\(\int_{-5 / 2}^{5 / 2}|x| d x\) is equal to :

The relation \(R\) in the set \(A=\{1,2,3\}\) given by \(R=\{(1,2),(2,1)\}\) is :

The integral \(I=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x\) is :

Which of the following is incorrect about the Linear Programming Problem (LPP)?

An urn I contains \(3\) white and \(4\) blue balls, while urn II contains \(5\) white and \(6\) blue balls. One ball is drawn at random from one of the urns and it is found to be white. The probability that it was drawn from urn II is:

If \(x, y\) and \(z\) are non zero real numbers, the inverse of matrix \(A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) is:

For a random variable z, probability distribution P(x) is given by \(P(x)=\frac{k}{6}(3-x), x=0,1,2\) then Match List-I with List-II

List-I	List-II
(A) \(k\) is equal to	(I)\(\frac{1}{2}\)
(B) \(P(x=0)\)	(II) 1
(C) \(P(x<2)\)	(III) \(\frac{1}{6}\)
(D) \(P(1<x \leq 2)\)	(IV) \(\frac{5}{6}\)

Choose the correct answer from the options given below:

Read the paragraph and answer the question.
Broadly, genetic disorders may be grouped into two categories - Mendelian disorders and Chromosomal disorders. Mendelian disorders are mainly determined by alteration or mutation in the single gene. These disorders are transmitted to the offspring on the same lines as we have studied in the principle of inheritance. The trait may also be linked to the sex chromosome as in case of haemophilia. It is evident that this X-linked recessive trait shows transmission from carrier female of male progeny.
What is the probability of having a haemophilic child to a carrier mother and a normal father ?

The parameter to be increased in order to increase the angular magnification of a simple microscope is

Which one of the following is a false fruit?

The \(C-O-H\) bond angle of alcohol is:

Match List - I with List - II

LIST-I (Differential Equations)	LIST-II ( Degree)
(A) \(\left(\frac{d y}{d x}\right)^3+y x=0\)	(I) 2
(B) \(e^{\frac{d y}{d x}}+y^2+y^{\prime \prime}=0\)	(II) 1
(C) \(x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0\)	(III) Not defined
(D) \(\left(y^{\prime \prime}\right)^2+y=0\)	(IV) 3

Choose the correct answer from the options given below :

In class XII, suppose \(5 \% \) of boys and \(0.25\%\) of girls are physically fit for a game.
A fit student is selected at random from this class having same number of boys and girls.
If the probability that the selected student is a girl is \(\frac{m}{n}\), \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to