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A subset of the additive group of real numbers which is not a sub group is

Forthe equation |x^(2)| + |x| -6=0, the roots are

{:(" "Lt),(n rarr oo):} ((1)/(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)/(sqrt(6n-3^(2)))+....+1/n)=

Evaluate int cot^(4) xdx

int tan^-1 sqrtx dx is equal to:

Evaluate the following:lim_(xtoinfty)log_e(1+a/x)^x

If (a + ib)^5 = alpha+ibeta then (b + ia)^5 is equal to

int (dx)/(sqrt(1 - x^2)) is equal to :

Assertion (A) (x^(2)-1)/(x^(2))e^(x^(2)+1)/x dx = e^(x^(2)+1)/x + c Reason ( R) intf^(')(x)e^(f(x))dx = f(x) +c

The shortest distance between the line r = (I + 2j + 3k) + t (I + 3j + 2k) and r = (4i +5j + 6k) + t (2i + 3j + k) is

Findthe areaof theregionboundedby theparabolay^2 = 2pxand x^2 = 2py.

Find the maximum and minimum values in the following functions :x^(3)-9x^(2)+15x-1,

Find the value of [a] if the lines (x-2)/3= (y +4)/2 =(z -1)/5" & " (x +1)/(-2) =(y -1)/3 = (z -a)/4 are coplanar (where [] denotes greatest integer function)

The solution of (x)^(2)+(x+1)^(2)=25 (where (.) denotes the least integer function) is

Rectangle A has twice the area of Rectangle B. The width of Rectangle A is less than 1/2 the width of Rectangle B. {:("Quantity A","Quantity B"),("The area of Rectangle A","The area of Rectangle B if its"),(,"width is increased by more"),(,"then 2"):}

If A is any aquare matrix of order 3xx3 then |3A| is equal to

If f(x+y)=f(x)+f(y) AA x, y in R and f'(0) exists and sum_(r=16)^(40)intf(x)dx=20900. Then find the area of the region R that in completely bounded by the graph of y_(1)=f(x)-1 and y_(2)=x^(2)-4.

Sigma_(r=1)^(oo)tan^(-1) (2/((r +2))) is

If (a+bi)^(11) = x + iy, where a, b, x, y in R, then (b + ai)^(11) equals

If a vector vecr is equall inclined with the vectors veca=costhetahati+sinthetahatj, vecb=-sinthetahati+costhetahatj and vecc=hatk, then the angle between vecr and veca is

If alpha, beta , gamma are the roots of 2x^(3)-2x-1=0, ( Sigma alpha beta)^(2) is equal to

Find k if the following pairs of circles are orthogonal x^2+y^2-16y-k=0 x^2+y^2+4x-8=0

Match the values of x in List II where derivative of the function in List I is negative.

Ifalpha , beta in (0,pi/2), sinalpha =4/5andcos( alpha+ beta) = ( -12)/(13)then sinbetais equalto

int_(0)^(1)(1-x)/(1+x)dx=

Let S be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting numbers is :

Let A = {1, 2, 3) and B= {a,b,c}, andf= {(1, a),(2, b), (P, c)} be a function from A to B. For the function f to be one-one and onto the value of P =

Evaluate int_(0)^(t)[|sin^(-1)(sinx)|]dx" where "tin(2npi,(8n+1)(pi)/(4)).

Find the value of the sqrt199correct to 4 decimal places

Let 'A' be the area bounded by the curves y^(2) = 4k_(1)x, k_(1) in [1/8, 1/4] x^(2) = 4k_(2) (2-y), k_(2) in [1/4, 1] and y-axis in the first quadrant. Then the least value of A is

If A(-2, 1), B(0, -2), C(1, 2) are the vertices of a triangle ABC, then the perpendicular distance from its circumcentre to the side BC is

The point of contact of 9x+8y-11=0 to the hyperbola 3x^(2)-4y^(2)=11 is

If an arithmetic series sumtn converges, which of the following is true about t_n?

Box-I contains 2 gold coins, while another Box-II contains 1 goldand 1 silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?

If (1)/(3){:[(1,2,3),(2,1,-1),(-2,2,-1):}] and A*A^(T)=I A^(-1) is

int(x^(9))/((4x^(2)+1)^(6)) dx

Solve the following Linear Programming Problems graphically : Maximise Z = 5x + 3y subject to 3x+5y le 15, 5x+2y le 10, x ge 0, y ge 0

Find the area of the region enclosed by the given curves . y=cosx , y=sin2x , x=0, x=(pi)/(2)

Which kind .............

If the line x=y=z intersect the line xsinA+ysinB+zsinC-2d^(2)=0=xsin(2A)+ysin(2B)+zsin(2C)-d^(2), where A, B, C are the internal angles of a triangle and "sin"(A)/(2)"sin"(B)/(2)"sin"(C)/(2)=k then the value of 64k is equal to

If thelocus of the complex number z given by arg(z+i)-arg(z-i)=(2pi)/(3) is an arc of a circle, then the length of the arc is

if |{:(a^(2)+lamda^(2),ab+clamda,ca-blamda),(ab-clamda,b^(2)+lamda^(2),bc+alamda),(ca+blamda,-bc+alamda,c^(2)+lamda^(2)):}||{:(lamda,c,-b),(-c,lamda,a),(b,-a,lamda):}|=(1+a^(2)+b^(2)+c^(2))^(3), then find the value of lamda

If f (x) ={{:( xcos ((1)/(x)) ,"for " xne 0),( 0,"for " x=0) :},then at x =0

Let x_(1), x_(2), …… , x_(n) be in an A.P. If x_(1) + x_(4) + x_(9) + x_(11) + x_(20) + x_(22) + x_(27) + x_(30) = 272, then x_(1) + x_(2) + x_(3) + ...... + x_(30) is equal to