A fair coin is tossed a fixed number of times. If the probability of getting 11 heads is equal to the probability of getting 13 heads, then the probability of getting 2 heads is:

If the matrix \(A=\left[\begin{array}{lll}0 & b & 1 \\ 2 & 0 & c \\ 3 & 4 & 0\end{array}\right]\) is a symmetric matrix, then the values of \(b\) and \(c\) are:

As per the graph given below:

Match List - I with List - II

LIst - I (Function/Area/point)	List - II (Representation)
(A) Consumers Surplus	(I) y = g(x)
(B) Supply function	(II) v
(C) Demand function	(III) s
(D) Equilibrium point	(IV) y = f(x)

Choose the correct answer from the options given below:

If it is 7:00 pm currently in the clock, what will the clock show (in am or pm) after 674 hours?

For the differential equation \(x \frac{d y}{d x}+2 y=x^2 \log _e x\)
(A) Integrating factor is \(2 x\)
(B) Integrating factor is \(x^2\)
(C) General Solution is \(y=\frac{x^2}{16}\left(4 \log _e|x|-1\right)+C x^{-2}\), where \(C\) is an arbitrary constant.
(D) General Solution is \(y=\frac{x^4}{16}\left(4 \log _e|x|-1\right)+C\), where \(C\) is an arbitrary constant.
Choose the correct answer from the options given below :

If A= \(\left[\begin{array}{cc}7 & 3 \\ 5 & -7\end{array}\right]\) be such that \(A^{-1}\) = kA, then k equals

Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Another Pipe can empty the full tank in 30 hours. If all three pipes are opened together, then the tank will be filled in:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
A haemophilic man marries a normal woman. What is the possibility that their child have haemophilia?

Read the given passage and answer the question.
ABO blood groups in human beings are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surfaces and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and I. The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles, IA and IB are completely dominant over I.
Select the correct option for number of alleles present in ABO blood groups:

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by - OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
The final product of the following reaction is:

Bt toxin produced by Bacillus thuringiensis is resistant to :

If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :

About linear programming problem (LPP), which of the following statements are correct ?
(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.
(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function \(Z=a x+b y\) never exists.
(C) The feasible region for an LPP is always conver.
(D) The common region determined by all the linear constraints of an LPP is called the feasible region.