If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below:

Given \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 4\end{array}\right]\), If \(A=B\), then \(x\) and \(y\) are :

Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\).
Which of the following is true?

If \(\left[\begin{array}{cc}a b & c d \\ a+c & b+d\end{array}\right]=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]\) where \(a, b, c, d\) are integers, then which of the following are true?
(A) \(a+d=0\)
(B) \(b+d=3\)
(C) \(b+d=1\)
(D) \(c+d=2\)
Choose the correct answer from the options given below :

A man rows downstream 30 km and upstream 20 km. If he takes 5 hours to cover each distance, then the speed of stream is

Let \(X\) denote the number of tails in two tosses of a coin. If the mean and the variance of \(X\) are \(\mu\) and \(\sigma^2\) respectively, then \(\mu+\sigma^2\) is equal to:

The function \(f(x)=x^3\), is increasing for:

\(\int \frac{\sin 2 x d x}{\sqrt{9-\cos ^4 x}}\) equals

In a college, 30 % students fail in Physics, 25 % fail in Mathematics and 10 % fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is

Read the passage and answer the question given below.
When a host is exposed to antigens, which may be in the form of living or dead microbes or other proteins, antibodies are produced in the host body. This type of immunity is called active immunity. Active immunity is slow and takes time to give its full effective response. Injecting the microbes deliberately during immunisation or infectious organisms gaining access into body during natural infection induce active immunity. When antibodies are directly given to protect the body against foreign agents, it is called passive immunity.
Match List I with List II

LIST I	LIST II
A. Physical Barrier	I. Saliva
B. Cellular Barrier	II. Interferons
C. Physiological Barrier	III. Skin
D. Cytokine Barrier	IV. Polymorpho-nuclear leukocytes

Choose the correct answer from the options given below:

Central Limit Theorem implies that as the size of the sample increases, the distribution approaches:

The Convention on Biological Diversity held in Rio de Janeiro in 1992 is popularly known as

Which of the following statements is not correct?