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Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards . What is the probability that i. all the five cards are spades? ii only 3 cards are spades? iii. none is a spade?

Obtain the following integrals : int sqrt(ax-x^(2))dx

(1)/(3)-(1)/(2).(1)/(9)+(1)/(3).(1)/(27)-(1)/(4).(1)/(81)+….oo=

If cos alpha+2cos beta+3cos gamma=sinalpha+2sinbeta+3singamma=0 then sin 3alpha+8sin3 beta+27sin 3gamma=

Draw the graph of followin function {:((i), y=4x^(3)-30x^(2)+72x-55,(ii), y=x^(3)+x^(2)+x-3),((iii), y=x^(4)-8x^(3)+22x^(2)-24x+8.5, (iv), y=x^(4)-6x^(2)-8x+13),((v),y=x^(4)-4x^(3)+8x^(2)-8x-21,(vi),y=x^(4)+2x^(2)+4x+1):}

Find the number of proper divisors of 38808 which are not divisible by 7. Also find their sum.

A bag contains 2 white and 1 red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If X denotes the number of red balls recorded in the two draws, describe X.

The straight line (x)/(4)+(y)/(3) =1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9) =1 at two points A and B, there is a point P on this ellipse such that the area of DeltaPAB is equal to 6(sqrt(2)-1). Then the number of such points (P) is/are

Show that the angle between the circles x^2+y^2=a^2, x^2+y^2=ax+ay is (3pi)/4

Let R be relation defined on the set of natural number N as follows : R = {(x,y) : x in N, y in N , 2x + y =41}. Find the domian and range of the relation R . Also verify whether R is reflexive, symmetric and transitive.

Arithmetic mean of the series2,-2,2,-2,…….., up to 100times is ___________

Given that veca*vecb=0andvecaxxvecb=vec0 . Whatcan you conclude about thevectors vecaandvecb?

Evaluate : int(logx)/(x)dx.

If A = (2, 3), B = (-2, -5), C =(-4, 6) and if P is a point on BC such that AP bisects the angle A, then P =

Evaluate the following integrals inttan^(-1)((2x)/(1-x^(2)))dx

Evaluateint(sin^(2)x)/(1+cosx)dx

If the three lines x-3y=p.ax+2y=q and ax+y=r from a right - angled triangle then.

A person stands at a point A due south of a tower and observes that its elevation is 60^(@). He then walks westwards towards B, where the elevation is 45^(@). At a point C on AB produced, he finds it to be 30^(@). Then AB/BC is equal to

If alpha, beta, gamma are the roots of the cubic equation x^(3)+qx+r=0 then the find equation whose roots are (alpha-beta)^(2),(beta-gamma)^(2),(gamma-alpha)^(2).

When the axes are rotated through an angle 45^@, the transformed equation of a curve is 17x^2-16xy+17y^2=225. Find the original equation of the curve.

1 +(1)/(4) +(1.3)/(4.8)+(1.3.5)/(4.8.12)+… isequalto

The mid-points of the sides of a triangle are (2,3,-1),(0,8,5)and(5,7,11). The distance of the origin from the vertex of the triangle which is farthest from it is

A tangent to x^(2)=32y meets xy=c^(2)at P & Q. The locus of mid-point of PQ is a parabola whose latus rectum is-

Let D, E and F be the middle points of the sides BC,CA and AB respectively of a triangle ABC. Then, AD + BE + CF equals to

Solvedy/dx+(2xy)/(1+x^(2))=(4x^(2))/(1+x^(2))

Let f:[0,1] rarr R be a function.such thatf(0)=f(1)=0 and f''(x)+f(x) ge e^x for all x in [0,1].If the fucntion f(x)e^(-x) assumes its minimum in the interval [0,1] at x=1/4 which of the following is true ?

Match the locus of the points in List-I with the curves in List-II (Here, p.4 and r are constants andt, theta and lamdaare parameters) The correct match is

int_(0)^(pi//2) (Cos x)/(1+Sin x) dx=

(A - B) cup (B - A) =

Choose the correct answer. Area lying between the curves y^2=4x and y=2x is :

Integrate the functions (6x+2)/(1+2x+3x^(2))

Draw the graph of the function f(x) = (1/x)^(x)

If [x] denotes the greatest integer function. Draw a rough sketch of the portions of the curvesx^(2) = 4[sqrt(x)] y and y^(2) = 4[sqrt(y)] x that lie within the sqaure {(x,y)|1le x le 4, 1 ley le 4} Find the area of the part of the square that is enclosessd by the two curves and the line x + y = 3

A circle of area 20 sq. units is enteredat the point O. Suppose DeltaABC is inscribed in that circle and has area 8 sq. units. The central angles alpha, beta and gamma are as shown in the figure. The value of(sin alpha+sin beta+sin gamma) is equal to :

If alpha, beta are the roots of x^(2)- p(x+1)-c=0 then (alpha^(2)+2alpha+a)/(alpha^(2)+2alpha+c)+ (beta^(2)+2beta+1)/(beta^(2)+2beta+1)=

If alpha, betaare the roots of the quadratic equation x^(2)+ax +b=0, (b ne 0), then the quadratic equation whose roots are alpha -(1)/(beta), beta-(1)/(alpha) is

Find the principal value of sin^-1(-1)

A straight line is drawn through the point P(1,4) Find the least value of the sum of intercepts made by line on the coordinates axes. Also find the equation of the line.

The value of the integral int(0)^(pi//2)(dx)/(1+(1)/(6)sin^(2)x) is

Find the area of the region enclosed between curves y = |x-1| and y=3-|x|.

A=[{:(0,0,-1),(0,-1,0),(-1,0,0):}],the correct statement is ......

If the points (2,0) (0,1), (4,0) and (0,a) are concylic then a=

Simplify : costheta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sintheta,-costheta),(costheta,sintheta):}]

Integrate the following : intx^31dx

An urn contains r red balls and b black balls. Now, match the following lists:

lim_(xto0)[x]

(d)/(dx) (log_(5) x^(2))= ……..