For any two matrices A and \(B , AB + BA\) is a possible matrix, then :

Let \(A\) be a matrix such that \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right]\) Then which of the following are TRUE?
(A) \(A\) is a non-singular matrix
(B) \(A^T=A\)
(C) \(A\) is not an invertible matrix
(D) \(A\) is not a skew-symmetric matrix
Choose the correct answer from the options given below :

The least positive integer \(x\) satisfying \(28=x(\bmod 6)\) is :

If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along the co-ordinate axes OX, OY and OZ respectively, then
(A) \(\hat{i} \times \hat{j}=\hat{k}\)
(B) \(\hat{k} \times \hat{i}=-\hat{j}\)
(C) \(\hat{j} \cdot \hat{j}=1\)
(D) \(\hat{j} \cdot \hat{k}=0\)
Choose the \{correct} answer from the options given below:

Resource		Found	Requirement units
	\(I (x kg)\)	\(II (y kg)\)
Calcium (units/kg)	3	2	9
Vitamin (units/kg)	4	1	5
Cost (Rs/kg)	40	60

Formulate the L.P.P. to minimize the cost

It is given that mean and variance of a binomial variate X are 2 and 1 respectively. Find the probability that X takes value greater than or equal to 1.

Area lying between the curves \(y^2=9 x\) and \(y=3 x\) is:

o-Nitrophenol is less soluble in water than p-nitrophenol because :

Which of the following statements are true?
(A) Rheostat can be used both as a variable resistance and a potential divider.
(B) An electrical circuit is functional only if all the components of the circuit are connected in proper order, assuming that all circuit components/ devices are in working condition and key is closed.
(C) An open circuit means a break in some part of a circuit which could be deliberate such as a key in open position or a fault such as broken wire or burnt out component(s) or loose connection.
(D) Rheostat as a potential divider gives variable resistance.
Choose the correct answer from the options given below:

The demand for a certain product is represented by the function \(p=300+25 x-x^2\) (in rupees), where \(x\) is the number of units demanded and \(p\) is the price per unit, then the marginal revenue when 15 units are sold, is

Which of the following compounds will respond to iodoform test?
(A) Acetone
(B) Ethyl methyl ketone
(C) Acetophenone
(D) Pentan-2-one
Choose the correct answer from the options given below:

Which of the following statements is correct for the identification of a diode using a multimeter?

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
The thermostable DNA polymerase is isolated from -