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Let f(x)=In(2x-x^(2))+"sin" (pix)/(2). Then

The value of int_(0)^(pi)dx/(1+5^(cosx)) is :

Find the equation of the common tangent of the following circles at their point of contact. x^2+y^2-8y-4=0 x^2+y^2-2x-4y=0

For 2le rlen,{:((n),(r)):}+2({:(n),(r-1):})({:(n),(r-2):})=

If A=[{:(0,1),(1,0):}], then A^(2) is equal to ......

If statements p.q. are both true and r,s, are both false, then indicate the truth -value of the compound statement [(Ptoq)]to(qtor)to(r,s)

Distance between the two planes 2x -2y + z= 5 and 6x-6y + 3z = 25 is …... Units.

Prove that : int_(0)^(pi//2) (dx)/(1+cot x)=(pi)/(4)

Consider f(x,y)=(xy)/(x^2+y^2) if (x,y) ne (0,0) and f (0,0) = 0 . Show that f is not continuous at (0,0) and continuous at all other points of R^2.

A unit vector perpendicular to the plane containing the vectors hati+2hatj+hatk and -2hati+hatj+3hatkis

If oversetrarra=4overset^i+noverset^j+3overset^k|oversetrarra|=13, what is the value of n ?

The angle between the circles x^2+y^2-2x-4y+3=0 and x^2+y^2-4x-6y+11=0 is

Find the derivative of tan^-1 (sqrt(1-x^2)/x)with respect to cos^-1x .

Three coins are tossed. Then the probability distribution of number of head is

If f(x)={{:((e^([2x]+2x+1)-1)/([2x]+2x+1),:,x ne 0),(1,":", x =0):}, then (where [.] represents the greatest integer function)

Let x( x-a) + y (y-1)=0 be a circle. If two chords from (a,1)bisected by X-axis are drawn to the circle then the condition is

Mean and standard deviation of 100 items are 50 and 4 respectively. The sum of all squares of the items is

A and B are two independent witnesses in a case. The probability that A will speak truth is 2/3 and the probability that B will speak truth in 3/4. A and B agree in a certain statement. Find the probability that the statement is true.

Let f:R to R be the function defined by f(x)={{:(5,if,xlt1),(a+bx,if,1ltxlt3),(b+5x,if,3lexlt5),(30,if,x ge 5):}then f is

Integrate the functions xsin^(-1)x

Method of integration by parts : int x^(2)sin2x dx=....

Using differentials, find the approximate value of each of the up to 3 places of decimal. (0.0037)^((1)/(2))

Let A and B are two independent events. Such that P(A)=1//3andP(B)=1//4. Then match the following lists:

A bag contains 2n coins out of which n-1 are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is 41/56, then the number of unfair coins in the bag is

Find the area of one of the curvilinear triangles formed by y=sin x, y = cos x and x-axis.

The value of (3 tan 5^@-tan^3 5^@)/(1-3tan^2 5^@) is :-

int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx

Find the area of the region bounded by y= 4x-x^(2)-3 and the x-axis

Differentiate cosec x + cot x

int(x-2)/(x(2logx-x))dx=....

Find (dy)/(dx)" if "x-y = pi.

cos x +(1)/(3)cos^(3)x+(1)/(5)cos^(5)x+…..oo=

p,q,r are distinct cube roots of non-zero complex number z. Let a,b,c be complex numbers satisfying ap+bq+crne0. Then find the value of ((aq+br+cp)(ar+bp+cq))/((ap+bq+cr)^2).

(1,5) is a pointin the region 2x-yge4,2x+5yle2

If int_0^((pi)/(2))(dx)/(1+tanx+cotx)=a and int_0^(pi/2)(tanx)/(1+tanx+cotx)=b then which of the following is/are correct

Two straight lines are perpendicular to each other. One of them touches the parabola y^(2) =4a ( x+a) , and the other touches y^(2) =4b (x+ b) .Then locus of point of intersection of two lines is

Find probability distribution P(X) of random variable X if sum of mean and variance is 24 and their product is 128.

Integrate the functions (sinx)/(1+cosx)

If C_(ij)is the co-factor of a_(ij) and A={:[(1,2,3),(2,3,2),(1,2,2)]:} then

Let P(a sec theta,b tan theta) and Q(a sec varphi, b tan varphi)where theta+varphi=(pi)/(2) be two points on the hyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If (h, k) is the point of intersection of the normals at P and Q, then k=

Differentiate tan^-1sqrt((1-x^2)/(1+x^2)) with respect to cos^-1""x^2

If alpha, beta , gamma are the roots of x^(3)+4x+1=0, then the equation whose roots are (alpha^(2))/(beta+gamma),(beta^(2))/(gamma+alpha),(gamma^(2))/(alpha+beta) is

Find the equation of tagents to the parabola y(2)=16x which are parallel and perpendicular respectivelyto the line 2x-y+5=0, also find the co-ordinates of the points of contact also.

The straight lines l_(2)||l_(2)||l_(3) and lies in the same plane A total of m points are taken on l_(1) ,n points on l_(2) and k point on l_(3), then maximum number of triangles formed with vertices at these points are

Solve the following Linear Programming Problems graphically : Minimise Z = -3x + 4y subject to x+2y le 8, 3x+2y le 12, x ge 0, y ge 0

Select the CORRECT order of I.E._2 ?

Find the equation of the common chord of the following pair of circles x^2+y^2+2x+3y+1=0 x^2+y^2+4x+3y+2=0