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Find the 20^(th) and n^(th) terms of the G.P. 5/2, 5/2, 5/8,….

A and B are two points in the horizontal plane through O, the foot of pillar OP of height h such that angle AOB=theta. If the elevation of the top of the pillar from A and B are also equal to theta, then AB is equal to

The radius of a cone is twice of its height and the radius is 10 cm. If there is an error of 0.01 cm in measure of radius, then find the approximate error in calculating its volume.

ABCD is a reactangularfield.Averticallamppostof height12 mstandsat thecornerA.If theanngle ofelevationof itstopfromB is60^@and fromC is45^@, thenthe areaof thefieldis

Statemnet 1 : If three positiveunequalnumbers a,b,c are in H.Pthen a^(2) +c^(2) gt 2b^(2) because Statement 2: A.M. gtG.M.gt H.M. for the unequal numbers.

A point is such that its distance from the point (3,0) is twice its distance from the point (-3,0). Find the equation of the locus.

List the members of the equivalence relation defined by{{1},{2},{3,4}} partitins on X={1,2,3,4}.Also find the equivalence classes of 1,2,3 and 4.

Let a differentiable function f (x) satisfies f (x). F '(-x) . F'(x) and f (0) -1. Find the value of int ^(-2)(dx )/(1+f(x)).

If the normal at the point t_(1) to the rectangle hyperola xy=c^(2) meets it again at the point t_(2) prove that t_(1)^(3) t_(2)=-1

List the members of the equivalence relation defined by {{1,2,3},{4}} partitins on X={1,2,3,4}.Also find the equivalence classes of 1,2,3 and 4.

A binary operation * defined on Z^(+) defined as a * b = 2^(ab). Determine whether * isassociative

A particle performing S.H.M . Undergoes displacement A/2 (where A= amplitude of S.H.M. ) in one second. At t=0 the particle was located at either extreme position or mean position. The time period of S.H.M. can be :( consider all possible cases )

List the members of the equivalence relation defined by {{1,2,3,4}} partitins on X={1,2,3,4}.Also find the equivalence classes of 1,2,3 and 4.

There are 9 objects and 9 boxes. Out of 9 objects, 5 cannot fit in three small boxes. How many arrangements can be made such that each object can be put in one box only.

The normal at a poitn P( theta)on the ellipse 5x^(2) +14y^(2)=70cuts the curve again at a point Q(2theta)then"cos" theta

If y ^(2) = (x-a)(x-b)then ( d ^(3))/(dx ^(3)) [((d ^(2) y)/(dx ^(2))^(-2//3))]=

Equation of a line and a plane are respectively (x+3)/(2)=(y-4)/(3)=(z+5)/(1) and 2x-3y+5z=1. Then

Thenumberof waysin which5 redbeedsand 4 yellowbeedsof differentsizescan bemadeoutto forma necklace so thatnotwoyellowbeadscometogether is

If X follows a binomial distribution with mean 4 and variance 2, find P(X ge5)

Integrate the function 1/(9x^(2)+6x+5)

Rolle's theorem is not applicable in which one of the followingcases?

Find the area of the region formed by the segment cut off from the parabola x^(2)=8y by the line x-2y+8=0.

int(1)/(x^(3))[logx^(x)]^(2)dx=...

One of the asymptotes (with negative slope) of a hypebola passes through (2,0) whose transverse axis is given by x -3y+ 2=0, then equation of hyperbola if it is given that the line y = 7x -11 can intersect the hyperbola at only one point (2,3) is given by

A A' is always a symmetric matrix for any matrix A .

A bag contains 2 white and 1 red balls. One ball is drawn at random and﻿ then put back in the box after noting its colour. The process is repeated again. If X﻿ denotes the number of red balls recorded in the two draws, describe X.﻿

Examine the applicability of Mean Value Theorem for all three functions f(x)= x^(2)-1, x in [1, 2]

The truth values of p,q are r for which (p^^q)vv(~r) has truth value F are respectively

The position vectors of the points A and B are respectively hat i - hat j + 3 hat k and3 hat i + 3 hat j + 3 hat k. The equation of the plane bar r. (5 hat i + 2 hat j - 7 hat k ) + 9 =0 Then points A and B.

State with reason, "All big rivers of India" is set or not ?

If p_1,p_2,p_3 denote the distance of the plane 2x-3y+4z+2=0 from the planes 2x-3y+4z+6=0, 4x-6y+8z+3=0 and 2x-3y+4z-6=0 respectively, then

Resolve (x^(2)-x+1)/((x+1)(x-1)^(2)) into partial fractions.

If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=overline(a)-overline(b)+overline(c), overline(q)=overline(a)+overline(b)-3overline(c),overline(r)=overline(a)+4overline(b)+moverline(c) are collinear then m=

IF thedomainof the functionf(x)=x^2 -6x +7 is(-oo , oo)then rangeof thefunction is

Which of the following is the converse of the statement? "if Billu secure good marks, then he will get a bicycle."

If A, B, C and D are the vertices of a square, find vec(AB) + vec(BC)+ vec(CD) + vec(DA).

Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6) + (7)/(2.4.6.8)+ (9)/(2.4.6.8.10)+……

Find delta f and df whenf(x) = sqrtx , x = 16, deltax = 0.3

Find the Principle values of the following : sin^(-1)(-1/2)

If two of the three feet of normals drawn from a point to the parabolay^(2) =4xbe ( 1,2) , (1,-2)then third foot is

if( cos A + cosB )/( sinA +sin B) = k ( (sin A - sinB)/ ( cosA- cos B)) then k is

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x)=0.005 x^(3)-0.02 x^(2)+30x+5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change oftotal cost at ant level of output.

4 fair coins are tossed and given that the first coin shows head. Find the probability that no two consecutive heads occur on the four coins.

Lt_(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

Probabilityof solvingspecific problemindependentlyby A and B are1/2and 1/3respectively.if bothtryto solvethe problemindependently, findthe probailitythat theproblemissolved .

Find int e^(x)sin x.

Let vecalpha,vecbeta,vecgamma be three unit vectors such that vecalpha*vecbeta=vecalpha*vecgamma=0 and the angle between vecbeta and vecgamma is 30^(@). Then vecalpha is

Evaluate the following integrals (vi) int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx

A bag contains 2 white and 1 red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If X denotes the number of red balls recorded in the two draws, describe X.

Let vecalpha,vecbeta,vecgamma be three unit vectors such that vecalphavecbeta=vecalphavecgamma=0 and the angle between vecbeta and vecgamma is 30^(@). Then vecalpha is