If A is a square matrix such that \(A^2=A\) then which of the following statements are TRUE?
(Where I is an identity matrix of same order as A)
(A) \((I+A)^4=I+15 A\)
(B) \((I+A)^2=I+3 A\)
(C) \((I+A)^6=I+30 A\)
(D) \((I+A)^3=I+7 A\)
Choose the correct answer from the options given below:

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000 ?

For a full wave rectifier, if the input frequency is \(5 0 ~ H z\), the output frequency will be

The integral \(I=\int e^x\left(\frac{x-1}{3 x^2}\right) d x\) is equal to:

If \(f(x)=\left\{\begin{array}{ll}\frac{x^2-9}{x-3}, & x \neq 3 \\ 5, & x=3\end{array}\right.\) then \(f(x):\)

The volume of parallelepiped whose co-terminous edges are given by \(-3 \hat{i}+7 \hat{j}+5 \hat{k},-5 \hat{i}+7 \hat{j}-3 \hat{k}\) and \(7 \hat{i}-5 \hat{j}-3 \hat{k}\) is :

The function \(f(x)=\frac{x-1}{x\left(x^2-1\right)}, x \neq 1, f(1)=1\), is discontinuous at:

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=-\hat{i}+\hat{j}\).
Then a vector \(\vec{c}\) satisfying \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}=8\) is equal to:

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Variable Number of Tandem Repeats are -

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
Identify the statements explaining biopracy
(A) Unauthorised exploitation of bio-resoures of a country
(B) Adequate compensation is given to one country from where bioresource is taken
(C) Exploitation of traditional knowledge to develop modern applications
(D) Equal benefit sharing between developed and developing nations
Choose the correct answer from the options given below:

A cell of emf 1.1 V and internal resistance 0.5 \(\Omega\) is connected to a 0.5 \(\Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

Consider the curve which is represented by the differential equation \(\frac{d y}{d x}=1+x+y+x y\). If it passes through the point \((0,0)\), then which of the following is/are true?
(A) it is a straight line.
(B) it is a parabola.
(C) it also passes through the point \(\left(-1, \frac{1}{\sqrt{e}}-1\right)\)
(D) Its equation is \(x y(x+1)\left(y-\frac{1}{\sqrt{e}}+1\right)=0\)
Choose the correct answer from the options given below :

Identify " \(Y\) " in the following reaction: