In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are \(\dfrac{1}{2}, \dfrac{3}{10}\) and \(\dfrac{1}{5}\) respectively. Each team gets 5 points for win, 3 points for draw and 0 points for loss in a game. After two games, find the probability that Jaipur has more points than Delhi.

If \(x=\frac{1-t}{1+t}, y=\frac{2 t}{1+t}\), then \(\frac{d^{2} y}{d x^{2}}=\)

Area bounded by the curve \(y=x^{3}\), the \(X\)-axis and the ordinates at \(x=-2\) and \(x=1\), is

If \(*\) be a binary operation on a set \(A\) and \(e\) be the identity element w.r.t. *, then \(b \in A\) is said to be inverse of \(a \in A\) w.r.t. * , if

Given the matrices \(A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 1 & 2 \\ 0 & 2 & 1 \end{bmatrix}\), then the minor \(M_{23}\) of the matrix \((A B^{-1})^{-1}\) is:

From a point \(P(a, b, c)\) perpendicular \(P A, P B\) are drawn to \(y z\) and \(z x\) planes. Find the equation of the plane \(O A B\), where \(O\) is the origin.

\(\cos ^6 A-\sin ^6 A \text { is equal to }\)

A voltmeter of resistance \(1000 \Omega .0 .5 \mathrm{~V} /\) div is to be converted into a voltmeter to make it to read \(=1 \mathrm{~V} / \mathrm{div}\). The value of high resistance to be connected in series with it is

\(\lim _{x \rightarrow \dfrac{\pi}{4}} \dfrac{\sec ^2 x-2}{\tan x-1}=\)

Coupling reaction is an example of

Which of the following is always true about a spontaneous cell reaction in a galvanic cell?

The main product obtained when a solution of sodium carbonate reacts with mercuric chloride is

Match the coordination compounds in Column I having the given type of hybridisation of \(\mathrm{M}^{\mathrm{n}+}\) ion and magnetic moment as given in Column II.
\(\begin{array}{|l|l|l|l|} \hline & \text { Coordination compounds. } & & \text { Hybridisation \& Magnetic nature. } \\ \hline \text { A } & \mathrm{Ni}(\mathrm{CO})_4 & \text { P } & \mathrm{sp}^3, \quad \mu=5.92 \mathrm{BM} \\ \hline \text { B } & {\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}} & \text { Q } & \mathrm{sp}^3, \quad \mu=2.84 \mathrm{BM} \\ \hline \text { C } & {\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-}} & \text { R } & \mathrm{sp}^3, \quad \mu=0 \\ \hline \text { D } & {[\mathrm{MnBr}]^{2-}} & \text { S } & \mathrm{dsp}^2, \quad \mu=0 \\ \hline \end{array}\)