\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

Match List 1 with List 2.

List - 1 (Matrix)	List - 2 (Determinants)
(A) \(\operatorname{Matrix}(A)=\left[\begin{array}{cc}1 & 7 \\ -3 & 5\end{array}\right]\)	(I) 24
(B) \(\operatorname{Matrix}(B)=\left[\begin{array}{cc}-2 & 5 \\ -3 & -3\end{array}\right]\)	(II) 32
(C) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(III) 21
(D) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(IV) 26

Choose the correct answer from the options given below :

The integral \(\int \log x d x\) is equal to to:

Area bounded between the parabola \(y=x^2-2\) and the line \(y=x\) in square units is:

The area (in sq. units) of the region bounded by the curve \(y=\sin x,-2 \pi \leq x \leq 2 \pi\) and the \(x\)-axis is :

The total cost of producing \(x\) generators is given by
\(TC =x^3-60 x^2+1500 x+2000\)
The Marginal Cost \(( MC )\), when \(x=10\) units is:

The value of the integral \(I=\int_{-1}^2|x| d x\) is :

Salicylaldehyde is formed as a main product from phenol by :

In aldehydes, the carbonyl group is bonded to a carbon and hydrogen, while in ketones it is bonded to two carbon atoms. The carbonyl compounds in which carbonyl group is bonded to oxygen are known as carboxylic acid and their derivatives.
Arrange the following steps of Aldol condensation in the correct order of their occurance.
A. Abstraction of proton
B. Protonation
C. Formation of Enolate
D. Nucleophilic Addition
E. Elimination
Choose the correct answer from the options given below:

Read the paragraph given below and answer the question.
Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone.
Identify the correct statements.
(A) Insulin was earlier extracted from the liver of slaughtered animals.
(B) Eli Lilly, an American company is producing insulin using r-DNA technique.
(C) Some diabetics developed allergy with the animal sourced insulin.
(D) Pro-insulin can control diabetes.
Choose the correct answer from the options given below :

If \(A=\left[a_{i j}\right]\) is a skew-symmetric matrix of order \(n\), then

The sum of two positive numbers is 60. If the sum of their squares is minimum, then the absolute value of the difference of their cubes is

In the decay chain given below the sequential order in which the radioactive radiations are emitted will be :
\(^{A}_{Z}X \to ^{A}_{Z+1}Y \to ^{A-4}_{Z-1}P^* \to ^{A-4}_{Z-1}P\)