A die is thrown again and again until three sixes are obtained. The probability of obtaining third six in sixth throw of the die is:

A problem in mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. The probability that the problem is solved is

Match List-l with List-ll.Find the derivatives from List-I.

List-l	List-II
(A) \(y=\sqrt{\sin x+y}\)	(I) \(\frac{-\sin x}{1+\cos y}\)
(B)\(\sin y=x \sin (a+y)\)	(II) \(\frac{\cos x}{2 y-1}\)
(C) \(y+\sin y=\cos x\)	(III) \(\frac{-1}{\sin ^2(x+y)}\)
(D) \(y=\tan (x+y)\)	(IV) \(\frac{\sin ^2(a+y)}{\sin a}\)

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ccc}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{array}\right]\), then the matrix \((\operatorname{adj} A) A\) is equal to

\(\int \frac{1}{x\left(x^5-1\right)} d x\) is equal to

Let \(A=\{1,2,3\}\) and \(R=\{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3)\}\) be a relation on \(A\). Then, \(R\) is:

The system of equations \(x+y-z=1,3 x+y-2 z=3, x-y+\lambda z=1\) has infinite number of solutions if \(\lambda\) is equal to

The molality of a solution made by dissolving 2.5 g of ethanoic acid (CH₃COOH) in 75 g of benzene is :

What is the increasing order of the oxidation state of the metal ion in following compounds?
(A). \(ScBr_{3}\)
(B). \(V_{2}O_{5}\)
(C). \(CrF_{6}\)
(D). \(Tc_{2}O_{7}\)
Choose the correct answer from the options given below:

The equation of the plane which passes through the point (3, 2, -1) and is perpendicular to the line with direction ratios 2, 1, 2 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. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
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. These must be supplied regularly in diet because they are readily excreted in urine and cannot be stored in our body.
Deficiency of which vitamin causes Rickets?

The function \(y=f(x)\) has extreme values at the points where ___________ .

The specific DNA sequence which is responsible for initiation of replication is known as: