If the elementary column transformation \(C_1 \rightarrow 2 C_1\) is carried out on the following matrix equation.
\(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}-1 & 2 \\ 5 & 0\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) Then the transformed equation will be:

The local minimum value of the function \(f(x)=|x|+2\), where \(x\) is a real number is :

In the given figure, shaded region represents the feasible solution to a LPP problem. The constraint represented by AD is:

The value of \(x\), for which the function \(f(x)=x(x-2)\) attains its minimum value, is:

The value of parameter k for which the function \(f(x)=1+k x, k \neq 0\) is the inverse of itself is:

Area of a rectangle having vertices \(P, Q, R\) and \(S\) with position vectors \(-\hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) and \(-\hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) respectively is :

Match List-l with List-ll

List-I	List-II
(A) The measurable characteristic of a population is called	(I) sample
(B) The measurable characteristics of a sample is called	(II) Alternative hypothesis
(C) A smaller group of a population selected to represent a population is caller	(III) Parameter
(D) The assumption made opposite to the null hypothesis is called	(IV) statistic

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
How is the osmotic pressure of a concentrated solution related to the osmotic pressure of a dilute solution of the same substance at a given temperature?

For a non ideal solution exhibiting positive deviation:
A. The vapour pressure is lower than that predicted by Raoult's law
B. The vapour pressure is higher than that predicted by Raoult's law.
C. The interaction at the molecular level are weaker than in the pure state.
D. The interaction at the molecular level are stronger than in the pure state.
E. Mixture of chloroform and acetone is a suitable example.
Choose the correct answer from the options given below:

Which of the following pairs is not an example of homology?

In alcohols, C-O-H bond angle is:

If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is

Identify the incorrect example of albuminous seed.