Ishita is rowing a boat. She takes 24 hours to row 72 km against the stream and she takes 9 hours to return to the starting point in the direction of the stream. The speed of the boat in still water is :

If the total cost and total revenue of a company that produces and sells \(x\) units of a particular product are \(C(x)=5 x+350\) and \(R(x)=50 x-x^2\) respectively, then which of the following is/are the breakeven values:
(A) \(x=10\)
(B) \(x=25\)
(C) \(x=45\)
(D) \(x=30\)
Choose the correct answer from the options given below:

The angle between the pair of lines given by \(\vec{r}=\hat{i}+2 \hat{j}-3 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{i}+\hat{j}+\hat{k}+\mu(3 \hat{i}-2 \hat{j}+6 \hat{k})\)

Due to which of the following, the irregular variations in a time series are caused:
(A) Floods
(B) Rise in prices before festivals
(C) A fire in a factory
(D) Epidemics
Choose the correct answer from the options given below:

Let \(A\) be a non-singular square matrix of order \(n\) with \(|\operatorname{adj} A|=64\) and \(|A|=4\), then ' \(n\) ' is :

Which of the following are correct?
(A) If \(A\) and \(B\) are symmetric matrices such that \(A B=B A\), then \(A B\) is symmetric.
(B) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A+B)\) is a symmetric matrix.
(C) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B-B A)\) is a symmetric matrix.
(D) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B+B A)\) is a skew-symmetric matrix.
Choose the correct answer from the options given below :

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with each entry either 0 or 1 .
Then the number of all such possible matrices is :

Parturition is the:

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
When DNA from different sources is cut by the same restriction enzymes, the resultant DNA fragments have the :

A copper wire of area of cross-section \( 2 \times 10^{-6} \, \text{m}^2 \) and electron density \( 10^{28} \, \text{m}^{-3} \) carries a current of 1.6 A. Time taken by an electron to drift from one end of a 1.0 m long wire to its other end will be

The shortest distance between the lines\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}\)and\(\frac{x-3}{4}=\frac{y-3}{6}=\frac{z+5}{12}\) is :

Which of the following is a complementary sequence of 5' GAATTC ---- 3'?

In which ecosystem, a larger fraction of energy flows through detritus food chain (DFC) than through grazing food chain (GFC)?