The area of the region bounded by parabola \(x^2=4 y\), straight line \(x=2\) and \(x\)-axis, is

For some constant 'k', if the system of linear equations
\(2 x-y+3 z=1\)
\(x-2 y+z=3\)
\(k x+y-z=0\)
has a unique solution, then

Probability that a man speaks truth is \(\frac{3}{4}\). He throws a die and reports that it is a six. The probability that it is actually a

The system of equations:
\(x+y+z=5\)
\(x+2 y+3 z=9\)
\(x+3 y+\lambda z=\mu\) has a unique solution, if

Given \(X=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\), then value of K if \(X^2=8 X+K I\) is :

Find the least non-negative remainder obtained when \(3^{128}\) is divided by \(7\) .

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

Match List-I with List-II

List-I (Drugs)	List-II (Sources/features)
(A) Alcohol	(I) Sedative and painkiller
(B) Crack	(II) Diacetylmorphine
(C) Morphine	(III) Liver cirrhosis
(D) Smack	(IV) Erythroxylum coca

Choose the correct answer from the options given below:

Which of the following statements are true ?
(A) Milk obtained from 'Rosie' is nutritionally more balanced for human babies than natural human milk.
(B) Biopiracy refers to the use of bioresources without proper authorization from MNCs.
(C) GEAC is the decisive body for safety and validity of GMOs and GM research respectively.
(D) Transgenic animals help us to understand the contribution of genes in the development of disease.
Choose the correct answer from the options given below:

Which of the following is correct about RNA ?
(A) Unstable and mutates slower
(B) Unstable and mutates faster
(C) Stable and mutates faster
(D) Stable and mutates slower
Choose the correct answer from the options given below :

Chloroform is largely used for

If the points \(A, B, C\) with position vectors \(20 \hat{i}+\lambda \hat{j}, 5 \hat{i}-\hat{j}\) and \(10 \hat{i}-13 \hat{j}\) respectively are collinear, then the value of \(\lambda\) 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 colour blind man marries a carrier woman. Choose the possible progeny outcome.