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The polars of points (1,7) (2,6) and (t,5) with respect to a circle concurrent then t=

Check the injectivity and surjectivity of the following functions . f : R rarr R , f(x) = x^(2)+7

If: Rto Rdefinedby f(x) = {:{ ((1 +3x^(2) - cos2x)/x^(2) , " for "x ne 0), ( k , " for "x =0):} is continuous at x = 0,then k is equal to

Evalute the following integrals int cos x cos 2x dx

intx^(51)(tan^(-1)x+cot^(-1)x)dx=...

Evaluate the definite integrals int_(0)^(pi/4)(2sec^(2)x+x^(3)+2)dx

For the curve y=4x^(3)-2x^(5), find all the points at which the tangent passes through the origin.

Prove that : Find the term independent of x (thatis the constant term) in the expansion of ((sqrt(x))/(3)+(3)/(2x^(2)))^(10)

Differentiate the following w.r.t. x : log (cos e^x)

If log_(5)(6+(2)/(x))+log_((1//5)) (1+(x)/(10)) le 1, then x lies in :

If A ={1,2,3} and consider the relation R = {(1,1), (2,2) , (3,3) , (1,2) ,(2,3), (1,3)} . Then R is .......

Prove that: (a) cot theta cot (60^(@)-theta)cot(60^(@)+theta)=cot 3 theta (b) cos 5 theta=16cos^(5)theta=-20cos^(3)theta+5 cos theta (c) sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

(x_(1),x_(2)) is the point of concurrencey of a family of lines. If the algebraic sum of the lengths of the perpendicular drawn to these lines from (2,0),(0,2)and(1,1) is zero, then (x_(1),y_(1)) =

A vertical pole stands at a point A on the boundary of a circular park of radius a and subtends an angle alpha at another point beta on the boundary. If the chord AB subtends an angle alpha at the centre of the park, the height of the pole is

Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}. Let Z = X + Y, then What is P(Z gt 11) equal to?

If the normals at P and Q meet again on the parabola y^(2) =4axthen the chord joining P and Q passes thorugha fixed point

Two balls are drawn from an urn containing 2 white, 3 red and 4 black balls one by onewithout replacement. What is the probability that at least one ball is red?

int (x^(3))/(sqrt(a^(8)-x^(8)))dx=

Which of the following is least ?

If C =1 + (cos x ) /(1!) +(cos 2X)/(2!) + (cos3x)/(3!) + ......and

int e^(-x) (1 - tanx ) Secx dx =

A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and OB are drawn to the circle x^(2)+y^(2)=8. Using this information, answer the following questions : The locus of circumcenter of DeltaAQB id t=2 is

Determine the area of parallelogram whose adjacent sides are the vector (1, -3, 1), (1,1,1)

Differentiate the following w.r.t. x: e^(sin^(-1)x)

If A and B be two events such that P(A)= (1)/(2)P(B) = (1)/(3) and P((A)/(B))=(1)/(4)thenP(AnnB) equals

If the regression equation of y x is given by x+ y =8, then estimate the value of y when x is 3.5 .

Determine P(E|F) A coin is tossed three times, where﻿ (i) E : head on third toss , F : heads on first two tosses﻿ (ii) E : at least two heads , F : at most two heads﻿ (iii) E : at most two tails F : at least one tail﻿

Find the area of region enclosed by the curve ((x-y)^2)/(a^2)+((x+y)^2)/(b^2)=2(agtb), the line y=x and the positive X-axis.

underset(x to -1)lim (sqrtx-sqrt(Cos^(-1)x))/(sqrtx+1)=

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= a(cos t+ log tan (t)/(2)),y= a sin t.

Area bounded by y=x^(3),y= 8 and x=0 is _______

Find the variance of the distribution:

(1020)^(1//5)~~....

int(1 - sinx)/(cos^(2)x)dx

Find the graph of linear inequation in xy planey-3 lt 0

int_(-pi//4) ^(pi//4) tan^(2) x sec (x)dx =

The system 2x+3y+z=5, 3x+y+5z=7 and x+4y-2z=3 has

If x= sec theta - cos theta, y = sec' theta - cos'' theta, then (dy)/(dx) =

If (x^(4)+2)/((x-1)^(2)(x+1))=Ax+B+C/(x-1)+D/(x-1)^(2)+E/(x+1) " then "A+D-2E=

int(logx)/((1+ logx)^(2))dx=

STATEMENT-1 : If a, b, c,d are positive and distinct number in H.P., thena + d gt + cand STATEMENT-2 :If a, b,c,d are in H.P. , then (a + d)/(ad) = (b + c)/(bc)

Area lying between the curves y^(2)=2x and y=x is

cosx(dy)/(dx)+ysinx=1

Verify that A=[[a,b],[c,d]]satisfies the equation A^2-(a+d)A+(ad-bc) I=0 where I is the 2x2 unit matrix.

The solution of dx + x dy = e^(-y) sec^(2) y dy is

If (x^(2)+5)/(x^(2)+2)^(2)=1/(x^(2)+2)+k/(x^(2)+2)^(2) " then " k=

Statement I In any triangle ABC a cos A+b cos B+c cos C le s. Statement II In any triangle ABC sin ((A)/(2))sin ((B)/(2))sin ((C)/(2))le 1/8

Find dy/dx when : xy+xe^(-y)+ye^(x)=x^(2).

Determine P(E|F) A coin is tossed three times, where (i) E : head on third toss , F : heads on first two tosses (ii) E : at least two heads , F : at most two heads (iii) E : at most two tails F : at least one tail