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If (1)/((1-2x)^(2)(1-3x))=(A)/(1-2x)+(B)/((1-2x)^(2))+(C)/(1-3x) then match the following {:("List - I","List - II"),("I) A","(a) 9"),("II) B","(b) -6"),("III) C","(c) -2"):}

int_(0)^(2a) sqrt(2ax - x^(2)) dx=

Express the 1 points geometrically in the Argrand plane.

Show that f(x) = sinx is continuous on R .

Integrate the functions xcos^(-1)x

Which of the following options is the only CORRECT combination ?

Which of the following options is the only CORRECT combination ?

Using method of integration, find the area (in sq. units) of the smaller portion enclosed between the curves, x^2 + y^2 = 4 and y^2 = 3x.

The remainder of n^(4)-2n^(3)-n^(2)+2n-26 when divided by 24 is

If f(x)={(|4x-5[x], , , "for" xgt1),([cos pix],,, "for" x le1):} where [.] is greatest integer function, then mis the number of points of discontinuity off(x) and n is the number of points of non-differentiability in [0,2]then evaluate(m+n).

Prove that x^3+y^3+z^3-3xyz =(x+y+z)(x+omegay+omega^2z)(x+yomega^2+z omega)

Which of the following species have partially filled d-subshell ?

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a balls is drawn at random.What is the probability that the second ball is red ?

The equation to the locus of the midpoints of chords of the circle x^(2)+y^(2)=r^(2) having a constant length 2l is

int(sqrtx)/(sqrt(x)+root(3)x)dx=

There are 10 seats in the 1st row of a movie theatre. 4 persons enter and take seats randomly in this row. Find the probability that out of any two seats located symmetrically about the middle of the row, atleast one is empty.

The points A,B,C are randomly selected on the circumference of a circle. Find the probability that the points lie on a semi circle.

If the tangents drawn from a point on the hyperola x^(2)-y^(2)=a^(2)-b^(2) to the ellipse x^(2)/a^(2)-y^(2)/b^(2)=1 makes angles alpha and beta with transverse axis of the hyperbola, then

The plane barr = s(i+2j-4k) +t(3i+4j-4k) +(1-t)(2i-7j+3k) is parallel to the line

Prove that the functions (a) f(x)=x+sin x, (b) f(x)=cos sqrt(x) are non-periodic.

Which of the following graphs represents the soution set for 5x - 10y gt 6 ?

IFtanA and tanBare therootsofabx^2- c^2 +ab =0 wherea,b,care thesidesof thetriangleABCthen thevalueofsin ^2+ sin^2B+ sin ^2 C is

The smaller area between the ellipse (x^(2))/(9)+(y^(2))/(16)=1 at the line (x)/(3)+(y)/(4)=1 is

If the point on y = x tan alpha- (ax^(2))/(24^(2) cos^(2) alpha) (alpha gt0) where the tangent is parallel to y=x has an ordinate u^(2)//4a, then cos^(2) alpha is equal to

Which of the following is equal to (13+17i)(4-9i)?

Let alpha be a root of the equation x^2-x+1=0, and the matrix A=[(1,1,1),(1,alpha,alpha^2),(1,alpha^2,alpha^4)] and matrix B=[(1,-1,-1),(1,alpha,-alpha^2),(-1,-alpha^2,-alpha^4)] then the value of |AB| is :

If x=alpha, y=beta, z=gamma is the solution of the system of equations x+y+z=4, 2x-y+3z=9, 3x+y+2z=8, "then "4alpha+2beta+3gamma=

The number of ways in which 10 candidates A_(1),A_(2),A_(3),.........,A_(10) can be ranked so that A_(1) is always above A_(10) is

Evaluate int(1)/(1+sinx+cosx)dx

If alpha+ beta + gamma = 6, alpha^(2) + beta^(2) + gamma^(2) = 14and alpha^(3) + beta^(3) + gamma^(3) = 36,then alpha^(4) + beta^(4) + gamma^(4) =

Assertion(A ) : the rootsx^4 -5x^2+6=0are+- sqrt(2) ,+-sqrt(3) Reason (R ) : theequation having the rootsalpha_1 , alpha_2 , ….., alpha_n is(x-alpha_1) ( x- alpha_2 )…. (x-alpha_n)=0

If x=cisalpha,y=cisbeta" then " x^3y^4-(1)/(x^3y^4)=

The regression equation of x on y is 9x-2y-38=0. If mean of x series is 6, then mean of y series is

A river flows due North, and a tower stands on its left bank. From a point A upstream and on the same bank as the tower, the elevation of the tower is 60^(@), and from a point B just opposite A on the other bank the elevation is 45^(@). If the tower is 360 m high, the breadth of the river is

x is equal to

Integrate the functions (x^(3)sin(tan^(-1)x^(4)))/(1+x^(8))

Find the common tangent of y=1+x^(2) and x^(2)+y-1=0. Also find their point of contact.

If (sin(xy))/(1+cos(xy))

Three bags contain a number of red and white balls as follows: The probability that bag i will be chosen and a ball is selected from it is (i)/(6), i = 1, 2, 3. What is the probability that, (i) a red ball will be selected ? (ii) a white ball is selected ?

Two particles A,B are moving on two concentric circles of radii R_1) and R_2 with equal angular speed omega. Att=0,their positions and direction fo motion are shown in the figure :

Find the area of the region {(x,y): x^2 +y^2 le 2ax , y^2 le ax , x le 0 , y le 0 }

If alpha,beta,gamma are the rootsof x^3-2x^2+3x-4=0 find the value of sumalpha^2

Integrate the following functions: 1/(sinx cos^3x)

An ionic solid PQ crystallises in rocksaltstructure with density 4.0gm//cm^(3).If theradius of cation and anion is 83 and 167 pm respectively, then the molar mass of solid is[N_(A)=6xx10^(23)]

If cos (alpha + beta) = 4/5, sin (alpha -beta) = 5/13 and alpha, betabetween 0 and pi/4, thentan 2 alphais equal to

If I_(n)=int_(0)^(pi//4) tan^(n)theta d thetafor 1,2,3,… then I_(n-1)+I_(n+1)=

Resolve (x^(2)+1)/(x^(4)+x^(2)+1) into partial fractions.

Find the area of the region in the first quadrant enclosed by x-axis, line x = sqrt3y and the circle x^(2) + y^(2) = 4.