If A is a 3 × 3 square matrix such that |A| = 2, then |3 adj A| is

The shortest distance between lines \(\frac{-x-3}{4}=\frac{y-6}{3}=\frac{z}{2}\) and \(\frac{-x-2}{4}=\frac{y}{1}=\frac{z-7}{1}\) is :

Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is :

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

Which of the following differential equation represents the family of circles touching the \(x\)-axis at the origin?

In a linear programming problem, the constraints on the decision variables \(x\) and \(y\) are \(x-3 y \geq 0, y \geq 0,0 \leq x\) \(\leq 3\). The feasible region :

The inverse of the matrix \(A=\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8}\end{array}\right]\) is

If the random variable \(X\) is normally distributed with mean 16 and standard deviation 4,
then the standard normal variable \(Z\) corresponding to \(X=17\) is

Read the passage carefully and answer the questions:
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their
molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, are

The separation between the plates of a charged parallel plate capacitor is increased. Which of the following quantities will change?
(A) charge on the capacitor plates
(B) potential difference across the capacitor
(C) energy of the capacitor
(D) energy density between the plates of the capacitor
Choose the correct answer from the options given below:

In the following sequence of reactions :
CH3–CH(NH2) - CH3 $\xrightarrow{HNO_2}$[A] $\xrightarrow{Oxidation}$[B] $\xrightarrow{H^{+}/H_{2}O}$ CH3MgBr
[C] The compound [C] is :

Factors, on which the capacitance of a parallel plate capacitor depends, are
(A) Charge on the plates
(B) Area of plates
(C) Permittivity of the medium between the plates
(D) Distance between the plates
Choose the correct answer from the options given below:

Which of the following equations represents the Ampere-Maxwell law?