A man rows 24 km upstream in 6 hours and 36 km downstream in 6 hours each time, then the speed of the boat in the still water is

If \(A=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{3} & 1\end{array}\right]\) then \(A^{48}\) is :

For \(x \neq-1\), if \(\int \frac{x e^x d x}{(1+x)^2}=\frac{a e^x}{(1+x)^b}+c\), where \(a, b\) are fixed numbers and \(c\) is the integration constant, then \(a+b\) is equal to

Let the determinant be \(\Delta=\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|\)
Which of the following statements are correct ?
(A) \(\Delta\) is independent of \(\theta\)
(B) \(\Delta\) is independent of \(x\)
(C) \(\Delta\) is independent of \(\theta\) and \(x\) both and is equal to 1
(D) \(\Delta\) depends upon both of \(x\) and \(\theta\)
(E) \(\Delta\) is independent of \(\theta\) and is equal to \(x^3\)
Choose the correct answer from the options given below :

The value of \(\int_{-5}^5|x+3|\) \(dx\) is

Two cards are drawn with replacement from a pack of 52 cards.
The probability distribution of number of aces is:

Differential equation of a parabola with vertex at origin and symmetric about \(x\)-axis is :

If the matrix \(A=\left[\begin{array}{ccc}x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0\end{array}\right]\) is skew-symmetric, then the value of \(2 x-3 y+5 z\) is equal to

The number of individuals in the reproductive age group is more than the number of individuals in the pre-reproductive age group, the shape of its age pyramid would reflect the growth status of the population as:

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
"Maltose" disaccharide is composed of

Select the correct expression for the parts per million (ppm) concentration term:

The demand for a certain product is represented by the function \(p=300+25 x-x^2\) (in rupees), where \(x\) is the number of units demanded and \(p\) is the price per unit, then the marginal revenue when 15 units are sold, is

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth \(6\%\) per annum compounded monthly?