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Find the number of positive integral solutions of x_1x_2x_3x_4x_5=210, such that x_1 ne 1

If int(1)/(x+x^(5))dx=f(x)+c, then the value of int(x^(4))/(x+x^(5))dx=.....

If denotes the area bounded by f(x)=|(sin x+ cos x)/(x)| x-axis , x=piand x=3x , then

Find the points on the curve y = x^(3) at which the slope of the tangent is equal to the y-coordinate of the point.

Identify the position isomer.

Examine the consistency of the system of linear equtions in 1 to 6 2x-y=5 x+y=4

For two vectors vec(a) and vec(b),|vec(a)|=4,|vec(b)|=3 and vec(a).vec(b)=6 find the angle between vec(a) and vec(b).

int_(-1)^(3)(Tan^(-1)""(x)/((x^(2)+1))+Tan^(-1)""(x^(2)+1)/(x))dx=

If f(x)={((x-2)2^(-(1/(|x-2|)+1/(x-2))),x!=2),(0,x=2):} then f(x) at x=2 is

Match the conics in column I with statements/ex- pressions in Column II.

The range of a random variable X is {0, 1, 2}. Given that P(X=0)=3c^(3),P(X=1)=4c-10c^(2),P(X=2)=5c-1 where c is constant. Find (i) the value of c (ii) P(X lt 1) (iii) P(1lt X le2) (iv) P(0lt X le3)

Using integration, find the area of the region bounded by the triangle whose vertices are (0, 1), (2,2) and (3, 1).

int (dx)/(x(x^(n) + 1)) = c

For which of the following function 9s) Lagrange's mean value theorem is not applicable in [1,2] ?

If A and B are two events such that A subset B and P(B) != 0, then which of the﻿ following is correct?﻿

Show that int_0^a f(x) g(x) d x=2 int_0^a f(x) d x, if f and g are defined as f(x)=f(a-x) and g(x)+g(a-x)=4

dx + dy = (x + y) (dx -dy) rArr log (x + y) =

For the reaction : N_(2)(g)+3H_(2)(g) to 2NH_(3)(g),DeltaH=-24KCal " at " 427^(@)C and 200 atm. Calculate magnitude of internal energy change ( in Kcal DeltaU), if 168 gm N_(2) gas and 30 gm H_(2) gas are allowed to react completely (100% reaction yield ) to form NH_(3) gas at 427^(@)C and 200 atm.

Sum of the coefficients of (1+2x-4x^2)^(2003)

One mole of N_(2) and 3.0 moles of PCl_(5) were placedin a 100-liter vessel and heated to 227^(@)C. The equilibrium pressure was 2.05" atm. "Assuming ideal behaviour, calculate X. Where X=1000xxK_(P) of the reaction at 227^(@)C.

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in GP.

Three persons A, B ,C in order toss a die. The person who first throws 1 or 2 wins. The ratio of the probabilities of their success is

Consider a quadraticequaiton az^(2) + bz + c=0, where a,b,c arecomplex number. The condition that theequation has onepurely imaginary root is

The value of I=int_(-pi//2)^(pi//2) sqrt( cos x - cos^(3) x)" "dxis

Ifalpha, beta , gammaare therootsof x^3 -6x -4=0thentheequationwhoserootsare(betagamma+(1)/( alpha)) ,(gammaalpha+(1)/(beta)) , (alphabeta+(1)/( gamma))is

Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+……..+ sqrt(n+n))/(nsqrt(n))

At anelectionthreewardsof atownof aarecanvassedbyby 3,4, and 5 menrespectivelyif 20menvolunteer, in howmanycan theybeallotedto thedifferentwards ?

Let f(x)=[sqrt(n)+1/2] where [.] denotes greatest integer function AA, n epsilonN Then sum_(n=1)^(oo)(2^(f(n))+2^(-f(n)))/(2^(n)) is equal to ………

If a,b,c are sides of DeltaABC such that |{:(c,bcosB+cbeta,acosA+balpha+cgamma),(a,c""cosB+abeta,bcosA+calpha+agamma),(b,acosB+b""beta,c""cosA+aalpha+bgamma):}|=0 ("where" alpha,beta,gamma in R^+ and angleA,angleB,angleC ne pi//2) then DeltaABC is

The position vector of a point lying on the line joining the points whose position vectors are hati+hatj-hatk and hati-hatj+hatk is

If f(x)= x^(2) sin ((1)/(x)), where x ne 0, then the value of the function f at x=0, so that the function is continuous at x= 0, is

Answer the following: If 6th term in the expansion of (x+*)^n is equal to "^nC_5x^(n-10) find *.

IfA= cos 15^(@) - cos 75^(@) , B= tan 15^(@) + tan 75^(@) , C=cos^(2) 45^(@) - sin^(2) 15^(@)then ascending order is

If : int_(0)^(pi)ln(sin x) dx = k, then : int_(0)^(pi//4)ln (1+tan x)=

A, B, C are three points on a vertical pole whose distances from the foot of the pole are in A.P. and whose angles of elevation at a point on the ground are alpha, beta and gamma respectively. If alpha + beta + gamma = pi, then tan alpha tan gamma is equal to

Find the equation of a straight line in the plane vecr.vecn=d which is parallel to vecr.vecn=d("where "vecn.vecb=0).

If the equation 3x^(2)+3y^(2)+10xy+16y+k=0 represents a pair of line, then k=

The oxidation state of Cr in K_(3)CrO_(8).

Find (dy)/(dx) in the following x^(2) + xy + y^(2) = 100

For the plane prod= 4x – 3y + 2z – 3 = 0, the points A = (- 2, 1, 2), B = (3, 1, - 2) 1) lie on the same side of prod = 0

If f(x) = int_0^x tsint dt, then find f^'(x)

int_(0)^(1)(2x+3)(sqrt(3-2x))dx

If f(t) = int_(-t)^(t) (e^(-|x|))/(2) dx, then underset(t to oo)(lim) f(t) is equal to

(dy)/(dx) + y = 1( y ne 1)

If the circles x^(2) + y^(2) - 2lambda x - 2y - 7 = 0 and 3 (x^(2) + y^(2)) - 8x + 29 y = 0 are orthogonal the lambda is equal to

The probability that a man can hit a target is 3/4. He tries 5 times the probability that he will hit the target at most one time is

If the plane 2x + 3y + 4z=1 intersects X-axis, Y-axis and Z-axis at the points A, B and C respectively, then the centroid of a Delta ABC is …....

Using elementary transformations, find the inverseof the matrices [(4,5),(3,4)]

If x = 1 + i is a root of x^(3) - ix + 1 - i = 0 , then the quadratic equation whoseroots are the remain - ing two roots of x^(3) - ix + 1 - i = 0 is

Let the images of the point A(2, 3) about the lines y=x and y=mx are P and Q respectively. If the line PQ passes through the origin, then m is equal to

If A and B are two events such that A subset B and P(B) != 0, then which of the following is correct?

Answer the following: If 6th term in the expansion of (x+)^n is equal to "^nC_5x^(n-10) find .