In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

The integral \(I=\int e^x\left(\frac{x-1}{3 x^2}\right) d x\) is equal to:

If \(x=a \sin ^3 t\) and \(y=a \cos ^3 t\), then \(\frac{d y}{d x}\) is equal to :

Assume \(A, B\) and \(C\) are matrices of order \(m \times n, n \times 3\) and \(3 \times q\) respectively. The restrictions on \(m, n\) and \(q\) so that \(A B+B C\) is defined are

A person creates a sinking fund to accumulate 60,000 in 5 years to buy a bike.
The amount to be deposited at the end of every quarter with a 12\% rate of interest compounded quarterly is :
Use \(\frac{0.03}{(1.03)^{20}-1}=0.0372\)

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

If \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then the value of \(A^{20}\) is :

Phenylketonuria is an example of:

Answer the question on the basis of passage given below:
Aldehydes are generally more reactive than ketones in nucleophilic addition reactions due to steric and electronic reasons. Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon more than aldehydes having only one such substituent Electronically aldehydes are more reactive than ketones because two alkyl groups reduce the elctrophilicity of the carbonyl more effectively than in former.
4-Hydroxy-4-methylpentan-2-one and 4-methylpent-3-en-2-one are the products obtained from A by aldol
condensation. \(A\) is:

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 :

The Nernst equation corresponding to the cell reaction given below, is
Ni(s) + 2Ag\(^+\)(aq) \(\rightarrow\) Ni\(^2+\)(aq) + 2Ag(s)

Match List-l with List-ll

List-l (Enzymes)	List-II (Used for)
(A). Protease	(I). RNA
(B). Chitinase	(II). Protein
(C). Lysozyme	(III). Fungus
(D). Ribonuclease	(IV). Bacterial cell

Choose the correct answer from the options given below:

The water and milk in two vessels are in the ratio 1:1 and 3: 8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4 : 7?