The number of equivalence relation on the set {1, 2, 3} containing (1, 2) and (2, 1) is

The solution of the differential equation \(\log(\frac{dy}{dx}) = ax + by\) is:

The angle between the line \(\frac{x+2}{3}=\frac{y-3}{2}=\frac{z+5}{6}\) and the plane 2x + 10y - 11z = 5 is:

For the linear programming problem (LPP),
Maximize \(Z=4 x+y\)
Subject to:
\(x+y \leq 5\)
\(3 x+y \leq 9\)
\(x, y \geq 0\)
Which of the following are NOT true?
(A) The given LPP has unbounded feasible region.
(B) The corner points of the feasible region are \((0,0),(0,5),(3,2)\) and \((3,0)\).
(C) The optimal value of the objective function is 12.
(D) The given LPP has a unique optimal solution.
Choose the correct answer from the options given below:

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.

Mr. X invested Rs. 4, 00, 000 in shares for 5 years.
The value of this investment was Rs. \(4,50,000\) at the end of the second year, Rs. \(4,90,000\) at the end of the third year and on maturity, the final value stood at Rs. \(6,00,000\).
The compound annual growth rate (CAGR) of this investment is :
[Given that \((1.5)^{1 / 5}=1.084\) ]

Which of the following are correct?
(A) For a square matrix \(A\), if \(A^3=I\), then \(A^{-1}=A^2\).
(B) The determinant of only a square matrix can be defined.
(C) If \(A\) is a square matrix of order 3 , then the number of minors of the matrix \(A\) is 3 .
(D) If \(A\) and \(B\) are two non-singular matrices of the same order, then \((A B)^{-1}=B^{-1} A^{-1}\).
Choose the correct answer from the options given below :

Match List-l with List-II

List-I (Disorders)	List-II (Features)
(A) Colour blindness	(I) 45 with 'XO'
(B) Haemophilia	(II) Trisomy of 21\textsuperscript{st} chromosome
(C) Down's Syndrome	(III) Mutation of certain genes on 'X' chromosome
(D) Turner's Syndrome	(IV) Protein involved in clotting of blood

Choose the correct answer from the options given below:

Arrange the following in the increasing order of oxidation state of nitrogen :
(A) \(NO\)
(B) \(NO_2\)
(C) \(N_2O_5\)
(D) \(N_2O\)
(E) \(N_2O_3\)
Choose the correct answer from the options given below :

The general solution of the differential equation \(\frac{d y}{d x}-\frac{y}{x}=x^2\) is :

In an experiment with Meter Bridge, with unknown resistance R in the left gap, the null point is obtained at \( l_1 = 40 \text{ cm} \) from the left end. Now a resistance of \( R' = 10 \Omega \) is connected in series with resistance R, the null point is obtained at \( l_2 = 70 \text{ cm} \) from the left end. The value of resistance R is

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?

An electrical circuit contains a battery of V = 4 V, and a resistance of R = 2 \( \Omega \). A galvanometer of resistance G = 40 \( \Omega \) shunted by S = 10 \( \Omega \) is used to measure current in the circuit. The reading of ammeter is