If \(f(x)=\left\{\begin{array}{ll}\frac{1-\tan x}{4 x-\pi} & x \neq \frac{\pi}{4} \\ k & x=\frac{\pi}{4}\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(k\) is

Which one of the following options is incorrect?
For a square matrix \(A\) in the matrix equation \(A X=B\).

The value of \(\frac{9}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)+\frac{9}{4} \sin ^{-1}\left(\frac{1}{3}\right)\) is :

Let \(\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}\), and \(\vec{c}=2 \hat{i}+\hat{j}+4 \hat{k}\).
A vector \(\vec{d}\) which is perpendicular to both \(\vec{a}\) and \(\vec{b}\) and satisfies \(\vec{c} \cdot \vec{d}=14\) is :

The total cost function is given by \(C(x)=\frac{1}{3} x^3-5 x^2+30 x-15\) and selling price per unit is Rs. 6. The profit is maximum if the value of x is:

Which of the following is not correct about the Central Limit Theorem?

If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :

The spermatids are transformed into spermatozoa by the process called as

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
How many varieties of rice India has?

The vector equation of the line passing through points \(A(3,4,-7)\) and \(B(1,-1,6)\) is:

The number of electrons in one coulomb of electric charge is :

All natural and artificial radioactive decay of unstable nuclei take place by

The length of a rectangle is decreasing at the rate of \(4\) cm / minute and the width is increasing at the rate of \(3\) cm / minute , then the rate of change of the perimeter is