If \(A\) is a square matrix and \(I\) is an identity matrix of same order such that \(A^2=A\), then \((2 I+A)^2-5 A\) is :

\(\int \frac{x}{x^2+x-12} d x\) is equal to

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is:

Let \(\left|\begin{array}{ll}3 & y \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|\) and \(x, y\) are natural numbers, then the number of solutions for the system is :

If \(C_{i j}\) represents the cofactor of element \(a_{i j}\) of the matrix \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5\end{array}\right]\), then the value of \(C_{23}+C_{31}-C_{22}\) is

If \(y=(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\) then \(\frac{d y}{d x}\) at \(x = -1\) is

A man wishes to ensure that he gets Rs. 75,000/- at the end of each year indefinitely. The amount that he invest now to produce the desired cash flow, if money is worth 2.5% compounded annually is:

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following is not a Sexually Transmitted Disease?

Let \(f\) be a function defined by \(f(x)=2 x^3-3 x^2-36 x+2\), then which of the following are correct ?
(A) The critical points of \(f ( x )\) are \(- 2\) and 3 .
(B) The function \(f(x)\) increases in the interval \((3, \infty)\)
(C) The function \(f(x)\) decreases in the interval \((-2,3)\)
(D) The function \(f(x)\) increases in the interval \((-2,3)\)
Choose the correct answer from the options given below :

Let \(\vec{a}\) and \(\vec{b}\) be unit vectors. If \(\sqrt{3} \vec{a}-\vec{b}\) is a unit vector, then the angle between \(\vec{a}\) and \(\vec{b}\) is

Decomposition of \(H _2 O _2\) follows a first order reaction.
In 50 min , the concentration of \(H _2 O _2\) decreases from 0.5 to 0.125 M.
When the concentration of \(H _2 O _2\) reaches 0.05 M.
the rate of formation of \(O _2\) will be (Given \(\log 2=0.3010\) ) :

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?

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 techniques is used to amplify a specific DNA sequence?