Consider the LPP: Max \(Z = 5x + 3y\) subject to \(3x + 5y ≤ 15, 5x + 2y ≤ 10 x ≥ 0, y ≥ 0\)
match List - I with List - II

List-I	List-II
(A) Objective function	(I) \(3x + 5y ≥ 15\)
(B) One constraint	(II) \(x, y ≥ 0\)
(C) Non-negative restrictions	(III) \(Z = 5x + 3y\)
(D) Point (1, 2) does not lie in the region	(IV) \(3x + 5y ≤ 15\)

Choose the correct answert from the option given below :

If A and B are two events such that \(P(A) \neq 0\) and \(P(A / B)=1\) then :

Match List I with List II

LIST I	LIST II
A. \(\int \sin x \cos x d x\)	I. \(\log _e\left(1+\sin ^2 x\right)+C\)
B. \(\int \frac{d x}{\sin ^2 x \cos ^2 x}\)	II. \(\tan \frac{x}{2}+C\)
C. \(\int \frac{\sin 2 x}{1+\sin ^2 x} d x\)	III. \(-\frac{1}{4} \cos 2 x+C\)
D. \(\int(1-\cos x)\operatorname{cosec}^2 x d x\)	IV. \(\tan x-\cot x+C\)

Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :

The value of the determinant \(D=\) equation \(\left|\begin{array}{lll}x & a & a+x \\ y & b & b+y \\ z & c & c+z\end{array}\right|\) is:

The value of the determinant \(\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|\) is:

Consider the curve which is represented by the differential equation \(\frac{d y}{d x}=1+x+y+x y\). If it passes through the point \((0,0)\), then which of the following is/are true?
(A) it is a straight line.
(B) it is a parabola.
(C) it also passes through the point \(\left(-1, \frac{1}{\sqrt{e}}-1\right)\)
(D) Its equation is \(x y(x+1)\left(y-\frac{1}{\sqrt{e}}+1\right)=0\)
Choose the correct answer from the options given below :

Which of the following pairs of transition metal ions is the strongest oxidizing agent?

Human protein, a-1-antitrypsin is used for the treatment of-

If A is a matrix of order \(m \times n\) and B is a matrix such that \(A B^T\) and \(B^T A\) are both well-defined matrices, then order of matrix B is

In coordinate compound \([Cr(NH_3)_6][Co(CN)_6]\)
what type of isomerism arises?

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
Process of accumulation of dark coloured amorphous substance is called:

Which one of the following is not associated with the process of transcription in bacteria?