The corner points of a bounded feasible region are \(( 0 , 5 ),( 6 , 1 ),( 1 7 , 2 )\) and \(( 4 , 2 9 )\).
If the maximum value of the objective function \(z=p x+q y\), where \(p>0\) and \(q>0\), occurs at two points \((17,2)\) and \((4,29)\), then the relation between \(p\) and \(q\) is :

The order and degree of the differential equation \(x\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2-3 \frac{d y}{d x}+y=0\) respectively, are:

Match List-I with List-II
An urn contains 4 white and 3 red balls. In a random draw of three balls, the probability of

List-I	List-II
(A) No red ball is	(I) \(\frac{12}{35}\)
(B) Only 1 red ball is	(II) \(\frac{1}{35}\)
(C) Exactly 2 red balls is	(III) \(\frac{4}{35}\)
(D) No white ball is	(IV) \(\frac{18}{35}\)

Choose the correct answer from the options given below :

The value of the integral \(I=\int_{-3}^3\left(x^3-x\right) d x\) is :

Match List - I with List - II

List - I (Differential Equations)	List - II (Order and degree)
(A) \(ydx + xlog(y/x)dy - 2xdy = 0\)	(I) Order: 2, degree:1
(B) \(\left(\frac{d^3 y}{d x^3}\right)^2+3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^2\)	(II) Order :1, degree:1
(C) \(\frac{d y}{d x}+\log \left(\frac{d y}{d x}\right)+x=y\)	(III) Order: 3, degree:2
(D) \(\left(\frac{d s}{d t}\right)^4+2 s \frac{d^2 s}{d t^2}=0\)	(IV) Order: 1, degree: Not defined

Choose the correct answer from the options given below:

The maximum number of equivalence relations on the set \(A=\{a, b, c\}\) is:

If the two lines \(\frac{x-1}{2}=\frac{y-3}{4}=-z\) and \(\frac{x-4}{3}=\frac{y-1}{-2}=z-1\) are contained in a plane then the equation of the plane is :

If \(A=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{3} & 1\end{array}\right]\) then \(A^{48}\) is :

Match List-l with List-ll

List-l (Name of the gene)	List-II (Encodes)
(A) 'i'	(I) Permease
(B) 'z'	(II) Repressor
(C) 'y'	(III) Transacetylase
(D) 'a'	(IV) β- Galactosidase

Choose the correct answer from the options given below:

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.
What is the probability of having a daughter to a couple expecting their first child?

The van't Hoff Factor, \(i\) for complete dissociation of (i) NaCl , (ii) \(MgSO _4\) and (iii) \(K _2 SO _4\) are

What is the reagent used in Clemmensen reduction?

A circular coil with 5 turns, each of radius 7 cm, carries a current of 1.4 A. The magnetic field at the center of the coil is: