Match List - I with List - II

List - I	List - II
(A) \(\int_{-\pi / 2}^{\pi / 2} \sin ^5 x d x\)	(I) \(\pi\)
(B) \(\int_{-\pi / 2}^{\pi / 2}\left(x^3+\tan ^3 x+1\right) d x\)	(II) \(\frac{\pi}{12}\)
(C) \(\int_0^{\pi / 2} \frac{\cos ^5 x}{\cos ^5 x+\sin ^5 x} d x\)	(III) \(\frac{\pi}{4}\)
(D) \(\int_1^{\sqrt{3}} \frac{d x}{1+x^2}\)	(IV) 0

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}4 & 3 \\ 2 & -1 \\ 1 & 0\end{array}\right]\) and \(B^T=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 1 & -1\end{array}\right]\), then \(A-B\) is equal to

If \(\frac{3 x-5}{6}+8 \geq 4+\frac{2 x}{3}\), then

The function \(f(x)=x^3-3 x\) is :

If a random variable \(X\) has the following probability distribution :

X	0	1	2	3
P(X)	K	\(\frac{K}{2}\)	\(\frac{K}{4}\)	\(\frac{K}{8}\)

then,
Match List-I with List-II

List-I	List-II
(A) The value of \(K\) is	(I) \(2 / 15\)
(B) \(P(0<X<2)\) is	(II) \(1 / 15\)
(C) \(P(1<X<3)\) is	(III) \(8 / 15\)
(D) \(P(X>2)\) is	(IV) \(4 / 15\)

Choose the correct answer from the options given below :

The cost of type 1 rice is Rs. 20 per kg and type 2 rice is Rs. 30 per kg. If both Type 1 and Type 2 are mixed in the ratio \(2: 3\), then the price per kg of the mixed variety is

Let \(A=\left[a_{i j}\right]_{3 \times 3}\) be a matrix, defined by \(a_{i j}=\left\{\begin{array}{ll}2 i+3 j & , i < j \\ 6 & , i=j \\ 3 i-2 j & , i > j\end{array}\right.\). The number of elements in A. which are greater than 6, is

If matrices \(A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\), then \(B A\) is equal to:

Identify the hormone releasing IUDs -

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
Which of the following compounds will undergo nucleophilic addition readily?

Arrange the given steps involved in Polymerase Chain Reaction.
(A) Annealing
(B) Extension
(C) Denaturation
(D) Amplification
Choose the correct answer from the options given below:

What is the structural formula for Freon-12.

An electron (mass \(9 \times 10^{-31} \text{ kg}\) and charge \(1.6 \times 10^{-19} \text{ C}\)) moving with a speed of \(5.0 \times 10^7 \text{ m/s}\) enters a region of uniform magnetic field of strength 0.04 T which is perpendicular to its velocity. The radius of the circular path it follows is: