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n/((n+1)!)+((n+1))/((n+2)!)+......+((n+p))/((n+p+1)!) is equal to .

Evaluate the following integrals (iii) int_(0)^(pi/4) (1+ sin 2 x)/(cos x + sin x) dx

If I_(n) = int (e^(ex))/(x^(n)) " dx then " I_(n) - (a)/(n-1) .I_(n-1) =

Water comes out from a conical funnel at the rate of 5 cm^(3)//s. When the slant height of a water cone is 4 cm, find the rate of decrease of slant height of a water cone. The semi vertical angle of a conical funnel is (pi)/(3).

Let x be a nonempty set and * be a binary operation on P(X) the power set of X defiend by A*B =A cap B for all A,B in P(x) ltrbgt (i)Find the identity element in P(x) (ii) show that X is the only inveritiableelement in P(x)

What are the last two digits of 7^(7^(7^(7))) ?

A circle of radius 5 units passes through A(-5, 0) and B(5, 0). If P(5cosalpha, 5(sinalpha), Q(5cosbeta, 5sinbeta) are two points on this circle such that alpha-beta=pi/2, then the locus of the point of intersection of the line AP and BQ is

Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) _ 2x in [1, 3]

f(x)= {(x+1",","if" x ge 1),(x^(2) + 1",","if " x lt 1):}

Find all numberx , y that satisfy the equation (sin^2 x +(1)/( sin^(2) x))^(2)+( cos^(2)x+(1)/(cos^(2)x))^(2)=12+(1)/(2) siny.

A firm has the following total cost and demand functions : C(x) = (x^(3))/(3) - 10x^(2) + 300 x, where x stand for output. Calculate output at which the Average cost is equal to the marginal cost.

A firm has the following total cost and demand functions : C(x) = (x^(3))/(3) - 10x^(2) + 300 x, where x stand for output. Calculate output at which the Average cost is minimum

If the vectors vec(a)+lambdavec(b)+3vec(c), -2vec(a)+3vec(b)-4vec(c) and vec(a)-3vec(b)+5vec(c) are coplanar, then the value of lambda is

The value of ((vec(a)xxvec(b))^(2)+(vec(a).vec(b))^(2))/(2|vec(a)|^(2)|vec(b)|^(2))" is"

Two forces, one with a magnitude of 3N and the other with a magnitude of 5N ,are applied to an object. For which orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least ?

Let f,g and h be continuous functions on [0,a] such that f(x) = f(a-x), g(x) = - g(a- x) and 3h(x) - 4h(a- x) = 5. Then int_(0)^(a) f(x) g(x) h(x) dx is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2). The equation f(x)-x-f(0)=0 have exactly

Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = 2hati-hatj-hatk, vecb = lambdahati+hatj+5hatk

If alpha" and "beta are the roots of the equation ax^(2)+bx+c=0, (c ne 0), then the equation whose roots are (1)/(a alpha +b)" and "(1)/(a beta +b) is

If X_(1)=(x_(1),y_(1) and (x_(2)=(x_(2),y_(2)) are two optimal solutionof a L.P.P then

If x^(2)+y^(2)+6x+2ky+25=0 to touch y-axis then k=

Find the eccentricity, length of latus rectum, centre, foci, vertices and the equatioin to the dircctriccs of the hyperola. (i) 4x^(2)-5y^(2)-16x+10y+31=0 (ii) 5x^(2)-4y^(2)+20x+8y-4=0 (iii) 4(y+3)^(2)-9(x-2)^(2)=1 (iv) 4x^(2)-9y^(2)-8x-32=0

If two numbers are selected randomly from 20 consecutive natural numbers, find the probability that the sum of the two numbers is (i) an even number (ii) an odd number.

Space between cornea and lens is :-

WriteP (phi)set in the intention(or specification form).

Find the probability of getting hearts cards, when a card is drawn from pack of 52 cards.

If the curve f(x) = int e^(x) dx passing through (0,1) then the ascending order of f(0), f(1), f(-1), f(2) is

On passing electric current through molten AlCl_(3) , 11.2 litre of Cl_(2) is liberated at N.T.P. at anode. The quantity of aluminium deposited at cathode is : (At.wt. of Al = 27) :-

Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined as below have inverses. Find f^(-1), if it exists. Note : Here we accept that inverse at function is unique. f = {(1, 1), (2, 2), (3, 3)}

Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined as below have inverses. Find f^(-1), if it exists. Note : Here we accept that inverse at function is unique. f = {(1, 2), (2, 1), (3, 1)}

Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined as below have inverses. Find f^(-1), if it exists. Note : Here we accept that inverse at function is unique. f = {(1, 3), (3, 2), (2, 1)}

For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly intersect in a straight line, when Q. cose^(-1)(l)+cos^(-1)(m)+cos^(-1)(n) is equal to

All the metal ions contains t_(2g).^(6)eg^(0) configuration which of the following complex will not be paramagnetic :

The solutionof theequilibrium[ sinx+ cosx ] ^(1+ sin2x)= 2, -pile x lepiis

By giving counter examples , show that for every real number x and y, x^2=y^2 implies x =y are not true:

If the sum of an infinite decreasing G.P. is 3 and sum of the cubes of its terms is 108/13, then common ratio is given by

Consider the non-empty set consisting of children in a family and a relation R defined as aRb, if a is brother of b. Then , R is ........

Find the equation of the chord of contact of the point (2, -3)with respect to the hyperbola3x^(2)- 4y^(2) = 12

If a_(n)=sqrt(7+sqrt(7+sqrt(7+.....))) having n radical signs then by method of mathematical induction which is true

ABC is a triangle. The radical centre of the circles with AB, BC, CA as the diameters is (-6, 5). If A(3, 2), B(2, 1) then C =

If a denotes the number of permutation of n different things taken all at a time, b the number of permutation ofn - 2 different things taken 10 at a time and c, the number of permutations ofn - 12different things taken all at a time such thata = 182 bc, then value of n is:

If n in N, then sum_(ilej)(""^(n)C_(i))(""^(n+i)C_(j)) equals

Integrate the following int2a^(x^2)xdx

Prove that (r+1)xx.^(n)C_(0)-rxx.^(n)C_(1)+(r-1)xx.^(n)C_(2)-(r-2).^(n)C_(3) + "...."+(-1)^(r)xx.^(n)C_(r)+"...."=(-1)^(r)xx.^(n-2)C_(r).

Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sqrt2 Find f'(x).

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003x^(3)+15x+4000. Find the marginal cost when 17 units are produced.

Integrate the rational functions (1-x^(2))/(x(1-2x))