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If A=sin(2pi)/(7)+sin(4pi)/(7)+sin(8pi)/(7) and B=cos(2pi)/(7)+ cos(8pi)/(7 ) then sqrt(A^(2)+B^(2)) is equal to

Find the are length of the curve x= (1)/(4) y^(2)- (1)/(2) ln y between the points with the ordinates y= 1 and y=2

The value of a, for which the points A, B, C with position vectors 2hat(i)-hat(j)+hat(k),hat(i)-3hat(j)-5hat(k),ahat(i)-3hat(j)+hat(k) respectively are the vertices of a right angled triangle with C=(pi)/(2)are

If b gt a, then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a, b) "" (b) Both roots in (-oo, a) (c) Both roots in (b, +oo) "" (d) One root in (-oo, a) and the other in (b, +oo)

f: R^(+)cup{0} rarrR^(+)cup{0},f(x) = sqrtx. g : R rarr R , g(x)=x^2 -1 then find fog .

The value of x that satisfies tan^(-1)(tan -3)=tan^(2)x is

Ifalpha, beta, gammaare therootsofx^3 +px^2 +qx +r=0then find sum(1)/( alpha )

Which of the following curve is represented by y^(2)=1-x?

Two persons A and B toss two coins one after another. The person who throws one head and one tail is the winner. If A starts the game the probability that B wins the game is

I : If (a + b) c = (a - b) c = 0 then (a xx b) xx c = 0 II : If a xx (b xx c) is a vector perpendicular to a,b,c

Let ABCDEF is a regular hexagon A(z_1),B(z_2),C(z_3),D(z_4),E(z_5), F(z_6) in argand plane where A,B,C,D,E and F are taken in anticlockwise manner. If z_1=-2, z_3=1-sqrt3i.

Which of the following sentences are propositions and which are not ? Write with reason :Is 9 lt 3 ?

|{:(sqrt(14)+sqrt3,sqrt(20),sqrt5),(sqrt(15)+sqrt(28),sqrt(25),sqrt(10)),(3+sqrt(70),sqrt(15),sqrt(25)):}|=.......

Find the probability of getting two aces when two cards are drawn from pack of 52 cards.

If int_(-20)^(-10)((x^(2)-x)/(x^(3)-3x+1))^(2)+dx+int_(1/21)^(1/11)((x^(2)-x)/(x^(3)-3x+1))^(2)dx + int_(21/20)^(11/10)((x^(2)-x)/(x^(3)-3x+1))^(2)dx=l then l+420/7939 is equal to

Determine the binomial distributionwhose mean is 9 and whose standard deviation is(3)/(2)

Prove that tan^(-1)(2/11) + tan^(-1)(7/24) = tan^(-1)(1/2)

If harmonic mean of three numbers 2,4, and x is 3, then x is equal to ____________

The order and degree of the differential equation y = ([5+((dy)/(dx))^(2)]^(4//3))/((d^(2)y)/(dx^(2))) is

Integrate the functions 2xsqrt(x^(2)+1)

A committee of 4 persons is to be formed from 2 ladies 2 old man and 4 youngmen suchthat it includes at least 1 lady, at least one old man and at most 2 youngmen. Then the total number of ways in whichthiscommitteecan be formed is

Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a thrice differentiable function such that|f (x) || le 1 AA x in [-1, 1],then choose the correct statement (s)

Let I_(n) = int _(0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx wheren in W. If l _(1)^(2)+l _(2)^(2) +l_(3)^(2)+ ……. + l _(20)^(2) =mpi^(2), then find the largest prime factor of m.

Given that the event A and B aresuch that P(A) = 1//2, P (Acup B) = 3 //5 and P(B) = P . Find p, if they aremutually exclusive

Find the slope of the lines whose inclinations are given.30^@ .

Which of the following statement is//arecorrect?

Simplify ((cos alpha + i sin alpha)^(4))/(sin beta + i cos beta)^(8)

Statement-I: int_(-4)^(-5)sin(x^(2)-3)dx+int_(-2)^(-1)sin(x^(2)+12x+33)dx=0 Statement-II: int_(0)^(2a)f(x)dx=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

int (x^(2))/(x^(4)-x^(2)-12)dx

x^(2)+6x+y^(2)-8y=56 If the above equation is written in the form (x-h)^(2)+(y-k)^(2)=r^(2), what is the value of r?

Point of intersection of tangents to the paraholu (y-2)^(2) = 4(x-1) at the ends of lutus rectum Is

If y= A sin x+ B cos x, then prove that (d^(2)y)/(dx^(2))+y=0.

The smallest A such that A cup {1,2} = {1,2,3,5,9} is

Number of 3 xx 3 non symmeteric matrix A such that A^(T)=A^(2)-I and |A| ne, 0 equal to

(p^(1/4)q^(-3))/(p^(-2)q^(1/2)) Which of the following is equivalent to the expression above, where p gt 1 andq gt 1?

f(x)= {((1)/(2)-x ",",0 le x lt (1)/(2)),(1",",x= (1)/(2)),((3)/(2)-x",",(1)/(2) lt x le 1):} Discuss the continuity of f(x)

Evaluate int x sqrt(4x + 3)dx.

Given f(x) is a periodic function with period 2 and it is defined as ""f(x) = {{:([cos""(pix)/(2)]+1",",,0lt x lt 1), (2-x",",,1 le x lt 2):} Here [*] represents the greatest integer le x. If f(0)=1, then draw the graph of the function for x in [-2, 2].

Show that the height of a cone of maximum volume inscribed in a sphare has the ration with the radius of sphere as 4 : 3.

Integrate the function is exercise. sqrt(1-4x-x^(2))

The system of circle orthogonal tox^(2) + y^(2) + 2gx + 10 = 0is

If possible , using elementary row transformations , find the inverse of the following matrices : (i) [{:(2,-1,3),(-5,3,1),(-3,2,3):}] (ii) [{:(2,3,-3),(-1,-2,2),(1,1,1):}] (iii)[{:(2,0,-1),(5,1,0),(0,1,3):}]

Evaluate the following integrals: int(x^3 +5x^2 -4)/x^2 dx

Find the unit vectors perpendicular to the vectors. hati+hatj, hati-hatk

If x is real then the range of (x^(2)-2x+9)/(x^(2)+2x+9) is

If the plane passing through the points hati+hatj+hatk,2hati-hatk and the origin meets the line passing through the points hati+3hatj-2hatkandhati-hatj+3hatk at the points A, then A=

IF therootsof x^3- 13x^2 +kx- 27=0are inG.Pthenk=

Leta _(l) = (7)/(4) ((2)/(3)) ^( l -1), j in N.lf b _(1) = a _(j) ^(2) + a _(j),sum of the infinite sereies formed by b _(j) 's is (10 + alpha ) where [ (1)/( alpha ) ] is equal to ([] represent greatest integer function)

f: [0,oo) rarr [0,oo) , f(x) = x/(1+x) then the function f is .........