The number of all possible matrices of order 2 × 2 with each entry 0 or 1 is:

Match List-I with List-II
If \(P(A)=\frac{3}{7}, P(B)=\frac{4}{7}\) and \(P(A \cup B)=\frac{5}{7}\)

List-I	List-II
(A) \(P(A \cap B)\)	(I) \(\frac{2}{3}\)
(B) \(P(A \mid B)\)	(II) \(\frac{5}{7}\)
(C) \(P(B \mid A)\)	(III) \(\frac{1}{2}\)
(D) \(P\left(A^{\prime} \cup B^{\prime}\right)\)	(IV) \(\frac{2}{7}\)

Choose the correct answer from the options given below :

Year (t)	2010	2011	2012	2013	2014	2015	2016
Sales (in Rs. crores) (y)	6	8	9	11	13	17	20

In reference to the above data, which of the following statements are correct?
(where \(x=t-2013\) )
(A) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2017 is 21.16.
(B) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2013 is 11.
(C) If the equation of the straight line trend is \(y=12+2.29 x\), then the trend value for the year 2015 is 17.
(D) If \(\left(t_1, y_1\right),\left(t_2, y_2\right), \ldots,\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of \(y\), then \(\sum\left(y-y_t\right)=0\).
Choose the correct answer from the options given below :

The value of \(\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)\) is

A random variable \(X\) has the following probability distribution

x	-2	-1	0	1	2	3
p	0.1	k	0.2	2k	0.3	k

Then the mean of X is :

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :

If \(2 f(x)+f\left(\frac{1}{x}\right)=x^2+1\), then \(\int f(x) d x\) is : (Here \(C\) is an arbitrary constant)

The wavelength will be minimum in the transitions of electrons from:

The area (sq. units) bounded by the curve \(y=\sin x, \pi \leq x \leq 2 \pi\) and the \(x\)-axis is

The slope of the normal to the curve \(y^2=16 x\) at the point \((1,4)\) is :

A single stranded DNA or RNA, tagged with a radioactive molecule is called as:

The relative lowering of vapor pressure is equal to the

The frequencies of a.c. generator depends on :