The linear inequalities satisfying the shaded feasible region given in the figure are

(A) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2\)
(B) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \leq 2\)
(C) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2, \quad x+2 y \leq 8, \quad x-y \leq 1\)
(D) \(x+2 y \geq 8, \quad x-y \geq 1\)
Choose the correct answer from the options given below:

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4, 18) and (6, 12). If objective function is Z = 30x + 20y then the sum of the maximum and the minimum values of Z is

Match List-I with List-II

List - I (Function)	List - II (Points of discontinuity)
(A) \(f(x)=\frac{x^2+1}{x}\)	(I) x = 4
(B) \(f(x)=\frac{|x-1|}{x-1}\)	(II) x = 2
(C) \(f(x)=\{x-1\), if \(x<2 ; x+1\), if \(x \geq 2\}\)	(III) x = 0
(D) \(f(x)=\frac{1-x}{x-4}\)	(IV) x = 1

Choose the Correct answer from the options given below :

For the system of equations \(A X=B\), which of the following is correct?

Match List-I with List-II

List-I	List-II
(A) The value of \(\int_0^4|x| d x\) is	(I) 3
(B) The value of \(\int_{-2}^2|x| d x\) is	(II) -1
(C) The value of \(\int_0^3[x] d x\) is	(III) 8
(D) The value of \(\int_{-1}^1[x] d x\) is	(IV) 4

Choose the correct answer from the options given below :

The area (in sq. units) of the triangle whose vertices are \((0,0),(a, 0),(0, b)\), is equal to

The value of the determinant \(\left|\begin{array}{lll}x & a & x+a \\ y & b & y+b \\ z & c & z+c\end{array}\right|\) is

The sex chromosomes of a female bird have:

A car starts from a point at time \(t = 0\) seconds and stops at Q.
The distance \(x\) in meters covered by it in \(t\) seconds is given by
\(x = t^2 \left( 2 - \frac{t}{3} \right)\).
The time taken by it to reach Q is:

Which type of linkage is present between the two nucleotides?

Electromagnetic wave carries

The range of the function \(f(x)=\frac{1}{1-x^2}, x \neq \pm 1\) is :

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which amine will have highest \(p K _{ b }\) value?