The area bounded by the y-axis, y = cos x and y = sin x when \(0 \leq x \leq \frac{\pi}{2}\) is :

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{ \imath }-\hat{ \jmath }\) and \(\hat{ \jmath }+\hat{ k }\)	(I) 0
(B) Angle between \(2 \hat{j}-\hat{k}\) and \(\hat{j}+2 \hat{k}\)	(II) \(\frac{2 \pi}{3}\)
(C) Angle between \(\hat{i}+2 \hat{j}\) and \(5 \hat{i}+10 \hat{j}\)	(III) \(\frac{\pi}{6}\)
(D) Angle between \(\sqrt{3} \hat{i}+\hat{j}\) and \(\hat{i}\)	(IV) \(\frac{\pi}{2}\)

Choose the correct answer from the options given below:

A copper ball of density \(8 ~ g / c c\) and \(1 c m\) diameter, immersed in oil of density 0.8 \(g / cc\), remains suspended in an electric field of \(600 \pi V / m\). The charge on the ball is :

If \(A\) is non-singular square matrix of order 3 and \(\left|A^{-1}\right|=24\), then the value of \(|2 A(\operatorname{adj}(3 A))|\), is

For the given five values \(15,24,18,33,42\), the three years moving averages are :

If a \(95 \%\) confidence interval for a population mean was reported to be \(132\) to \(160\) and sample standard deviation \(\sigma=50\), then the size of the sample in the study is:
(Given \(Z_{0.025}=1.96\) ):

If \(\left[\begin{array}{cc}2 & 3 \\ 5 & 7\end{array}\right]\left[\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right]=\left[\begin{array}{cc}-4 & 6 \\ -9 & x\end{array}\right]\), then the value of \(x\) is:

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
The following equation represents the reaction taking place in a Galvanic cell:
Mg(s) + 2Ag\(^+\)(0.001 M) \(\rightarrow\) Mg\(^2+\)(0.01 M) + 2Ag(s)
Calculate its \(E_{\text {cell }}\) at 298 K if \(E_{\text {cell }}^{\circ}=2.91 \mathrm{~V}\).

If A and B are non-singular square matrices of the same order, then \(\left(A B^{-1}\right)^{-1}=\)

If two substances A and B have \(P^o_A: P^o_B = 1 : 2\) and have mole fraction in the ratio \(1:2\), then mole fraction of A in vapours is:

Three charges, +Q, q and +Q are placed with q at mid point of the line joining the other two charges. For the system of charges to be in equilibrium, the value of q is

The correct IUPAC name of the following compound is

The current and voltage in an a. c. circuit are given as
\( I = 50 \sin(50t) \text{ mA} \),
\( V = 100 \sin(50t + \pi/3) \text{ volt} \).
The power dissipated in the circuit is