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The equation of the locus of 2 such that |(z-i)/(z+i)|=2, where z = x + iy is a complex number , is

If A'=[(-2,3),(1,2)] and B=[(-1,0),(1,2)] then find (A+2B)'

Let R be the set of all real number and f: [-1,1] to R is difined by f (x) = {{:( x sin "" (1)/( x ) "," , x ne 0 ), ( 0"," , x =0 ) :}. Then

Compute P for n=11,r=0

If f(x) = cos x an g (x) = sin x then inta(logf(x))/((f(x))^(2))dx

Two cards are drawn from the well shuffled pack of 52 playing cards with replacement. Find mean and standard deviation of the number of queens.

If Integration using rigonometric identities : int (cos 4x+1)/(cot x-tan x)dx=A cos 4x+c then A=....

If a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle between b and c is (2pi)/3, then [(a, b, c)] is equal to

Cards are drawn one by one with replacement from pack of cards until red card appears. Findthe probability of getting king card in last draw.

If int_(0)^(alpha)(dx)/(1-cos alpha cosx)=(A)/(sin alpha)+B(alpha ne 0), then possible values of A and B are

A point P moves on x-y plane such that PS +PS' = 4 where S(K,0) and S'(-K,0), then which of the following is not true about the locus of P?

The volume of the parallelepiped whose edges are vec(OA)=2hat(i)-3hat(j),vec(OB)=hat(i)+hat(j)-hat(k),vec(OC)=3hat(i)-hat(k) is

Let bara,barb and barc are three mutually perpendicular unit vectors and a unit vector barr satisfying the equation (barb times barc) times (barr times bara)+(barc times bara) times (barr times barb)+(bara-barb) times (barr -barc)=0 then barr is

(1/(1!) +1/(2!) +1(3!) + .....oo) (1/(2!) +1/(3!) +1(4!)-1/(5!) .....oo)

Evaluate : (i) int_(0)^(2pi) {sin(sinx)+sin(cosx)}dx , (ii) int_(0)^(pi) (dx)/(5+4cos2x) (iii) int_(pi//2)^(0)(2 lnsinx-ln sin2x)dx , (iv) int_(0)^(pi//2) (asinx+bcosx)/(sinx+cosx)dx , (v)int_(0)^(pi//2) (sinx-cosx)/((sinx+cosx)^(2))dx

If a set A has 12 elements. Find the number of subsets of A having 4 elements

Find the number of 5 letter words that can be formed using the letters of the word 'MIXTURE' which begin with an vowel when repetitions are allowed.

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then The minimum number of values where f ''(x) vanishes on [0,2] is :

If numberof pointsofthefunctionf(x) =[2+10sin x],i nx in[0,(pi)/(2)] is sameas numberof points of non- differentiablity of the functiong(x)=(x-1)xx(x-2)|(x-1)(x-2). . .(x-2m(|,(m in N) i nin (-oo,oo) ,thenthevalueof m is

The position vector of a point R which divides the line joining P(6, 3, -2) and Q(3, 1, -4) in the ratio 2 : 1 externally is

Consider the following two statements: P : If 7 is an odd number, then 7 is divisible by 2. Q : If 7is a prime number, then 7 is an odd number. IfV_(1) is the truth value of the contrapositive of P and V_(2) is the truth value of contrapositive of Q then the ordered pair (V_(1),V_(2)) equals:

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(0) ^(1) f (1-t ) e ^(-cos pit) dt - int _(1) ^(2) f (2-t) e ^(cos pit) dtis equal to :

Given the graph of y= f (x)

Prove that the line joining two points of an ellipse the difference of whose eccentric angles is constant touches a fixed ellipse

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

Examine the function f(x)=2x^(2)-5 for its continuity at the point x = 3.

A and B throw a dice alternately til any one gets a 6 on the and win the game. If A begins the game find the probabilities of winning the game.

LetA={x inZ : 0lele 12}. showthat R={(a,b):|a-b| isa multipleof 4 is (i)reflexive, (ii)symmetric and (iii)transitive. Findthe setof elementsrelatedto 1.

If d/(dx)(tan^(-1)(2^(x+1)/(1-4^(x))))=a^(x+1)/(1+b^(x))loga, find the value of a and b.

The square root of -5 - 12i is

A(-1, 2, 3), B(1, 1, 1) and C(2, -1, 3) are three points in the plane. The unit vector perpendicular to the plane ABC is …………..

Let ABCD be a cyclic quadrilateral such that AB=2, BC=3, angle B =120^(@) and area of quadrilateral =4sqrt3. Which of the following is/are correct ?

Let ** be a binary operation on the set Q of rational numbers as followsa**b=a^2+b^2. Is the binary operation commutative and associative ?

Writephiset in the intention(or specification form).

Evaluate the following integrals inte^(x)(tanx+logsecx)dx

Find the square root of -47 + i8sqrt3

For two independent events A and B, which of the following pair of events need not be independent ? a)A^',B^' b)A,B^' c)A^',B d)A-B,B-A

The solution of log((dy)/(dx)) = ax + by is

A school has 3 freshmen for every 4 sophomores and 5 sophomores for every 4 juniors. If there are 240 juniors in the school, how many freshmen are there?

r_1, r_2are the radii of two non intersecting circles having A , B as centres. If 'P' is the mid- point of AB ,then the perpendicular distance of P from their radical axis is

Letvec(a) = xhat(i) + 3hat(j) and = (x – 1)hat(i) – 2hat(j) and angle between vec(a) and vec(b) is obtuse then number of possible integral values of x is

In the value circuit, C=(sqrt(3))/(2)muF,R_2=20omega, L=sqrt(3)/(10)H, and R_1=10omega .Current in L-R_1 pathsis I_1 and in C-R_2 path it is I_2. The voltage of A.C source is given by, V=200sqrt(2)sin(100t) volts. The phase difference between I_2 and I_2 is :

ptoq is equivalent to

Solve 27x^3+42x^2-28x-8=0 given that its roots are in geometric progressive.

If the sum of all the binomial coefficients in (x+y)^n is 512 , then the greatest binomial coefficient is

Compound A(C_7H_8O)is insoluble in water, dilute HCl & aqueous NaHCO_3, it dissolves in dilute NaOH.When A is treatedwith Br_2 water it is converted into a compound C_7H_5OBr_3 rapidly. The structure ofA is

If A={1,2,3},B={1,4,6,9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is

e^(log(cosh^(-1)(2))) is equal to

Let be a binary operation on the set Q of rational numbers as followsab=a^2+b^2. Is the binary operation commutative and associative ?