The mean number of heads in two tosses of a coin is:

\(A\) random variable \(X\) has the following probability distribution:

X	0	1	2	3
P(X)	0.2	0.1	0.3	0.4

The variance of \(X\) will be

Let \(f:[0, \infty) \rightarrow[0,2]\) be defined by \(f(x)=\frac{2 x}{1+x}\), then \(f\) is:

If \(\mathbf{A}=\left[\begin{array}{ccc}0 & 0 & \sqrt{7} \\ 0 & \sqrt{7} & 0 \\ \sqrt{7} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} \mathbf{A}|\) is equal to

\(\text { If } I=\int \frac{x}{x-\sqrt{x^2-4}} d x=\alpha x^3+\beta\left(x^2-4\right)^{\frac{3}{2}}+\gamma\) where \(\gamma\) is a constant of integration, then

At \(6 \%\) converted quarterly, the present value of a perpetuity of ₹ 900 payable at the end of each quarter is :

The area of the region bounded by the lines x = 2y + 3, x = 0, y = 1 and y = - 1 is:

Answer the question on the basis of passage given below :
Nitrogen differs from rest of the members of group 15 due to its small size, high electronegativity, high ionization enthalpy and non-availability of d orbitals. Nitrogen has unique ability to form pa - pa multiple bonds with itself and with other elements having small size and high electronegativity. Heavier elements of this group do not form pa - pr bonds as their atomic orbitals are so large and diffuse that they cannot have effective overlapping.
Group 15 elements forms oxides of type \(E _2 O _3\). Acidic oxides are formed by
A. Bi
B. Sb
C. P
D. As
E. N
Choose the correct answer from the options given below:

The number of vectors of unit length perpendicular to both the vectors \(\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + 3\hat{k}\) is:

The refractive indices of glass and water are 3/2 and 4/3, respectively. If light passes from glass to water, the critical angle is

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
The alcohol which cannot be used to prepare carbonyl compound through oxidation is

A resistor, an inductor and a capacitor are connected in series with a variable frequency source of alternating emf. At resonance, the amplitude of current depends on :
(A) Resistance
(B) Inductance
(C) Capacitance
(D) Frequency of source
Choose the correct answer from the options given below :

Arrange the following compounds in the order of their increasing boiling point :
Pentan-1-ol, n-butane, pentanal, ethoxy ethane