The range of the function \(f(x)=\frac{1}{1-x^2}, x \neq \pm 1\) is :

Consider the following hypothesis test:
\( \begin{array}{l} H_0: \mu \leq 12 \\ H_a: \mu>12 \end{array} \)
A sample of 25 provided a sample mean \(\bar{x}=14\) and a sample standard deviation \(S=4.32\). If \(t_{0.05}=1.711\), then which of the following is correct?
(A) The test statistic is defined as \(t=\frac{\bar{x}-\mu}{S / \sqrt{n}}\).
(B) The value of the test statistic is 1.31 .
(C) At \(\alpha=0.05\), the null hypothesis is rejected.
(D) If the value of the \(t\)-statistic is less than \(t_\alpha\), then null hypothesis is accepted.
Choose the correct answer from the options given below:

A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

Increase in the number of patients in the hospitals due to heat stroke is:

Which of the following are first order linear differential equations?
(A)\(\frac{d x}{d y}+P_1(y) x=Q_1(y): P_1(y)\) and \(Q_1(y)\) are functions of y or constant functions
(B)\(\frac{d y}{d x}+P_2(x) y=Q_2(x): P_2(x)\) and \(Q_2(x)\) are functions of a or constant functions
(C)\((x+y) \frac{d y}{d x}=x-2 y\)
(D)\(\left(1+x^2\right) \frac{d y}{d x}-2 x y=x^2+3\)
Choose the correct answer from the options given below:

Which of the following are correct about the Sinking Fund?
(A) It is a fixed term account.
(B) It is a set-up for a particular upcoming expense.
(C) A fixed amount at regular intervals is deposited in the Sinking Fund.
(D) It can be used in any emergency.
Choose the correct answer from the options given below:

The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) is :

What is the product of nitration of Benzoic acid?

Area of a rectangle having vertices A, B, C, D with position vectors \(-\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) and \(-\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) respectively is:

Let \(E\) and \(F\) be two events such that \(P(E)=\frac{1}{3}, P(F)=\frac{1}{4}\) and \(P(E \cap F)=\frac{1}{5}\).
Then the value of \(P(F \mid E)\) is equal to

Cloning of alien DNA by the host involves -

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which reagent is used for the conversion of acetamide into ethylamine?

The reaction of aliphatic and aromatic primary amines with chloroform in the presence of ethanolic potassium hydroxide to produce compound with fouling smell, is known as