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(dy)/(dx) = 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

Let O be the vertex and Q be any point on the parabola ,x^(2) =8y . If the point P divides the line segment OQ internally in the ratio 1: 3 then the locus of P is:

In which of the following situations, it is possible to have a DeltaABC ? (All symbols used have usual meaning in a triangle)

if O is the point inside the triangle ABC such that /_OBC = A/2, /_OCA = B/2, /_AOB = C/2, then (sin(A - C/2)sin(B - A/2)sin(C - B/2))/(sin""(A)/2 sin""(B)/2 sin""(C)/2) equal :

By rotating the coordinate axes in the positive direction about the origin by an angle alpha, if the point (1, 2) is transformed to ((3sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+3)/(2sqrt(2))) in new coordinate system Then, alpha =

If 4x + y = 14 and 3x + 2y = 13, then x - y =

Integrate the following functions: sin^4x

If a,b,c in Rthen number of ordered triplet (a,b,c) which satisfy the equations a^(2)+2b=6,b^(2)+4c=-7andc^(2)+6a=-13is

Find the shortest distance between the following lines:(x-3)/1=(y-5)/(-2)=(z-7)/1and (x+1)/7=(y+1)/(-6)=(z+1)/1

A function f :R to R is given by f (x) = {{:(x ^(4) (2+ sin ""(1)/(x)), x ne0),(0, x=0):}, then

If z_(1) and z_(2) are two of the 8^(th) roots of unity such that arg(z_(1)/z_(2)) is last positive, then z_(1)/z_(2) is

The second term of an A.P is (x - y) and fifth term is (x + y), then the first term is

The value (int_(0)^(pi//2) (sinx)^(sqrt2+1)dx)/(int_(0)^(pi//2)(sinx)^(sqrt2-1)dx) is -

If f(x) is a polynomial in x(gt0) satisfying the equation f(x)+f(1//x)=f(x).f(1//x) then f(x)=

Find the middle term (s) in the expansion of (3x^2 + (5)/(x^3))^12

If f : R to R is defined by f (x) = 2x + 3 , then f^(-1) x

Find the odd function f(x) such that the area bounded by the x -axis the curve y = f(x) and the lines x = - 1 and x = 1 is equal to in (t^(2) + 1), AA t ge 0.

If f(x)=(|x|)/(x)" for "x ne 0, f(0)=0," then f(x) at x=0 is "

i. Mean = a (3 median - mode) II. Mean - Mode = b(Mean - Median) (iii) Median = Mode + c (Mean - mode)

Two vertices of an equilateral triangle are (-1,0) and (1,0) then its circumcircle is

Let |bar(a)|=7, |bar(b)|=11, | bar(a)+bar(b)|=10 sqrt(3) What is the angle between (bar(a)+bar(b) and (bar(a)-bar(b))?

Integrate the rational functions (3x-1)/((x-1)(x-2)(x-3))

Find derivatives of the following functions.tan^3x

An isosceles triangle of a given perimeter 2p=12 revolves about its base. Write the function V(x), where V is the volume of the solid of revolution thus obtained and x is the length of the lateral side of the triangle.

Prove the following overset((pi)/(2)) underset(0) int sin^(3)xdx=(2)/(3)

If int (1)/(4 + 5 sin x) " dx "= (1)/(3) log |f (x)| + c then f(x) =

Find derivatives of the following functions.sin^2 x cos^2 x

Find the area bounded between the curves y^(2)=4ax , x^(2) = 4by (a gt 0, b gt 0).

Statement 1 : Equation of the pair of lines bisecting the angle between the pair of lines ax^2+by^2+2hxy+2gx+2fy+c=0 can be written as x^2-y^2-((a-b)/h) xy +lamdax+muy+c'=0 because Statement 2 : Equation of any pair lines parallel to the lines ax^2+by^2+2hxy=0 is ax^2+2hxy+by^2+Ax+By +c''=0 .

If sum _(x =pi-"" ^(10)C_(r))^(pi + "" ^(10)C _(r))sin x ^(0) =0, then value of r is "_________"

veca,vecb,vecc be three vectors such that V_(1)=[(veca, vecb, vecc)]=1and V_(2)=[(vecaxxvecb)xxvecc(vecbxxvecc)xxveca(veccxxveca),vecb)] then the value of sum_(r=1)^(6)V_(1)^(r)+V_(1)V_(2)^(r) is

Ifthe chord joining two points whose eccentric angles are alpha and beta cut the major axis of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distancefrom the centre then tan (alpha)/(2).tan (beta)/(2) =

Integral part of the area of figure bounded by the tangents at the end of latus rectum of ellipse (x^(2))/9+(y^(2))/4=1 and directices of hyperbola (x^(2))/9=(y^(2))/72=1is

Areabounded bythe ellipse(x^2 )/(4)+(y^2)/(16)=4 is …….

Given P=[[2,-3],[-1,2]] . Findthe inverse of P by elementary row operation.

Find the n ^(th) term of the series 1,3,8,16,27,41,……

Evaluate the integral underset(0)overset(pi)int (1+cosx)^(3) dx

If z =e^((x +y)/(x -y)) then x (del xz)/(del x) + y (del z)/(dely)=

An equilateral triangle with side a revolves about an axis parallel to the base and situated at a distance b gt a from the base. Find the volume of the solid of revolution.

Letintsqrt((5-x)/(2+x))dx equal

Let A = {1, 2, 3}, B { 4, 5, 6} and let f = {(1,4),(2,5)(3,6)} be a functionfrom A to B. Show that f is one-one.

Choose the correct answer int((10x^(9)+10^(x)log_(e)10) dx)/(x^(10)+10^(x)) equals

f(x) is a twice differentiable function such that f"(x)=-f(x) and f'(x)=g(x). If h(x)=(f(x))^(2)+(g(x))^(2) and h(l)=2, then h(2)=

Let y=x^(3)-8x+7 and x=f(t) given t=0, x=3 Find the value of (dy)/(dt).

A circle with center (2,1) has a tangent to the circle at (3,6). The equation of the tangent is

Integration using trigonometric identities : int(1)/(1+sin^(2)x)dx=....

Find the values of k if area of triangle is 4 sq. units and vertices are(k,0),(4,0),(0,2)

""^((2n + 1))C_0 + ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 + ……+""^((2n + 1))C_n =