Five current carrying conductors meet at a point $\mathrm{P}$. What is the magnitude and direction of the current in the fifth conductor?

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

Along the \(x\)-axis, three charges \(\frac{q}{2},-q\) and \(\frac{q}{2}\) are placed at \(x=0, x=a\) and \(x=2 a\) respectively. The resultant electric potential at a point \(P\) located at a distance \(r\) from the charge \(-q(a < r)\) is \(\left(\varepsilon_0\right.\) is the permittivity of free space)

If the frequency of a wave is increased by \(25 \%\), then the change in its wavelength is (medium not changed)

Two charges \(+q\) and \(-q\) are kept apart. Then at any point on the right bisector of line joining the two charges

Block \(A\) of mass \(100 \mathrm{~kg}\) is kept above another block \(B\) of mass \(300 \mathrm{~kg}\). \(A\) is tied to the wall \(C\) with a horizontal string. The coefficient of friction between \(A\) and \(B\) is 0.35 and that between \(B\) and the horizontal surface is 0.5 . Find the horizontal force \(p\), necessary to move the block \(B\).

Work done to increase the temperature of one mole of an ideal gas by \(30^{\circ} \mathrm{C}\), if it is expanding under the condition \(V \propto T^{2 / 3}\) is, \((R=8.314 \mathrm{~J} / \mathrm{mol} / \mathrm{K})\)

Given below is the distribution of a random variable \(X\)
\(\begin{array}{ccccc}\mathbf{X}=\mathbf{x} & 1 & 2 & 3 & 4 \\ \mathbf{P}(\mathbf{X}=\mathbf{x}) & \lambda & 2 \lambda & 3 \lambda & 4 \lambda\end{array}\)
If \(\alpha=\mathrm{P}(X < 3)\) and \(\beta=\mathrm{P}(X>2)\), then \(\alpha: \beta=\)

If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{k}}\), then
\(\frac{[(\mathbf{b} \times \mathbf{c}) \times(\mathbf{c} \times \mathbf{a})(\mathbf{c} \times \mathbf{a}) \times(\mathbf{a} \times \mathbf{b})(\mathbf{a} \times \mathbf{b}) \times(\mathbf{b} \times \mathbf{c})]}{[\mathbf{b}+\mathbf{c} \mathbf{c}+\mathbf{a} \mathbf{a}+\mathbf{b}][\mathbf{b} \times \mathbf{c} \times \mathbf{a} \mathbf{a} \times \mathbf{b}]}\)

The osmotic pressure of sea water is 1.05 atm . Four experiments were carried as shown in table. In which of the following experiments, pure water can be obtained in part-II of vessel.

If \(a>0, \lim _{x \rightarrow a} \frac{a^x-x^a}{x^x-a^a}=-1\), then \(a\) is equal to

100 mL of \(\frac{M}{10} \mathrm{Ca}\left(\mathrm{NO}_3\right)_2\) and 200 mL of \(\frac{M}{10} \mathrm{KNO}_3\) solutions are mixed. What is the normality of resulted solution with respect to \(\mathrm{NO}_3^{-}\)?

\(a, b, c\) are the sides of a scalene triangle \(A B C\). If angles \(\alpha, \beta, \gamma\) lie between 0 and \(\pi\) such that \(\cos \alpha=\frac{a}{b+c}, \cos \beta=\frac{b}{c+a}\) and \(\cos \gamma=\frac{c}{a+b}\), then \(\tan ^2 \frac{\alpha}{2}+\tan ^2 \frac{\beta}{2}+\tan ^2 \frac{\gamma}{2}=\)