A random variable takes values with probabilities , b respectively, where . Let and respectively be the mean and standard deviation of such that Then is equal to :...

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A random variable X takes values 0123 with probabilities : null (Mathematics)

A random variable

X

takes values

0,1,2,3

with probabilities

\frac{2 \mathrm{a}+1}{30}, \frac{8 \mathrm{a}-1}{30}, \frac{4 \mathrm{a}+1}{30}

, b respectively, where

\mathrm{a}, \mathrm{b} \in \mathbf{R}

. Let

\mu

and

\sigma

respectively be the mean and standard deviation of

X

such that

\sigma^{2}+\mu^{2}=2.\\

Then

\frac{\mathrm{a}}{\mathrm{b}}

is equal to :

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :

The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

The integral int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} {dx}, where [.] denotes the greatest integer function is equal to

For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is

Let Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated, is

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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