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Find the 10^("th")" term of "(3-4x)^(-2//3).

Examine whether the function f given by f(x)=x^(3)is continuous at x =0

Examine the consistency of the system of equations 3x-y -2z =2 2y - z =-1 3x- 5y =3

Thevalueofxin( 0, pi/2) satisfyingthe equation sinx cosx= 1/4is

Prove that the points (9, 7), (11, 3) lie on a circle with centre at origin. Find the equation of the circle.

The volume of the solids obtained by revolving the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 about major and minor axes in the ratio (a gt b).

Show that f(x) = log_a x "on" (0,oo ),(a gt 0 "and" a != 1) functions are injective.

If the solution of (dy)/(dx) = (x-y)/(x+y) is ax^(2) + bxy + cy^(2) = k, k gt 0 then the ascending order of a,b,c is

Which of these unclear reactionsis possible ?

underset(e)int_(0) ^(r//2) sqrt((1-sin2x)/(1+sin2x))dx=

Show that the three distinct points (a^2,a) (b^2,b) and (c^2,c) can never be collinear.

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=1?

If x_(1) epsilonN and x_(1) satisfies the equation. If x^(2)+ax+b+1=0, where a,b!=-1 are integers has a root in natural numbers then prove that a^(2)+b^(2) is a composite.

Solve the following system of equations bymatrix inversion method. {{:(x + 2y + z = 7 ),(" "x + 3z = 11),(" "2 x - 3y = 1 ):}

Out of (4n + 1) tickets numbered m, m+1, m+2, …., m + 4n, five tickets are chosen at random without replacement. Find the probability that these tickets are in A.P.

Toremovethe2^( nd )termof the equationx^4 - 8x^3+ x^2-x +3=0,diminishthe rootsby

Find the number of ways of arranging the letters of the word. INDEPENDENCE

If inverse of A=[{:(1,-1,1),(2,1,-3),(1,1,1):}]is (1)/(10)[{:(4,2,2),(-5,0,alpha),(1,-2,3):}] then alpha =…..

Solve for x: sin^(-1)(1-x)-2sin^(-1)x=pi/2

Find the area in the first quadrant between y^(2)=4x, y6(2)=16x and the straight line x=9.

Solve (3(x-2))/(5) le (5(2-x))/(3)

Let h(x)=f(x)=f_(x)-g_(x), where f_(x)=sin^(4)pix and g(x)=In x. Let x_(0),x_(1),x_(2) , ....,x_(n+1_ be the roots of f_(x)=g_(x) in increasing order. In the above question, the value of n is

The solution of the equation dy/dx= 2y tan x = sin xsatisfying y = 0 whenx = pi/3'is

Write relations in tabular form and determine their type for R={(x,y):2x-y=0} on A={1,2,3,…,13}

lim_(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

If p,q,r are three positive real numbers then the value of (p + q) (q + r) (r + p) is

If the normal subtends a right angle at the focus of the parabola y^(2)=8x then its length is

Thesolutionset of(x-1)(X-3) (x-5) (x-7) =9is

7 boys and 3 girls sit in a row at random, Match the following

If f(x) = (1)/( 2^n)when (1)/( 2^(n+1) ) lt x le (1)/( 2^n), n= 0,1,2… then "lt"_(n to oo)int_(t//2^n) ^(1) f(x) dx equals

If 2sinh^(-1) (a/(sqrt(1-a^(2))))= log ((1+x)/(1-x))then x =

Find the number of values of x satisfyingint_(0)^(x)t^(2)sin (x-t)dt=x^(2) in [0, 100].

Let f(x)=sinx+cos(sqrt(4-a^(2)))x. Then, the integral values of 'a' for which f(x) is a periodic function, are given by

The remainder obtained when 5^(124) is divide by 124 is

The condition that the circle x^(2) +y^(2) + 2gx+ 2fy + c = 0 to bisect the circumference of the circle x^(2) + y^(2) + 2g^(1)x + 2f^(1)y + c^(1) = 0 is

The sum of the fourth powers of the roots of the equation x^(5) + px^(3) + qx^(2) + s = 0is

{:("Quantity A","Quantity B"),("The tenths digits of the product","The tenths digit of the product"),("of two even integers","of an even and an odd integer"),("divided by 4","divided by 4"):}

If Q(x) = (1)/(2) a_(0) + a_(1) cos x + b_(1) sin x+ a_(2) cos 2x +…+ a_(n) cos nx + b_(n) sin nx, then the value of int_(0)^(2pi) Q(x) sin kx dx (k=1,2,…n)

Evaluate the integrals by using substitution int_(0)^(1)sin^(-1)((2x)/(1+x^(2)))dx

lim_(n to oo)(int_(1//(n+1))^(1//n)tan^(-1)(nx)dt)/(int_(1//(n+1))^(1//n)sin^(-1)(nx)dx) is equal to

Integrate the following function : int(x-1)/(sqrt((x+1)(x-2)))dx

Consider an ellipse E:x^(2)/a^(2)+y^(2)/b^(2)=1, centered at point 'O' and having AB and CD as its major and minor axes respectively if S_1be one of the focus of the ellipse, radius of the incircle of ∆OCS_1 be 1 unit and OS_1=6units.Q. The equation of the director circle of (E) is

A purse contains 4 copper and 3 silver coins while another purse contains 6 copper and 2 silver coins. A purse is drawn at random and coin is drawn. Then ....... is the probability that selected coin is of copper.

Parametric form of the equation of the planeis bar r =(2hati + hatk ) + lambda hati + mu (hati + 2hati-3 hatk) lambda and mu are parameters. Find normal to the plane and hence equation of the plane in normal form. Write its Cartesion form.

If for x in (0,1/4) , the derivation of tan^(-1)((6xsqrtx)/(1-9x^3)) is sqrt(xg(x) , then find g(x).

The truth table of p vv (~q) rArr p is

int3x^2dx' is equal to :

int_(-1)^(1){((x+2)/(x-2))^(2)+((x-2)/(x+2))^(2)-2}^(1//2)dx=

If a point P is moving such that the lengths of tangents drawn from P to the circles x^(2) + Y^(2) -4x -6y -12 = 0 and x^(2) +y^(2) + 6x + 18 y + 26 = 0are in the ratio 2 : 3, then find jthe equation of the locus of P.