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If a_(K)=(1)/(K(K+1)) for K=1, 2, 3....n, then (sum_(K=1)^(n)a_(K))^(2)=

If y = tan ^(-1)((2x)/( 1+15x^(2)) ) , and (dy)/(dx)= ( lambda)/( 1+25x^(2))-( mu)/( 1+9x^(2))," then "lambda + muequal

Solve(2sqrt(xy-x)dy+dx=0

The sum of the series(12)/(2!)+(28)/(3!)+(50)/(4!)+(78)/(5!)+…is

Consider the regions A = {(x,y)|x^(2)+y^(2) le 100} and = {(x,y) | sin (x+y) gt 0}in the plane. Then the area of the region Ann B is -

Using differentials, find the approzimate value of each of the following up to 3 places of decimal :(26)^((1)/(3))

Sum to n terms of the series (1)/(1.4.7) + (1)/(4.7.10) + (1)/(710.13) +…….

Compute the are length of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1

{:("Column A","a and b are positive".(a + b):(b + 6) = 5 : 6,"Column B"),(b,,1):}

Consider the circle x^2 + y^2 + 8x + 10y- 8 = 0 (i) Find its radius of the circle x^2 + y^2 + 8x + 10y - 8 = 0 (ii) Find the equation of the circle with centre at C and passing through (1,2).

Sum of coefficients of terms of odd powers of in (1+x - x^2-x^3)^8is

int_(0)^(pi//4) [sqrt(tan x) + sqrt(cot x)] dx is equal to

Solve by matrix method: 4x+3y+2z=60, x+2y+3z=45, 6x+2y+3z=70

Area of the triangle formed by the lines 3x^(2) - 4x y + y^(2) = 0 , 2x- y = 6is ,

If the 7^(th) term of n A.P is 40. Then the sum of its first 13 terms is

If A.M and G.M of x and y are in the ratio p:q, thenx:y is

Leta = - (x) /(1 + x^(2)) + (1)/(3) ((x)/(1 +x^(2)))^(3) + (1)/(5) ((x)/(1 + x^(2))^(5) + … andb = x (2)/(3) x^(3) + (1)/(5) x^(5) +(1)/(7) x^(7) - (2)/(9) x^(9) … then

How many of them are divisible by 5

A stone thrown at an angle theta to the horizontal reaches a maximum height h. The time of flight of the stone is:-

Integrate the functions (x^(2)+x-1)/((x+1)^(2)(x+2))

If x ^(3) + y ^(3) = 3axy then y _(2) =

Express in the form a+ib:(3+5i)/(2-3i)

The value of .^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m) is equal to

If vertex and fous of a hyperbola are (2,3) and (6,3) respectively and eccentricity e of the hyperbola is 2, then equation of the hyperbola is :

Let A(1/2,0),B(3/2,0),C(5/2,0) be the given points and P be point sashaying max (PA+PB,PB+PC)lt2. If area of region of point P is sqrt(3) ((pi)/a-(sqrt(3))/b) then a+b is

AB and CD are two equal and parallel chords of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1. Tangents to the ellipse at A and B intersect at P and at C and D at Q. The line PQ

Classify 10^(-19)coulomb measures as scalar and vector.

Identify the correctoption

if y=sqrt((1-cos x )/(2)), the n prove that (dy)/(dx)=1/2cos" x/2.

Write down the set of letters forming that word Misrepresentation?

Match List I with List II and select the correct answer using code gien below the lists:

Let G,O,E and L be positive real numbers such that log(G.L)+log(G.E)=3,log(E.L)+log(E.O)=4, log(O.G)+log(O.L)=5 (base of the log is 10) If the minimum value of 3G+2L+2O+E is 2^(lamda)3^mu5^nu ,Where lamda,mu,and nu are whole numbers, the value of sum(lamda^(mu)+mu^(nu)) is

Find thedistanceof thepoint(3,-2,1)fromthe plane 2x -y+2z +3=0

Consider the differential equation (dy)/(dx)=(y^(3))/(2(xy^(2)-x^(2))): Statement-1 : The substitutionz=y^(2) transforms the above equation into a first order homogeneous differential equation. Statement-2 : The solutionof this differential equation is y^(2)e^(-y^(2)//x)=C.

Let G,O,E and L be positive real numbers such that log(G.L)+log(G.E)=3,log(E.L)+log(E.O)=4, log(O.G)+log(O.L)=5 (base of the log is 10) If the value of the product (GOEL) is lamda, the value of sqrt(loglamdasqrt(loglamdasqrt(loglamda....))) is

The natural ...............

Find the total number of lone pair in poly phosphoric acid having four phosphorous atoms.

lim_(x to oo) ((x+5)/(x +2 ))^(x +3) equals

If 0 lt a lt b, then int_(a)^(b) (|x|)/(x) dx=

Mean of the binomial distribution is 100 then it standard deviation lies in ………… interval.

Evaluate |[2,4],[-5,-1]|

Find the area enclosed by circle x^(2) + y^(2) = 4 ,parabola y = x^(2) + x + 1 , the curve y = [|sin^2 ""(x)/(4) + cos""(x)/(4)|] and x-axis

In the line3x-y= kis a tangent to the hyperbola3x^(2) -y^(2) =3 ,then k =

Find the number of even proper divisors of 2^(3)3^(2)5^(3)

The probabilty of hitting a target is 1/3. The least number of times to fire so that the probability of hitting the larget atleast once is more than 90% is

Smaller of (19^10 + 20^10) and 21^10 is

At what values of a willthe curve y = x^(4) +ax^(3) + + 3/2 x^(2)+1

If x,y,z are non-zero real numbers, then the inverse of A=[[x,0,0],[0,y,0],[0,0,z]] is

If the argument of (z-a)(barz-b) is equal to that of ((sqrt(3)+i)(1+sqrt(3)i))/( 1+i) , where a,b are two real numbers and barz is the complex conjugate of the Argand diagram. Find the values of a and b so that be locus becomes a circle having its centreat (1)/(2)(3+i).