In a region of uniform electric field of intensity \(E\), an electron of mass \(m_e\) is released from rest. The distance travelled by the electron in a time \(t\) is

A particle is projected at an angle of \(60^{\circ}\) with the horizontal from the ground with a velocity \(10 \sqrt{3} \mathrm{~ms}^{-1}\). The angle between velocity vector after \(2 \mathrm{~s}\) and initial velocity vector is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)

A battery of emf \(10 \mathrm{~V}\) is connected to a uniform wire \(A B\) of \(1 \mathrm{~m}\) length and having a resistance of \(10 \Omega\) in series with a \(10 \Omega\) resistor as shown in the figure. Two cells of emf \(2 \mathrm{~V}\) and \(3 \mathrm{~V}\) having internal resistance \(2 \Omega\) and \(3 \Omega\), respectively are connected as shown in the figure. If the galvanometer shows null deflection at point \(J\) on the wire, then the distance of point \(J\) from the point \(B\) is.

A glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over, if the coefficient of linear expansion of glass is ${\alpha }_g$ and coefficient of volume expansion of the liquid is ${\gamma }_L$

Assertion(A) In an elastic collision of two billiard balls, the total KE is conserved during the short time of collision of the balls
(i.e., when they are in contact).Reason(R) Energy spent against friction does not follow the law of conservation of energy.
Codes

Match the following List-I with the List-II
\begin{array}{|c|c|c|}
\hline List - I & & List - II \\
\hline A)Gauss's law & I) & Surface charge density \\
\hlineB) Faraday's law & II) & Electric charge and energy conservation \\
\hline C)Ampere's law & III) & Change in magnetic flux \\
\hline D) Kirchhoff's law & IV) & Change in electric flux \\
\hline & V) & Total electric flux \\
\hline
\end{array}
The correct answer

A body of mass \(m_1=4 \mathrm{~kg}\) moves at \(5 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\) and another body of mass \(m_2=2 \mathrm{~kg}\) moves at \(10 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\). The kinetic energy of centre of mass is

Out of molar entropy (I), specific volume (II), heat capacity (III) and volume (IV), extensive properties are

\(V\) is the set of points on the curve \(y^3-3 x y+2=0\) where the tangent is vertical then \(\mathrm{V}=\)

If Rolle's theorem is applicable for the function \(f(x)=x(x+3) e^{-\frac{x}{2}}\) on \([-3,0]\). then the value of \(c\) is

If the length of an antenna is \(150 \mathrm{~cm}\), the transmission frequency is ____ \(\mathrm{MHz}\). (Speed of light in vacuum \(=3 \times 10^8 \mathrm{~ms}^{-1}\))

If the axes are rotated through an angle \(45^{\circ}\), then the co-ordinates of the point \((4 \sqrt{2},-6 \sqrt{2})\) in the new system are ____

If \(E_1\) and \(E_2\) are two events of a random experiment such that \(P\left(E_1\right)=\frac{1}{8}, P\left(E_1 \mid E_2\right)=\frac{1}{3}\), \(P\left(E_2 \mid E_1\right)=\frac{1}{4}\), then match the items of List-I with the items of List-II.
\(\begin{array}{lllc}
\hline & \text { List-I } & & \text { List-II } \\
\hline \text { (A) } & P\left(E_2\right) & \text { I. } & \frac{3}{16} \\
\hline \text { (B) } & P\left(E_1 \cup E_2\right) & \text { II. } & \frac{3}{29} \\
\hline \text { (C) } & P\left(\bar{E}_1 \mid \bar{E}_2\right) & \text { III. } & \frac{3}{32} \\
\hline \text { (D) } & P\left(E_1 \mid \bar{E}_2\right) & \text { IV. } & \frac{26}{29} \\
\hline & & \text { V. } & \frac{13}{32} \\
\hline
\end{array}\)
The correct match is