Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below:

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is : [Given \(e^{-2}=0.135\)]

Evaluate \(: 3^{15} \bmod (7)\)

The distance between the y-axis and the point (1, 2, 3) is:

\(g(x)=\left\{\begin{array}{ll}\frac{\alpha x}{|x|}, & x<0 \\ 5, & x \geq 0\end{array}\right.\) is continuous at \(x=0\), then the value of \(\alpha\) is

If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then

A die is thrown again and again until three sixes are obtained. The probability of obtaining third six in sixth throw of the die is:

If \(R\) be a relation on the set of integers \(Z\), given by \(R=\{(a, b):(a-b)\) is a multiple of 3\(\}\), then \(R\) is :

In an intrinsic semiconductor at room temperature ;

The adaptive radiation is represented by which of the following?
(A) Darwin's finches
(B) Koala and Wombat
(C) Tiger cat and Sugar glider
(D) Spotted cuscus and lemur
(E) Anteater and Numbat
Choose the correct answer from the options given below :

The magnetic flux through a coil of resistance \( 6 \text{ } \Omega \), perpendicular to its plane, is varying according to \( \phi = 6t^3 + 5t^2 + 4t - 6 \text{ Wb} \). What will be the induced current through the coil at \( t = 2 \text{ s} \)?

For n-type semiconductor, which of the following statements is true?

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
The process of breaking down of detritus into smaller particles is called: