If \(\hat{a}, \hat{b}\) and \(\hat{c}\) are three units vectors and \(\hat{a}+\hat{b}+\hat{c}=\overrightarrow{0}\), then the angle between \(\hat{a}\) and ( \(-\hat{b}\) ) is

If \(f(x) = \frac{x^6}{6} - 2x^2\), then \(f''(4)\) =?

If \(A=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]\) and \(A^4=\left[\begin{array}{ll}1 & 0 \\ k & 1\end{array}\right]\), then the value of \(k\) is :

If \(A=\left[a_{i j}\right]_{3 \times 3}\), where \(a_{i j}=\frac{(-1)^{i+j}-1, i=j}{(-1)^{i+j}, i \neq j}\) then the value of \(A+A^T\) is:

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

In a game of carrom of 100 points, A can give B 20 points and C 40 points, then points B can give C is:

If the minimum value of \(a\) is \(-\frac{k}{2}\), such that the function \(f(x)=x^2+a x+5\) is increasing in \([1,2]\). Then value of \(k\) is

Heavy water and __________ is one of the substance used as moderator in reactors.

The absolute maximum value of the function \(f(x)=4 x-\frac{1}{2} x^2\) in the interval \(\left[-2, \frac{9}{2}\right]\) is

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
Among the following, water-soluble vitamin is

An astronomical telescope uses two lenses of power 10 D and 2 D. The distance between the objective and the eye lens in normal adjustment would be

To avoid the medical condition called 'bends' in scuba divers, the composition of gas filled in the tank is

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is: