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The value of (d)/( dx) int_(x^2)^(x) sqrt( cos t) dt at x= 0 is

From a bag containing 4 red and 2 white balls two balls are drawn. The probability that both the balls are red is:

Find the mean and variance for the frequency distribution.

C_0 -C_2 + C_4 - C_6 +….....

The solution of xdx + ydy = x^(2) y dy - xy^(2) dx is

15 coins are tossed. If the probability of getting at least 8 heads is equal to p, then (8)/(p) is equal to

If A,B ,C are the maximum velocities of the particles moving according to the law s=60t -5t^3,s=6t-1/2t^2,s=10t-7t^3 respectively then the ascending order of A,B,C is

{{:(hx +4y=-10),(kx +3y=-15):} If the graphs of the lines in the system of equations above intersect at (-3,1), what is the value of k /h ?

If 0lexle1/2, then Sin^(-1)x+Sin^(-1)(x/2-sqrt(3-3x^(2))/2)=

The value of the integral, int_(3)^(6)(sqrtx)/(sqrt(9-x)+sqrtx)dx is

Find the value of x for which: |{:(3,x),(x,1):}| = |{:(3,2),(4,1):}|

The numberofways in which4 letters canbe putin 4addressedenvelopesso that I :Atlestone lettergoesintowrongenevelope is 23.II: nolettergoesintothe envelopementfor it is 9 .

Numbers are selected at random one ata time from the two digit numbers 00, 01, 02, 03 ….99 with replacement . An event E occurs if the product of the 2 digits of a selected number is 18. If four numbers are selected, the probability that the event E occurs atleast 3 times is

Evaluation of definite integrals by subsitiution and properties of its : int_(1)^(e)(1+xlogx)(e^(x))/(x)dx=...........

If f(x)=1/x and g(x) = 0 then fog is

Find the magnitude of the vector vec(PQ), its scalar components and the component vectors along the co-ordinate axes, if P and Q have the co-ordinates P(-1,30, Q(1,2)

Find the volumes of the solids enclosed by the surfaces generated by revolving the lines y=e^(-x),x=0,y=0(0lexlt+oo): (a) about the x-axis (b) about the y-axis.

Find the magnitude of the vector vec(PQ), its scalar components and the component vectors along the co-ordinate axes, if P and Q have the co-ordinates P(-1,-2), Q(-5,-6)

If A+B=[{:(4,3,2),(4,1,7),(3,2,0):}]andA-B=[{:(6,1,4),(-4,3,9),(5,8,2):}]Then find A and B.

2 tanh^(-1)(1/2) is equal to

Evaluate the following integrals intsinsqrt(x)dx

Let the tangent at a point P on the ellipse meet the major axis at B and the ordinate from it meet the major axis at A. If Q is a point on the AP such that AQ=AB, prove that the locus of Q is a hyperbola. Find the asymptotes of this hyperbola.

Thevalue of int(1+sinx)/(1-sinx)dx

For every real number x. let f(x) = (x)/(1!)+(3)/(2!)x^(2)+(7)/(3!)x^(3)+(15)/(4!)x^(4)+cdots Then the equation f(x) = 0 has

If f(x)=(x-[x])sin""1/x, then at x=0, f(x) is

If the circles of the maximum area inscriabed in the region bounded by the curves y=x^(2)-2x-3 and y=3+2x-x^(2) , then the area of region y-x^(2)+2x+3le0,y+x^(2)-2x-3le0 and sle0.

Draw the graph of y = log_(e) (sin x).

If A(x)=|(1,1,1),((e^(x)+e^(-x))^(2),(pi^(x)+pi^(-x))^(2),2),((e^(x)-e^(-x))^(2),(pi^(x)-pi^(-x))^(2),-2)| then A(x) =

Evaluate |[x^2-x+1,x-1],[x+1,x+1]|

Let Z=re^(itheta)(r gt 0 and pi lt theta lt 3pi) is a root of the equation Z^(8)-Z^(7)+Z^(6)-Z^(5)+Z^(4)-Z^(3)+Z^(2)-Z+1=0. the sum of all values of theta is kpi. Then k isequal to

{:(I. |a xx b + b xx c + c xx a|, a. "Area of" Delta ABC),(II. |AB xx cd + BC xx AD + CA xx BD, b. 2 xx "Area of" Delta ABC),(III. |(a - c) xx (b - d)|, c. 4 xx "Area of" Delta ABC),(IV. (1)/(2) |(a - b) xx (b - c)|,d. 2 xx "Area of quandrilateral" ABCD),( , e. "none"):}

For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+....x^(2)/2+x+1, f'(1)=mf ' (0), where m is equal to

Find the number of quintuples (x,y,z,u,v) of positive integers satisfying both equations x+y+z+u= 100 and x+y+z+v= 70

Consider the system of simultaneous linear equation 2x-3y+5z=12 3x+y+lambdaz=u x-7y+8z=17 {:(,"List-I",,"List-II",),((P),"for unique solution" ,(1),lambda=2.mu ne, 7),((Q),"For infinite solutions",(2),lambda ne 2. mu in R,),((R),"For no solution",(3),lambda = 2. mu = 7,):}

int_(ln lambda)^(ln(1/lambda))(f(x^(2)/3)(f(x)+f(-x)))/(g(3x^(2))(g(x)-g(-x)))dx=

The value of root(3)(5+2sqrt(13)) + root(3)(5-2sqrt(13)) is= ……………..

Sketch the graphs of the following functions. f(x) = (x-1)^2

If the 5th term is the term independent of x in the expansion of (x^(2//3) + 1/x)^n then n=

Assertion (A) : The number of real solutions of the equation sin x = x^(2) + 3x + 4 is zero Reason (R): -1 ge sin xle 1, AA x in R

The range of f(x) is a subset of the given set

Integrate the following int(cosec^2x)/(1+cotx)dx

Let A(x_1,y_1),x_1 ne 0, be a point of the curve y^2=x^3. Tangent at A meets the curve again at B(x_2,y_2). M and N are foot of perpendicular drawn to x-axis from point A and B respectively. T is the point where tangent at A meets x-axis, then :

If nobjectsare arrangedin arowthen the numberof waysof selectingthreeof theseobjectsso thatnotwoof themare nextto eachother is

I: If a and b are positive real numbers then sqrt(-a) xx sqrt(-b) = -sqrt(ab) II : The Arg [(1 + isqrt3)/(1 - isqrt3)] is 240^(@) Which of the statements are true

If y= (sin^(-1) 2x)^(2) + (cos^(-1) 2x)^(2), then (1-4x^(2))y_(2) - 4xy_(1)=

Fundamental theorem of definite integral : I=int_(0)^(1)(sinx)/(sqrtx)dx and J=int_(0)^(1)(cosx)/(sqrtx)dx then which of the following statement is true ?

Evaluate the following inegrals int(dx)/(x^(2)-3x+2)

Let A and B be events with P(A)= 3/8, P(B)= 1/2 and P(A cap B) = 1/4, Find P(A^c cap B)

If x, y are positive real numbers satisfying the system of equations x^(2) + ysqrt(xy) = 336, y^(2) +xsqrt(xy) = 112,then x + y equals: