The natural frequency of an \(L-C\) circuit is \(1,25,000 \mathrm{cycle} / \mathrm{s}\). Then the capacitor \(C\) is replaced by another capacitor with a dielectric medium of dielectric constant \(K\). In this case, the frequency decreases by \(25 \mathrm{kHz}\). The value of \(K\) is

The ratio of radii of two wires is \(1: 2\) and the density of their materials are in the ratio \(1: 4\). If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is

A spring has a spring constant \(200 \mathrm{Nm}^{-1}\). If it is stretched by \(1 \mathrm{~cm}\) then the potential energy stored in it is

The radii and Young's moduli of two uniform wires \(A\) and \(B\) are in the ratio \(2: 1\) and \(1: 2\) respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire \(A\) is one percent, the percentage increase in length of the wire \(B\) is

The waves having maximum wavelength among the following electromagnetic waves is

When the ideal gas is compressed isothermally, then its pressure

When a sound wave of wavelength \(\lambda\) is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

Suppose a triangle of area 27 sq. units is formed by \(18 x^2-9 x y+y^2=0\) and \(y=c\). Then the centroid of the triangle is

A liquid of mass $250 \mathrm{g}$ is kept warm in a vessel using an electric heater. The liquid is maintained at $57 °\mathrm{C}$ when the power supplied by the heater is $30 \mathrm{W}$ and surrounding temperature is $27 °\mathrm{C}$. As the heater is switched off, it took $10 \mathrm{s}$ time for the temperature of the liquid to fall from $47 °\mathrm{C}$ to $46.9 °\mathrm{C}$. The specific heat capacity of the liquid is

\(\vec{a}=\hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}-2 \hat{k}, \vec{c}=2 \hat{i}-3 \hat{j}-\hat{k}, \vec{d}=2 \hat{i}+\hat{j}+\hat{k}\)
are four vectors then \((\vec{a} \times \vec{c}) \times(\vec{b} \times \vec{d})=\)

The rate constant of a first order reaction is \(3.46 \times 10^{-2} \mathrm{~s}^{-1}\) at 298 K . What is the rate constant of the reaction at 350 K if its activation energy is \(50.1 \mathrm{~kJ} \mathrm{~mol}^{-1} ?(\mathrm{R}=8.314 \mathrm{~J}\) \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )
\((\log 2=0.3010)\)

The bond order of which of the following two species is same?