If \(A\) is a square matrix, then \(\left(A^T-A\right)\) is-

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=\sin x\) is :

The number of all possible matrices of order 2 × 2 with each entry 0, 1 or 2 are:

If \(\vec{a}\) and \(\vec{b}\) represent the diagonals of a square, then

If \(A\) is a square matrix and \(|A|=4\), then the value of \(\left|A A^{\prime}\right|\) where \(A^{\prime}\) is transpose of \(A\) is:

The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{\frac{2}{3}}=4 \frac{d^3 y}{d x^3}\) respectively are:

If \(A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]\) is such that \(A^2=I\), then:

In a typical microsporangium, the function of tapetum is -

The shortest wavelengths in the hydrogen spectrum, in decreasing order, for spectral series Pfund, Balmer, Brackett, and Lyman are :

Choose the correct answer from the options given below:
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\) is \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{y-3}{-2}\)
B. Equation of line passing through (1, 2, 3) and parallel to the line given by \(\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}\) is \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z+3}{6}\).
C. Equation of line passing through the origin and (5, -2,3) is \(\frac{x}{5}=\frac{y}{-2}=\frac{z}{3}\).
D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is 2(x - 1) + 3(y - 2) - (z - 3) = 0.
E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is 2x + 3y + 4z = 1

Match List-I with List-II

List -I Physical Quantity	List II Dimensional Formula
(A) Capacitance	(I) \( [M L^3 T^{-3} A^{-1}] \)
(B) Electric Flux	(II) \( [M L^2 T^{-3} A^{-1}] \)
(C) Potential	(III) \( [L^{-2} A T] \)
(D) Polarisation	(IV) \( [M^{-1} L^{-2} T^4 A^2] \)

Choose the correct answer from the options given below:

A galvanometer of resistance \(76 \Omega\) gives full scale deflection when only \(5 \%\) of total current passes through it. The value of shunt is :

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then P\((0< x \leq 2\)) is equal to