If \(A = \begin{bmatrix} 1 & 2 & -1 \\ 2 & 3 & 0 \\ 1 & -1 & 2 \end{bmatrix}\), then Adj(A) is:

If A and B are symmetric matrices then \((A B+B A)\) is:

The area of the region bounded by the curve \(y=\sin x\) and the \(x\)-axis between \(x=\pi / 2\) and \(x=3 \pi / 2\) is :

If \(x=\frac{a}{1+t}\) and \(y=\frac{a}{(1+t)^2}\) where \(a>0\), then \(\frac{d^2 y}{d x^2}\) at \(t=1\) is:

The points of discontinuity of the function \(f\) defined by \(f(x)=\begin{cases} x + 2 & x \leq 1 \\x - 2 & 1 < x < 2\text { are: } \\0 & x \geq 2 \end{cases}\)

Two events A and B are dependent if :

If A and B are two matrices of order 2 × 2 such that A is a symmetric matrix and B is a skew-symmetric matrix, then:

If \(A\) and \(B\) are independent events, then
A. not \(A\) and not \(B\) are independent
B. \(A\) and not \(B\) are independent
C. not \(A\) and \(B\) are not independent
D. \(P(A \cup B)=P(A)+P(B)\)
E. \(P(A \cap B)=P(A) P(B)\)
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Equationof Lines)	List-II (Information)
(A) \(\vec{r}=(3 \hat{i}-2 \hat{j}+\hat{k})+\lambda(\hat{j}-2 \hat{k})\)	(I) Direction ratios are \(2,4,-1\)
(B) \(\frac{2-x}{1}=\frac{2 y+1}{4}, z=2\)	(II) Perpendicular to \(2 \hat{i}-\hat{j}+\hat{k}\)
(C) \(\frac{x}{1}=\frac{y-3}{2}=\frac{3-4 z}{2}\)	(III) Passing through the point \((3,-2,1)\)
(D) \(\vec{r}=(3 \hat{i}+2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\)	(IV) Direction ratios are \(-1,2,0\)

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Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Which one of the following enzyme helps to join DNA?

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of the coordinate axes, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is

The following reaction is given :
\[CH_3-CH(Br)-CH(Br)-CH_3 \xrightarrow[\Delta]{2 NaNH_2} A\]
Identify \(A\) from the following:

Arrange the following compounds in increasing order of their reactivity towards HCN .




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