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If 1,alpha,alpha^(2),.......,alpha^(n-1) are the n^(th) roots of unity, then sum_(i=1)^(n-1)(1)/(2-alpha^(i)) is equal to:

If displacement s, time t are related by s=sqrt(t) then I : Acceleration is proportional to velocity. II : Velocity is inverslyproportional to displacement.

If1 , omega , omega^(2)are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

A square is inscribed in the circel x^(2)+y^(2)-2x+7y-8=0 whose diagonals are parallel to axes and a vertex in the firstquadrant is A then OA is

Consider the matrix A=[(4,1),(1,5)] on applying elementary row operations R_(2)toR_(3)-n_(1), it becomes [(4,3),(-11,-4)], then the value of n=

Ifalpha=2vec(i) +3vec(j) -5vec(k) and beta= vec(i)-vec(j) , then find the value of alpha xx beta

Obtain the following integrals : int(x^(2))/(1-x^(4))dx

The slope of a line is 3 times the slope of the other line and the tangent of the angle between them is 4/13, sum of their slopes is equal to

If f(x) = {(-2sinx,for xle -pi/2)(asinx+b,for -pi/2ltxltpi/2)(cosx,for xgepi/2):} everywhere then the ordered pair(a,b) is

Simplify tan^(-1)[(a cos x -b sin x)/(b cos x +a sin x)] if a/b tan x gt -1

Solve y log y dx + (x-log y) dy = 0.

State with reason, "Collection of all winged horses " is set or not ?

The loucs of the midpoints of the chords of the circle 4x^(2)+4y^(2)-12x+4y+1=0 which subtend an angle of pi//3 as its centre is a circle of radius

A circle passes through origin and meets the axes at A and B so that (2,3) lies on bar(AB) then the locus of centroid of DeltaOAB is

Position of a particle moving in straight line is x=t^3-3t^2.If average speed of particle in interval 0-4 sec is 'a' and average velocity in same period is 'b'. Then what is the value of a/b.

A cone with its height equal to the diameter of the base is expanding in volume at the rate of 50 cm^(3)//sec. If the base has area 1 m^(2) , the radius is increasing at the rate ……….

If f(x)= |sin x|, then

The solution of the differential equation y' = (1)/(e^(-y) - x) is

A square matrix A, of order 3, has |A|=5, find |A.adj A|.

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

Absorption of water, simple sugar and alcohol take place in :-

Find a unit vector perpendicular to each of the vector veca+vecbandveca=3hati+2hatj+2hatkandvecb=hati+2hatj-2hatk.

Find the equation of the circle passing through the origin and having the centre at (-4,3)

int(x+sqrt(x^(2)+1))^(n)dx

Let S = {x in R : sqrt(x^(2) + 19 x ) - sqrt(x) + sqrt(x + 19) = x + 6 . 08} , "then" sum_(x in S) x = ________

Evaluate the following definite integrals . int_(0)^(4)(x+e^(2x))dx

A telephone exchange receives on an average 180 calls per hour. Find the probability that it will receive only 2 calls in a given minute.

From a point A(1,0) on the circle x^(2) + y^(2) - 2x + 2y + 1 =0, a chord AB is drawn and it is extended to a point P such that AP = 3AB. The equation of the locus of P is

If nsinx=log_(e)x has exactly 1 root, then find the possible value of n(ninN).

Find the number of ways of arranging the letters of the word SPECIFIC. In how many of them the two C's come together

The sequences {x_(n)}is definedby x_(k+1)=x_(k)^(2)+x_(k) and x_(1) =1/2Let S = [ 1/(x_(1)+1)+1/(x_(2)+1)+...+1/(x_(m)+1)] ( where [.] denotes the freatest integar function )

(1-1/(1!) +9/(2!) +(27)/(3!) + .....oo) (1+9/(1!) +(81)/(2!)+(729)/(3!)+ .....oo)=

Vapour density of an ideal gas which has a density 2.16 g//L at 1.12 atm pressure & 273 K temperature (R=0.0821)

Compute {:(" Lt"),(xrarr0):}((sinax)/(sinbx))bne0,aneb

Determine 'a' such that x^2 - 11x + a and x^2 - 14x + 2a may have a common factor.

Show that every polynomial function is continuous.

Find the equation of lines joining the points. (a,a,a) and (a,0,a)

Find the conditions that the tangents drawn from the exteriorpoint (g,f)toS= x^(2) + y ^(2) + 2gx + 2fy + c=0are perpendicular to each other.

If underset(x to 0)lim (x^(-3) sin 3x+ax^(-2) +b) exists and is equal to 0, then

If U_(n)=int_(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of zero, then The value of U_(n) is

Draw the graph of y=tan^(-1)((2x)/(1-x^(2)))

Evaluate the following integrals. int(1)/(sqrt(x^(2)+2x+3))dx

A unit vector perpendicular to each of the vectors 2hat(i)-hat(j)+hat(k)and 3hat(i)-4hat(j)-hat(k) is

Find the coordinates of the centre of gravity of the catenary y=(1)/(2) (e^(x) + e^(-x))= cos h x between A(0, 1) and B(a, cosh a).

Equation of a circle with centre (-4,3) touching internally and containing the circle x ^(2) + y ^(2) =1 is

The middle term in the expansion of (x/3-2/sqrt(x))^(6) is

Write the equation of the plane passing through the point (2, 3, 1) andperpendicular to the line.(x-1)/1=(y-2)/-1=(z+1)/3