The differential equation \(\frac{d y}{d x}+\frac{x}{y}=0\), represents the family of curves:

If \(A\) and \(B\) are matrices of same order, then ( \(A B^{ T }-B A^{ T }\) ) is always:

The domain of \(y = \cos^{-1}(x^2 - 4)\) is:

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

Probability distribution of random variable \(X\) is:

x	\(0\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(X)\)	\[3k\]	\(3k\)	\(2k\)	\(2k^2\)	\(3k^2\)	\(4k^2\)

The value of \(k\) is:

Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is:

The particular solution of the differential equation \(\frac{d y}{d x}=8 y x\) when \(y=1\) at \(x=0\) is:

The composition of starch in amylopectin is

Match List - I with List - II.

List - I	List - II
(A) Kaolinite	(I) \(FeCO _3\)
(B) Siderite	(II) \(ZnCO _3\)
(C) Malachite	(III) \(\left[ Al _2( OH )_4 Si _2 O_5\right]\)
(D) Colamine	(IV) \(CuCO _3 \cdot Cu ( OH )_2\)

Choose the correct answer from the options given below :

Match List-I with List-II

List-I (Function f(x))	List-II (Interval)
(A) \(f(x)=x|x|\)	(I) Decreases on \((0, \infty)\)
(B) \(f(x)=x^2+2 x-5\)	(II) Increases on \((3, \infty)\)
(C) \(f(x)=x^2-6 x+9\)	(III) Decreases on \((-\infty,-1)\)
(D) \(f(x)=-x^2\)	(IV) Increases on \((-\infty, \infty)\)

Choose the correct answer from the options given below:

Which of the following is correct about the compound annual growth rate (CAGR)?

In a p-n junction, the magnitude of the drift current is lower than the magnitude of the diffusion current when the junction is

The current flowing through a wire as a function of time is given as : \( I = 3t^2 + 2t + 5 \). The charge flowing through any cross-section of the wire in first 2 s is :