Water of mass 5 kg in a closed vessel is at a temperature of \(20^{\circ} \mathrm{C}\). If the temperature of the water when heated for a time of 10 minutes becomes \(30^{\circ} \mathrm{C}\), then the increase in the internal energy of the water is
(Specific heat capacity of water \(=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) )

A material has Poisson's ratio 0.50 . If a uniform rod made of this material suffers a longitudinal strain of \(2 \times 10^{-3}\), then the percentage change in volume is

The expressions below give current \(I\) through an electronic component as a function of applied potential \(V . I_0\) and \(V_0\) are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?
(A) \(I=I_0\left(e^{\frac{2 V}{V_0}}+1\right)\)
(B) \(I=I_0\left(e^{\frac{v}{2 V_0}}-1\right)\)
(C) \(I=I_0 V_0\left(e^{\frac{V}{V_0}}-1\right)\)
(D) \(I=I_0\left(\frac{V}{V_0}\right)\left(e^{\frac{V}{V_0}}-1\right)\)

Two slabs \(A\) and \(B\) of different materials but of the same thickness are joined end to end to form a composite slab. The thermal conductivities of \(A\) and \(B\) are \(k_1\) and \(k_2\) respectively. A steady temperature difference of \(12^{\circ} \mathrm{C}\) is maintained across the composite slab. If \(k_1=\frac{k_2}{2}\), the temperature difference across slab \(A\) is

A block of mass 5 kg is placed on a rough horizontal surface having coefficient of friction 0.5 . If a horizontal force of 60 N is acting on it, then the acceleration of the block is (Acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\) ).

Ionosphere acts as a reflector for the frequency range of

A stone thrown with velocity ' \(u\) ' at angles ' \(\theta^{\prime}\) and \(\left(90^{\circ}-\theta\right)\) with the horizontal reaches to maximum heights \(\mathrm{H}_1\) and \(\mathrm{H}_2\) respectively. Its horizontal range is

If \(\bar{i}+\bar{j}-\bar{k},-\bar{i}+2 \bar{j}+\bar{k}, \bar{j}+2 \bar{k}, 2 \bar{i}-\bar{j}+2 \bar{k}\) are the position vectors of four points \(A, B, C, D\) respectively, then the shortest distance between the lines \(A B\) and \(C D\) is

Match the following lists.
\begin{array}{|c|c|c|c|}
\hline & List I & & List II \\
\hline A & \begin{array}{l}\text { Zeroth law of } \\
\text { thermodynamics }\end{array} & 1 & \begin{array}{l}\text { Direction of flow of } \\
\text { heat }\end{array} \\
\hline B & \begin{array}{l}\text { First law of } \\
\text { thermodynamics }\end{array} & \| & Work done is zero \\
\hline\underline{\mathrm{C}} & Free expansion of a gas & III & Thermal equilibrium \\
\hline D & \begin{array}{l}\text { Second law of } \\
\text { Thermodynamics }\end{array} & IV & \begin{array}{l}\text { Law of conservation } \\
\text { of energy }\end{array} \\
\hline
\end{array}
The correct answer is
\(\begin{array}{lccccccccc} & \text { A } & \text { B } & \text { C } & \text { D } \end{array}\)

5 boys and 6 girls are arranged in all possible ways. Let X denote the number of linear arrangements in which no two boys sit together and \(Y\) denote the number of linear arrangements in which no two girls sit together. If \(Z\) denote the number of ways of arranging all of them around a circular table such that no two boys sit together, then \(X: Y: Z=\)

A capillary tube of radius ' \(r\) ' is immersed in water and water rises to a height of ' \(h\) '. Mass of water in the capillary tube is \(5 \times 10^{-3} \mathrm{~kg}\). The same capillary tube is now immersed in a liquid whose surface tension is \(\sqrt{2}\) times the surface tension of water. The angle of contact between the capillary tube and this liquid is \(45^{\circ}\). The mass of liquid which rises into the capillary tube now is, (in \(\mathrm{kg}\) )

If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x)=\frac{x^6}{x^6+2020}\), \(\forall x \in \mathbf{R}\), then the range of \(f\) is .......

The product of the perpendicular distances drawn from the points \((3,0)\) and \((-3,0)\) to the tangent of the ellipse \(\frac{x^2}{36}+\frac{y^2}{27}=1\) at \(\left(3, \frac{9}{2}\right)\) is