the normal to the curve perpendicular to the line \(2 x -12 y =15\) does NOT pass through the point.

A block of mass \(m\) slides down the plane inclined at angle \(30^{\circ}\) with an acceleration \(\frac{ g }{4}\). The value of coefficient of kinetic friction will be :

If the distance of the point \(P(43, \alpha, \beta), \beta<0\), from the line \(\vec{r}=4\hat{i}-\hat{k}+\mu(2\hat{i}+3\hat{k}), \mu\in R\) along a line with direction ratios \(3, -1, 0\) is \(13\sqrt{10}\), then \(\alpha^{2}+\beta^{2}\) is equal to ___ .

Let \([ t ]\) denotes the greatest integer \(\leq t\). Then \(\frac{2}{\pi} \int \limits_{\pi / 6}^{5 \pi / 6}(8[\operatorname{cosec} x]-5[\cot x]) d x\) is equal to

Let \(S={\theta \in\left(0, \frac{\pi}{2}\right): \sum_{m=1}^{9}}\) \(\sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\) Then.