The number of all possible matrices of order 2 × 2 with each entry 0, 1 or 2 are:

\(\int \frac{1}{x \sqrt{x^2-9}} d x\) is equal to (given that C is constant of integration)

The function \(f(x)=x^x\) has a critical point at :

The matrix \(A=\left[\begin{array}{lll}0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0\end{array}\right]\) is a :
(A) Diagonal matrix
(B) Scalar matrix
(C) Square matrix
(D) Symmetric matrix
Choose the correct answer from the options given below :

If \(y = x^2 \log_e x\), then \(\frac{d^2y}{dx^2}\) is equal to:

If the vectors \(\vec{a}=3 \hat{i}-p \hat{j}+5 \hat{k}\) and \(\vec{b}=-6 \hat{i}+14 \hat{j}+q \hat{k}\) are collinear, then the value of \(p\) and \(q\) are :

Rajesh calculated \(95\%\) confidence level. What does he mean by that?
(A) He can be \(95\%\) confident that his sample will include the population parameter.
(B) He can be \(95\%\) confused that his sample will include the population parameter.
(C) He can be \(5\%\) confident that his sample will not include the population parameter.
(D) He can be \(5\%\) confident that his sample will include the population parameter.
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
The reagents needed for the preparation of Benzoic acid from ethyl benzene is :

Let us consider an annuity whose periodic payment is ₹ R payable at the end of each payment period for ' \(n ^{\prime}\) periods, interest paid r% per period or \(i=\frac{r}{100}\), so the amount.

Haloalkanes can be represented by the formula

The potential of a charged spherical conductor of radius r is 20V. The potential at a point r/4 from its center is:

The refractive index of a glass prism is minimum for

The same current is flowing in two AC circuits. The first circuit contains a pure inductor and the second, a capacitor. If the frequency of the AC is increased, then the current will :