Let \(M_{i j}\) and \(A_{i j}\) denote respectively minors and co-factors of the element in the ith row and jth column of the matrix \(A=\left[\begin{array}{ccc}1 & 2 & -1 \\ 3 & 2 & 3 \\ 4 & -1 & 0\end{array}\right]\). Then
(A) \(M_{32}=6\)
(B) \(M_{23}=9\)
(C) \(A_{32}=-6\)
\((D) A_{23}=-9\)
Choose the correct answer from the options given below :

If \(\vec{a}=3 \hat{i}-6 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are such that \(\vec{a} \| \vec{b}\), then \(3 \lambda+2=\)

Match List-I with List-II

List-I (Differential Equation)	List-II (Order and Degree)
(A) \(\left(\frac{d^2 y}{d x^2}\right)^2-e^x\left(\frac{d y}{d x}\right)^4+1=0\)	(I) order \(=1\) and degree \(=2\)
(B) \(\left(\frac{d y}{d x}\right)^2+x y=0\)	(II) order \(=2\) and degree \(=1\)
(C) \(\left(1+\frac{d y}{d x}\right)^{3 / 2}=4\left(\frac{d^2 y}{d x^2}\right)^2\)	(III) order \(=2\) and degree \(=2\)
(D) \(\sqrt{\frac{d^2 y}{d x^2}}+1=\frac{d y}{d x}\)	(IV) order \(=2\) and degree \(=4\)

Choose the correct answer from the options given below :

The edge of a cube is increasing at a rate of \(7 cm / s\). The rate of change of area of the cube when edge of the cube is 3 cm is :

The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

Match List I with List II

LIST I	LIST II
A. Range of \(\operatorname{cosec}^{-1} x\)	I. \((0, \pi)\)
B. Range of \(\tan ^{-1} x\)	II. \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)
C. Range of \(\sec ^{-1} x\)	III. \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)
D. Range of \(\cot ^{-1} x\)	IV. \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)

The mean of the number of heads in a simultaneous toss of three coins is :

In aldehydes, the carbonyl group is bonded to a carbon and hydrogen, while in ketones it is bonded to two carbon atoms. The carbonyl compounds in which carbonyl group is bonded to oxygen are known as carboxylic acid and their derivatives.
The hybridisation of the \(C\) in the carbonyl group is:

The correct increasing order of basic strength of amine is :
(A) \(\text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3 < \text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\)
(B) \(\text{NH}_3 < \text{C}_6\text{H}_5\text{NH}_2 < \text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\)
(C) \(\text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\)
(D) \(\text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH} < \text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3\)
Choose the correct answer from the options given below :

The probability distribution of a random variable X is

X	0	1	2	3	4
P(X)	0.2	k	k	2k	k

Match List-I with List-II

List-I	List-II
(A) value of \(k\)	(I) \(\frac{16}{25}\)
(B) \(P(x \geq 2)\)	(II) \(\frac{9}{25}\)
(C) \(P(X=3)\)	(III) \(\frac{4}{25}\)
(D) \(P(X<2)\)	(IV) \(\frac{8}{25}\)

Choose the Correct answer from the options given below :

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following is not used as a vector in recombinant DNA technology?

The binding energy per nucleon is 1.1 MeV for \({ }_1^2 H\) and 7.0 MeV for \({ }_2^4 He\). The energy released in the given fusion reaction will be:
\({ }_1^2 H+{ }_1^2 H \rightarrow{ }_2^4 He\)

Which of the following statements are correct about azeotropic mixtures?
A. They have same composition in liquid and vapour phases.
B. They can be separated by fractional distillation.
C. They are formed at a specific composition.E. The azeotrope of ethanol and water is formed by \(8 0 \%\) ethanol and \(2 0 \%\) water.
Choose the correct answer from the options given below: