The matrix \(A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 3 \end{bmatrix}\) then \(A^{-1}\) is equal to:

The angle between the pair of straight lines given by \(\vec{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is :

If \(y=3 e^{2 x}+2 e^{3 x}\), then \(\frac{d^2 y}{d x^2}+6 y\) is equal to:

Let \(P=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix and let \(Q=\left[b_{i j}\right]\) where \(b_{i j}=2^{i+j} a_{i j}, \forall 1 \leq i, j \leq 3\). If the determinant of \(P\) is 2 , then the determinant of \(Q\) is:

The sum of order and degree of the differential equation \(\left(x^2 \frac{d^2 y}{d x^2}\right)^{\frac{3}{4}}=5\left(\frac{d y}{d x}\right)^2-3\) is equal to :

Which of the following statements is/are correct?
(A) \(|x|\) is continuous everywhere in its domain.
\((B)|x|\) is differentiable everywhere in its domain.
(C) \([x]\) is continuous at every integral point.
\((D)[x]\) is discontinuous at every integral point.
Choose the correct answer from the options given below :

The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when side is 10 cm is:

When an n-p-n transistor is used as an amplifier, then :

If the wavelength of light in an experiment on photoelectric effect is increased, then
(A) the photoelectric emissions will not take place
(B) the photoelectric emission may or may not take place
(C) the stopping potential will increase.
(D) the stopping potential will decrease
Choose the correct answer from the options given below:

Which of the following two STIs can be transmitted through contaminated surgical equipment and are not completely curable?

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Arrange the following in the increasing order of their \(p K_{ a }\) values :
(A) \(CF _3- COOH\)
(B) \(O _2 N- CH _2- COOH\)
(C) \(NC - CH _2- COOH\)
(D) \(H - COOH\)
Choose the correct answer from the options given below :

Which one of the following will show Tyndall effect ?

Choose the correct statements from the following:
(A) Electromagnetic waves do not follow the principle of superposition.
(B)The variations in the electric field and in the magnetic field of electromagnetic waves, if any, never happen simultaneously.
(C) Electromagnetic waves are produced by accelerated charges
(D) The energy of electromagnetic waves is divided equally into electric and magnetic field vectors.
Choose the correct answer from the options given below: