A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

The area bounded by the curve \(y=2 x-x^2\) and the straight line \(y=-x\) is :

The corner points of the bounded feasible region for an LPP are (0, 20), (3, 12), (6,8), (0, 15).
The objective function is \(Z=a x+\beta y\), where \(a, \beta>0\).
If the maximum of Z occurs at the corner points (3, 12) and (6,8), then the relationship between \(a\) and \(\beta\) is:

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:

Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing is

Which of the following vitamins are water soluble ?
(A) Thiamine
(B) Riboflavin
(C) Pyridoxine
(D) Ascorbic acid
Choose the correct answer from the options given below :

Transmission of HIV-Infection occurs by-
(A). Using infected needles by the health staff or by drug abusers
(B). Transfusion of contaminated blood and blood product
(C). Sexual contact with infected person
(D). Sharing food and sanitation facilities
Choose the correct answer from the options given below:

Lanthanoids (Ln) when heated with S, generally give _________ .

Irregular variations in a time series are not caused by:

The area (in sq. units) enclosed by the curve \(y=\frac{1}{2} x|x|\) and the line \(y=x\) is :

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
Identify the correct formula of Mohr's salt and potash alum, respectively.