If A is a square matrix such that \(A^2=A\), then \(|A|\) equals :

If \(\left|\begin{array}{ccc}1 & \cos \theta & 0 \\ \sin \theta & 1 & \cos \theta \\ \cos \theta & 1 & -\sin \theta\end{array}\right|=A \sin \theta+B \cos \theta+C \sin \theta \cos \theta\) then :

The value of k for which the function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+3 x-10}{x-2} & x \neq 2 \\ k & x=2\end{array}\right.\) is continuous at x = 2 is:

For \(x \in\left(0, \frac{\pi}{2}\right), \int \frac{1}{\sin ^2 x+\sin 2 x} d x\) is equal to

Solution of the differential equation \(y \log _e y d x-x d y=0\) is (Where \(c\) is an arbitrary constant)

A person can row a boat at \(5 km / hr\) in still water. If the speed of water current in a river is \(1 km / hr\), and it takes him \(1\) hour to row to a place and come back, how far off is the place?

If the area of the triangle with vertices A(x, 4), B(-2, 4) and C(2,-6) is 35 sq units, then the values of 2 are:

The differential equation that represents the family of lines parallel to x + y = 2 is:

The proteins secreted by virus infected cells are known as:

Which of the following features are required to facilitate cloning?
(A) Presence of origin of replication (Ori) in the cloning vector
(B) Presence of a selectable marker in the cloning vector
(C) Presence of a single recognition site (preferably) for restriction enzyme in the cloning vector
(D) Presence of more than two promoter regions in the cloning vector
Choose the correct answer from the options given below:

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis.
Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Identify a component of starch from among the following.

Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then \(\left(A^{-1}\right)^T\) equals

The probability of a shooter hitting a target is \(\frac{2}{3}\)
Minimum how many number of times must the shooter fire so that the probability of hitting the target at least once is more than 0.98.