Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:

Three bad eggs are mixed with 7 good ones
If two eggs are drawn one by one without replacement
then the probability distribution of the number X of bad eggs drawn is

A company purchased a machine for ₹ 15,00,000 and its effective life is estimated to be 10 years. A sinking fund is created for replacing the machine at the end of its effective life when its scrap value is ₹ \(2,42,000\). What amount company should provide at the end of every year out of profits for the sinking fund if it accumulates an interest of \(5 \%\) per annum? [Given: \((1.05)^{10}=1.629\)]

The area (in sq. units) of a triangle formed by vertices \(O, A\), and \(B\) where \(\overrightarrow{O A}=\hat{i}+2 \hat{j}+3 \hat{k}\) and \(\overrightarrow{O B}=-3 \hat{i}-2 \hat{j}+\hat{k}\) is

For any real numbers x and y, we define x R y if and only if \(\operatorname{cosec}^2 x-\cot ^2 y=1\). The relation R is:

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots \infty}}}\) then \(\frac{d y}{d x}\) equals to

The maximum value of \(Z=2 x+3 y\) subject to the constraints \(x \geq 0, y \geq 0, x+y \leq 10,3 x+4 y \leq 36\) is:

The typical angiosperm embryo sac at maturity has:

The amount of money needed to ensure for a prize of Rs 5000 at the beginning of each year indefinitely if money is worth \(5 \%\) compounded annually is :

Answer the question on basis of passage given below :
Lyophobic sols like those of metals (Au, Ag, etc) are unstable and are easily precipitated by addition of electrolytes. However, it is observed that the addition of certain lyophilic colloids like gums, soaps, gelatine, etc. to lyophobic colloids (like a metal sol) render lyophobic colloids difficult to coagulate by the addition of electrolytes. The process is known as 'protection' and the lyophilic colloids are termed as Protective colloids. It is believed that the protective action of the lyophilic colloids is due to the covering up of the particles of the lyophobic colloid by those of the lyophilic colloid.
Evidently, smaller the gold number of a protective colloid, the greater is its protective action.
Which of the following does not form a lyophilic colloid?

Two events A and B are independent, if
(A) A and B are mutually exclusive
(B) \(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
(C) \(P\left(A^{\prime}\right)=P\left(B^{\prime}\right)\)
(D) P(A) + P(B) = 1
(E) P(A) = P(B)

Match List-l with List-ll

List-l	List-II
(A) \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x}\)	(I) \(\frac{5}{2}\)
(B) \(\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}\)	(II) 5
(C) \(\lim _{x \rightarrow 1} \frac{x^5-1}{x^2-1}\)	(III) 2
(D) \(\lim _{x \rightarrow 0} \frac{(x+1)^5-1}{x}\)	(IV) 0

Choose the correct answer from the options given below:

Choose the correct order of increasing acidic strength of following compounds:
(A) 3-Nitrophenol
(B) Phenol
(C) Propan-1-ol
(D) 3,5-Dinitrophenol
Choose the correct answer from the options given below: