\(60 \%\) members of a committee favour a certain proposal and \(40 \%\) members oppose the proposal.
A member is selected and let the random variable \(X=0\) if he opposes and \(X=1\) if he is in favour.
Then the variance of the random variable \(X\) is

If \(A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 0 & 2 \\ x & 1 & 1\end{array}\right]\) and \(A^{-1}=\frac{1}{4}\left[\begin{array}{ccc}-2 & 0 & y \\ 5 & -2 & -1 \\ 1 & 2 & -1\end{array}\right]\), then values of \(x\) and \(y\) are:

The corner points of the LPP Minimize \(z=5 x+7 y\) subject to the constraints
\(
\begin{array}{l}
2 x+y \geq 8 \\
x+2 y \geq 10 \\
x, y \geq 0 \\
\text { are } A(10,0), B(2,4), C(0,8)
\end{array}
\)
The minimum value of the objective function is :

If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs is :

A coin is tossed 6 times. The probability that tail appears odd number of times is:

The corner points of the bounded feasible region for an LPP are : \((5,5),(15,15),(0,20)\) and \((0,10)\).
Let \(z=3 x+9 y\) be the objective function.
Then the value of maximum \((z)-\operatorname{minimum}(z)\) is :

The length of a rectangle is decreasing at the rate of \(4\) cm / minute and the width is increasing at the rate of \(3\) cm / minute , then the rate of change of the perimeter is

What is the IUPAC name of m-cresol?

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 kingdon. 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 oxidixing 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.
Formalin which is used to preserve biological specimen is an aqueous solution of

If \(A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\), then the value of \((A+I)^3-4 A\) is:

Identify the carbohydrate which is not a polysaccharide

Cells responsible for the synthesis and secretion of testicular hormones are:

Two point charges \( +4 \mu C \) and \( -2 \mu C \) are placed at a certain distance in air. They experience an attractive force \( F \). If they are brought in contact with each other and then separated to the same distance, the new repulsive force between them will be :