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Find the number of ways of arranging 6 red roses and 3 yellow roses of different sizes into a garland. In how many of them no two yellow roses are together

If f'(x)=sqrtx and f(1)=2 then find f(x).

Two matrices are equalif they have same number of rows and same number of columns .

Out of 800 boys in a school , 224 played cricket,240 played hookey and 336 played basketball. Of the total , 64 played both basketball and hockey , 80 played cricket and basket ball and 40 played cricket and hockey 24 played all the three games. number of boys who did not play any game is

Ifalpha, beta , gammaare therootsof x^3+2x^2 -3x -1=0 thenalpha^(-2)+ beta^(-2)+ gamma^(-2)=

Write the vector form of the equation of the line (x-3)/3=(y+4)/7=(z-6)/2

If |z_(1) + z_(2)| = |z_(1) - z_(2)| then the difference in the arguments of z_(1) and z_(2) is

Find the rate of change of the area of a circle with respect to its radius r when (a) r=3 cm "" (b) r=4 cm

Let p, q be prime numbers such that non n^(3pq)-nis a multiple of 3pq for all positive integers n. Find the least possible value of p + q.

Choose the correct answer If d/(dx)f(x)=4x^(3)-3/(x^(4)) such that f (2) = 0. Then f (x) is

Let A(theta) and B(phi) be the extrenities of a chord of an emplise. If the slope of AB is equal to the slope of the tangent at a point C(alpha) on the ellipse, then value of alpha is

The normal ata point P on the parabola y^(2)=4axcuts the curve again at Q . If M is the midpoint of PQ then the product of the ordinates of P and M is

Let f be a continuous function satisfying f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5 then lim_(x to 4) f(x) is equal to

Prove that following i) 2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)

Pick out a function which is one - one but not onto

Let R = {(a,a^3) | ais a prime number less than 10}.Find dom R^(-1).

Find the point at which the tangent to the curve y=sqrt(4x-3)-1 has its slope (2)/(3).

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t additional number of workers x is given by (dP)/(dx) = 100 - 12 sqrtx. If the firm employs 25 more workers, then the new level of production of items is

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ","you will receive a promotion" Translate p^^q^^rstatements into English language.

I:(1)/(1!)+(1+2)/(2!)+(1+2+2^(2))/(3!)+....=e^(2)-e II:(2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+....=e

A die is thrown three times. Events A and B are defined as below:﻿ A : 4 on the third throw﻿ B : 6 on the first and 5 on the second throw﻿ Find the probability of A given that B has already occurred.

consider the function f(x) =1+(1)/(x)^(x) The range of the function f(x) is

Differentiate the following with respect to x: cos^(-1) (e^(x))

int_0^(pi//2)(sqrttanx+sqrtcotx)dx

Which of the following is not a requirement of binomial distribution?

If int(2e^(5x)+e^(4x)-4e^(3x)+2e^(x))/((e^(2x)+4)(e^(2x)-1)^(2))dx=tan^(-1)(e^(x//2))-(K)/((e^(2x-1)))+C then K is equalto

int_(-1)^(1) (17x^(5)-x^(4)+29 x^(3) -31 x +1)/(x^(2)+1)dx=

If a_1,a_2,a_3….a_r are in G.P then show that |{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}| is independent of r

Probability distribution of random variable X is as follows: WhereC gt 0 Find (i) C (ii) P(X lt 2) (iii) P(1 lt X le 2).

Draw the graph of y = tan^(2) x.

int (x^2)/((2 + 3x^3)^(3))dx

If a variable takes the values 0, 1, 2,…,n with frequencies proporiotnal to binomial coefficient n_(C_(0)), n_(C_(1)), n_(C_(2)),….n_(C_(n)), then mean of distribution is

Mean of the following probability distribution is …………

If X is a poisson variate such that P(X = 2) = 9P(X = 4) + 90P(X = 6) then find mean of X.

The period T and length l are increasing at the same rate is T = 2pi sqrt(l//g). Then the length l in terms of pi and g is

If vec(a), vec(b), vec(c) are the position vectors of vertices A, B, C of a triangle ABC, Show that the area of the triangle is (1)/(2) |vec(b) xx vec(c) + vec(c) xx vec(a) + vec(a) xx vec(b)|

Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents are parallel to the X-axis.

Each of the following defines a relation of N : x+y = 10 , x , y in N Determine which of the above relations are reflexive , symmetric and transitive .

In howmanywayscan 52cardsbe dividedamong4playersso thateach mayhave 13is

If a=hat(i)-2hat(j)+hat(k), b=hat(i)+3hat(j)-2hat(k), c=2hat(i)+hat(j)-hat(k) " and "d=hat(i)+hat(j)+hat(k), then the volume (in cubic units) of the tetrahedron having (a times b) times c, b, d as its coterminuous edges is

cos (alpha + beta + gamma ) + cos (alpha - beta - gamma) + cos ( beta - gamma- alpha ) + cos ( gamma - alpha - beta )=

A, B, C are the centres of three circles of equal radii which donot touch extranally pairwise whose centers are non-collinear. The radical centre of the circles for triangle ABC is

Derivative of sin x^(2) w.r.t. x^2 is

find the order and degree of the differential equation:

Integrate the following : int(sqrtx+2)^2/x^4dx

Obtain the following integrals : int(2x-1)/(2x+3)dx

Discuss the continuity of the function f, where f is defined by f(x)={{:(3," if "0 le xle 1),(4," if "1 lt x lt 3),(5," if "3 le x le 10):}.

If the vectors a=hat(i)+a hat(j)+a^(2) hat(k), b=hat(i)+b hat(j)+b^(2) hat(k) and c=hat(i)+chat(j)+c^(2) hat(k) are three non-coplanar vectors and |(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0, then the value of abc is

If ax ^2 + 2bx+ c=0 , a_1x^2+ 2b _1x +c_1=0havea commonroot, thenthe rootsof theequation( b^2 -ac )x^2+(2b b_1 - a a_1 - a_1 c ) x+ (b_1^2-a_1 c_1 ) =0 are

A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw B : 6 on the first and 5 on the second throw Find the probability of A given that B has already occurred.