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Find (dy)/(dx), if x = a cos theta, y= a sin theta

Find the asymptotes of the hyperbola 4x^(2)-9y^(2)=36

For any two complex number z_1,z_2 and any real numbers a and b, |az_1-bz_2|^2+|bz_1+az_2|^2=….

The points (1, 2, 3), (3, 4, 7), (-3, -2, -5) are

Integrate the following functions : int(x-2)sqrt(x^(2)-4x+7)dx

((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)

Find the equation of the circle whose centre is (-1,2)and which passes thorugh (5,6)

Let the derivative of f(x) be defined as D^(**)f(x)=lim_(hto0)(f^(2)x+h-f^(2)(x))/(h), where f^(2)(x)={f(x)}^(2). If u=f(x),v=g(x), then the value of D^(**)((u)/(v)) is.

int_(-1)^(1)(ax^(3)+bx)dx=0 for

I is the incentre of DeltaABC. Forces barP,barQ,barR acting along IA,IB,IC respectively are in equilibrium. Then abs(barP) : abs(barQ) : abs(barR)=

If A, B, C are three mutually exclusive and exhaustive events such that 2P(A) = 3P(B) = 4P(C). Find the odds against A uu B.

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways can 3 balls be drawn from the box if atleast one black ball is to be included in the draw is

There are three sections in a question paper each containing 4 questions. If a candidate has to answer only 5 questions from this paper without leaving any sections then number of ways the candidate can make the choice of questions is

Integrate the following functions (4x+2) sqrt(x^2+x+1)

IfC_(0) , C_(1), C_(2), …, C_(n) are the binomial coefficients in the expansion of(1 + x)^(n) , prove that (C_(0) + 2C_(1) + C_(2) )(C_(1) + 2C_(2) + C_(3))…(C_(n-1) + 2C_(n) + C_(n+1)) ((n-2)^(n))/((n+1)!) prod _(r=1)^(n) (C_(r-1) + C_(r)).

Equation of a family of circles, such that each member of the gamily psses through the origin and makes an intercept on the line y = 2x which is twice the intercept made on the line x = 2y is (lamda being a parameter)

If L_(T')L_(N')L_(ST) and L_(SN) denote the lengths of tangent, normal sub-tangent and sub-normal, respectively, of a curve y = f(x) at a point P(2009, 2010) on it, then

Which of the following expansion will have term containing x^3 ?

If x is nearly equal to 1 then find the value of (mx^m- nx^n)/(m- n)

If A+B+C=180^@ and cis A=x,cis B=y,cis C=z, them xyz=

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points (x_(1),y_(1))" for "i=1,2,3 and" 4 then "y_(1)+y_(2)+y_(3)+y_(4) equals

If theta is real then the modulus of (1)/(1 + cos theta + isin theta)is

If x^(2) - x + 1 divides the polynomial x^(n+1) - x^(n) + 1, then n must be of the form

Evaluate the following integrals int(dx)/((1+x^(2))sqrt(1-x^(2)))

A set of events E_1,E_2,.........E_n are said to be a partition of the sample space, then which of the following conditions is always not true

int_(-pi//2)^(pi//2) sin|x| dx is equal to

Find all positive intogers x,y aatisfying (1)/(sqrtx)i(1)/(sqrty)=(1)/(sqrt20).

The value of cot[{Sigma_(n=1)^(23){cot^(-1))1+Sigma_(k=1)^(n)2k}] is

Solve sqrt3sintheta-costheta=sqrt2

Find the differential equation of the curve. (x^(2)-y^(2))=c (x^(2) + y^(2))^(2)

A rectangular solid consisting of 18 smaller cubes that are identical is positioned in the standard (x,y,z) coordinate system, as shown below . Vertex M has coordinates of (-1,3,0) and point O on the y-axis has coordinates of (0,3,0). What are the coordinates of vertex N ?

Let P be a point in the plane of Delta ABC such that the triangles PAB,PCA all have the same perimeter and the same area. If P lies outside the Delta ABC,then Delta ABC

Let P be a point in the plane of Delta ABC such that the triangles PAB,PCA all have the same perimeter and the same area. If P lies inside the Delta ABC, then Delta ABC

Let P be a point in the plane of Delta ABC such that the triangles PAB,PCA all have the same perimeter and the same area. If P lies outside the Delta ABC, then the quadrialteral formed by A, B, C and P is necessarily

Using the vertices of a polygon having 8 sides a triangle is constructed at random. The probability that the triangle so formed is such that no side of the polygon is side of the triangle is

If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(4), where g(x) is differentiable function, then (where {.} denotes fractional part of x).

The tangents at the extremities of the latus rectum of the ellipse 3x^(2)+4y^(2)=12 form a rhombus PQRS. Area (in sq. units) of the rhombus PQRS outside and ellipse is equal to

Three cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is heart, find the probability that the lost cards were all hearts

Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

int(x-x^2)/(x^2-2x-3)dx=

Differentiate the functions with respect to x (sin (ax+b))/(cos (cx+d))

If a circle through the point (2, 3) cuts x^2 + y^2 = 8 orthogonally then the locus of its centre is

If S and S' are the foci of the ellipse (x^(2))/( 25)+ ( y^(2))/( 16) =1, and P is any point on it then range of values of SP.S'P is

Let f(x) be a function which satisfy the equation f(xy)=f(x)+f(y) for all xgt0,ygt0 such that f'(1)=2. Find the area of the region bounded by the curves y=f(x),y=|x^3-6x^2+11x-6| and x=0.

Find the derivative of (log x)^(tan x)

The position vectors of the vertices A,B,C of a triangleABC are hati-hatj-3hatk,2hati+hatj-2hatk and -5hati+2hatj-6hatk respectively . The length of the bisector AD of the angle angleBAC where D is on the line segment BC, is : -

2.4^((-1)/(4))*8^((1)/(9))*16^((-1)/(16))*32^((1)/(25))*64^((-1)/(36))*……….oo=

The set A has 4 element and the set B has 5 elements then the number of injective mappings that can be deifned from A to B is

If A +B =C then cos ^(2) A+cos ^(2)B + cos^(2)C -2 cos A cos b cos C is equal to

Let the derivative of f(x) be defined as D^()f(x)=lim_(hto0)(f^(2)x+h-f^(2)(x))/(h), where f^(2)(x)={f(x)}^(2). If u=f(x),v=g(x), then the value of D^()((u)/(v)) is.

2.4^((-1)/(4))8^((1)/(9))16^((-1)/(16))32^((1)/(25))64^((-1)/(36))*……….oo=