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Find (dy)/(dx), " if "y=12 (1-cos t), x= 10(t-sin t), -(pi)/(2) lt t lt (pi)/(2).

Evaluate int(1)/(4+5sinx)dx

If sin^(-1)(x)+sin^(-1)(1-x)=cos^(-1)(x), then x belong to

A : If |a| = 13, |b| = 19, |a + b| = 24 then |a -b| = 20 R: for any vectors a,b, |a + b|^(2) + |a - b|^(2) = 2 (|a|^(7) + |b|^(2))

int((lnx-1)/((lnx)^(2)+1))dx is equal to

The solution of cos y log (sec x + tan x)dx = cos x log (sec y + tan y) dy is

Consider the system of linear equation ax+by=0, cx+dy=0, a, b, c, d in {0, 1} Statement-1 : The probability that the system of equations has a unique solution is 3/8. Statement-2 : The probability that the system has a solution is 1.

Construct a 3xx2 matrix whose elements are given by a_(ij)=e^(i.x)-sinjx.

Consider the parabola (x-1)^(2)+(y-2)^(2)=((12x-5y+3)^(2))/(169) and match the following lists :

Form the differential equation representing the family of curves y= asin(x+b) where a,b are arbitrary constant.

How many numbers can be formed using all the digits 1,2,3,4,3,2,1 such that even digits always occupy even places ?

If the median of a Delta ABC through A is perpendicular to AC, then (tan A)/(tan C)=

int_(0)^(pi) [cot x] dx, where [*] denotes the greatest integer function, is equal to

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. Number of ways of choosing P and Q so that PcapQ contains exactly one element is

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. i) The number of ways of choosing P and Q so that PcapQ=phi is

Integrate the following functions 1/(x-sqrtx)

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. P and have equal number of elements is

Which of the following distribution of probabilities of a random variable X is the probability distribution ?

A bag contains 'a' white and 'b' black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw till one of them drawn a white ball and wins the game. If the probability of A winning the game is three times that of B, then find the ratio a : b.

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

cot^(2)x-(1)/(2)cot^(4)x+(1)/(3)cot^(6)x -(1)/(4)cot^(8)x+…oo=

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Find the vector equation of the plane passing through the points bar(i)-2bar(j)+5bar(k), -5bar(j)-bar(k), -3bar(i)+5bar(j).

Find the area enclosed by y^2=x, x=0,y=1

The volume of the tetrahedron having the edges hati+2hatj-hatk, hati+hatj+hatk, hati-hatj+lambdahatk as coterminous, is (2)/(3) cu unit. Then, lambda equals

If h denotes the arithmetic mean and k denotes the geometric mean of the intercepts made on the coordinate axes by the lines passing through the point (1, 1), then the point (h, k) lies on

Aline makes acute angle of alpha, beta and gamma with the coordinate axes such that cos alpha cos beta cos gamma = (2)/(9) and cos gammacos alpha = (4)/(9), then cos alpha + cos beta + cos gamma is equal to

Evaluate int(1)/(sqrt(4-9)x^(2))dx

If y = a^((1)/(2) log_(a) cos x), find (dy)/( dx)

Match the column

Prove that the inverse of the discontinuous function y= (1+ x^2) sing x is a continuous function.

The vertices of a hyperbola are(2,0 ) ,( -2,0) and the foci are (3,0) ,(-3,0) .The equation of the hyperbola is

if f(x)={((log_(e)x)/(x-1),,,x!=1),(k,,, x=1):} is continuous at x=1, then the value of k is

Examine if Rolle's theorem is applicable to the following functions : f(x) = |x| on [-1,1]

Examine if Rolle's theorem is applicable to the following functions : f(x) = [x] on [-1,1]

If the normal subtends a right angle at the focus of the parabola y^(2)=4ax then its length is

If |{:(x,e^(x-1),(x-1)^(3)),(x-lx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos^(2)x):}|=a_(0)+a_(1)(x-1)+a_(2)(x-1)^(2)cdots The value of lim_(xto 0) (sin x)^(x) is

Define an objective function.

Using integration, find the area of the quadant of the circle x ^(2) + y ^(2) =4.

If overline(a), overline(b), overline(c) are non-coplanar vectors, then the vectors given by overline(p)=2overline(a)-2overline(c), overline(q)= 3overline(a)+overline(b)+5overline(c) andoverline(r)= 2overline(a)-4overline(b)+3overline(c)are

Find the equation of all common tangents of the circles (i) x^(2)+y^(2)=9 and x^(2)+y(2)-16x+2y+49=0 (ii) x^(2)+y^(2)+4x+2y-4=0 and x^(2)+y^(2)-4x-2y+4=0

Find the number of ways to arrange 8 persons around a circle by taking 4 at a time.

Equation of the curve passing through the point (a,1) and has length of subtangent = a is

int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=