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Assertion (A) : X is a binomial distribution with parameters n = 100 and p . If P (x = 50) = P ( x = 49) then p = (1)/(2) Reason (R) : For the binomial distribution (q + p)^n , P (x = k) = ""^(n) c_(k) .q^(n-k) .p^(k)

Find the volume of the solid of revolution when the region bounded by y=sqrt(x), y=2 and x=0 is rotated about the x axis .

A: The plane 2x + 3y + 5 = 0 is parallel to x-axis. R: The plane ax + by + cz +d=0 is parallel to x-axis if a = 0.

Let z be a purely imaginary number such that Im (z) < 0. Then arg (z) is equal to

A certain mass of an ideal gas is expanded from (1L, 10 bar) to (4L,5bar) against a constant external pressure of 1 bar. If initial temperature of gas is 300 K and the heat capacity of process is 50J//""^(@)C. Then the enthalpy change during the process is :

If int f(x)dx=f(x), then int[f(x)]^(2)dx=...

Show that straight line 7x+6y=13 is a tangent to the parabola y^(2)-7x-8y+14=0 and find the point of contact.

If R(t)=[(cost,si nt),(-si nt,cost)], then R(s)R(t) equals

For each binary operation ** defined below, determine whether ** is commutative or associative on Z, define a**b=a-b

int (1)/(x^(2)(x^(4)+1)^(3//4))dx is equal to___________

The solution of the equation int_(0)^(x) (1)/(xsqrt(2^(2)-1))dx=(pi)/(12), is

Evaluate int (1)/(2x^(2) + x - 1) dx

Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is

For each of 3 years , the table below gives the number of different routes a runner ran , the number of runs she ran , and the total number of miles she ran . To the nearest tenth of a mile , what is the average number of miles the runner ran per run in 2005 ?

Let o lt p lt q and a ne 0 such that the equation px^(2) +4 lambda xy +qy^(2) +4a (x+y +1) = 0 represents a pair of straight lines, then a can lie in the interval

Using elementary row transformations , find the inverse of [{:(1,3,-2),(-3,0,-5),(2,5,0):}]

The number of ways of arranging the letters of the word 'SUCCESSFUL' so that Two C's are together but no two S's are together is

The vector equation of line passing through origin and parallel to (x-2)/(3)=(y-3)/(-1)=(z+1)/(2) is

Construct a 2xx3 matrix having element:a_(ij)=i+j

Construct a 2xx3 matrix having element:a_(ij)=i-j

Construct a 3 xx 4 matrix, elements are given by a_(ij) = |-3i + 4j|.

For real x, the equation |x/(x-1)|+|x|=x^2/(|x-1|) has

Findproduct: [[1,2],[3,4]][[1,0],[0,1]]

If A, G, H denote respectively the AM, GM and HM between two unequal positive numbers, then

Number of positive integral values of N such that characteristic of N with base 'a', is 'c' are (a,cin N) :-

Findtherepeatedroots ofx^5 -3x^4 -5x^3 +27 x^2 -32 x+12=0

Consider f(x)=int_(-1)^(x)(e^((x-t)/(x-2-t))dt)/(x-2-t)^(2) Q. The greatest integer in range of f(x) is

Integrate the following functions x sin 3x

For n in N, int_(0)^(2pi) (x sin^(2n)x)/(sin^(2n) x + cos^(2n) x) dx=

int (3x + 3)/(sqrt(x^(2) + 2x +5))dx =

If z = 3 + 3i then, z^(2)+z+15 =

Compute the value of 'c' satisfied by the Rolle's theorem for the function . f(x) =x^(2)(1-x)^(2), x in [0,1].

Let f : N rarr R be the function defined by f(x) = (2x-1)/(2) and g : Q rarr R be another function defined by g(x) = x + 2. Then (gof) ((3)/(2)) is

int_(pi/6)^(pi/4) " cosec "x dx

If a is an integer and a in (-5,30] then the probability that the graph of the function y=x^(2)+2(a+4)x-5a+64 is strictly above the x-axis is

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(4028)(f(x))/(f(x)+f(4028-x))dx=..............

Let a,b,cberealnumbersa ne 0ifalphais a rootsofa^2x^2+ bx+c=0 , betais a rootsofa^2 x^2 -bx-c=0and 0 ltalpha lt beta, thenthe equationa^2 x^2 + 2bx+ 2c=0has a rootgamma hasa root gammathatalwayssatisfies

IF 0< a

IF ina DeltaABC, thealtitudesfromthe verticesA,B,Con oppositesidesare inH.P ,thensin A , sin B, sin Care in

If S -= x^(2) +y^(2) -2x =0, S' -= x^(2) +y^(2) +3x =0and if overset -( AB )is a direct common tangent to the two circles (A, B are the point of contcact ) then overset- (AB)subtends at origin an angle.

Find the number of 4-letter words that can be formed using the letters of the word "ARTICLE which do not contain E

Three dice are rolled 4 times . The probability of getting sum 17 exactly 3 times is

If the equation ax^2+2hxy+by^2=0 represents a pair of lines then prove that the equation of the pair of angular bisection is h(x^2-y^2)=(a-b)xy=0.

Prove that for any two statements p and q the statements ~(pharr~q)andpharrq are equivalent.

A bomb of mass 9kg initially at rest explodes into two piece of masses 3 kg and 6 kg. The kinetic energy of the 3 kg mass is 216 J. The kinetic energy of the 6kg mass will be :-

For each binary operation defined below, determine whether is commutative or associative on Z, define a**b=a-b