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int sin sqrtx dx

Let P(x) be a polynomial with real coefficients such that int_(0)^(1)x^(m) P(1 -x)dx = 0 AA minNcup{0}, then

Find [vec(a)vec(b)vec( c )] if vec(a)=hati-2hatj+3hatk,vec(b)=2hati-3hatj+hatk and vec( c )=3hati+hatj-2hatk.

int_(0)^((pi)/(2)) (1)/(1 + cot x)dx

Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A+I=O, where I is 2xx2 identity matrix and O is 2xx2 zero matrix. Using this equation find A^(-1)

If x =(4)/((sqrt(5)+1)(root4(5)+1)(root8(5)+1)(root16(5)+1)). Then the value of (1+x)^(48) is-

If f (x) ={{:(xlog_(e)x",",x gt0),(0",",x=0):}"not conclusion of LMVT holds " at x = 1 in the interval [0,a] for f(x), then [a^(2)] is equal to (where [.] denotes the greatest interger) "_______".

If the line (x)/(1)=(y)/(2)=(z)/(3) intersects the line 3beta^2x+3(1-2alpha)y+z=3=-(1)/(2){(6alpha^2x+3(1-2beta)y+2z)} then point (alpha, beta, 1) lie on the plane

ABCD is a square with side a. If AB and AD are taken as positive coordinate axes then equation of circle circumscribing the square is

Prove that: x/(log x) lt log (1+x) lt x if x gt 0.

If A and B are two events of a sample space S such that P(A)=2.0, P(B)=0.6 and P(A|B)=0.5 then P(A^(1)|B)=

If (3,1) is a focus and x= 0 is the corresponding directrix of a conic with accentricity 2, then its vertices are

A quadratic polynominal maps from [-2,3] onto [0,3] and touches X-axis at x=3, then the polynominal is

IF a setAhas12elements, thenthe numberof subsetsof Ahavingatleast3 elements is

Examine the continuity of f, where f is defined by f(x)= {(sin x- cos x",","if" x ne 0),(-1,"if" x = 0):}

Intergrate the following: intcos5x cos2xdx

Consider the sequence 1,3,3,5,5,5,5,5,7,7,7,7,7,7,7,…… and evaluate its 2016 ^(th) term.

If x^(2) + 9y^(2) + 25z^(2) = xyz((15)/(x)+(5)/(y)+(3)/(z)), then -

Find the area of the region bounded by the parabola y=x^2" and "y= |x|.

Let A_(n)=[-1/n,1/n], n in N, and A = overset(infty)underset(n=1)cap A_(n) rArr a cancel(in) underset(n ne 1)overset(infty)cap A_(n)=A, and B={0},then

If (a + 2)(a - 3)(a + 4) = 0 and a > 0, then a =

If a gt0, then int_(-pi)^(pi) (sin^2 x)/(1+a^x)dx is equal to

Findproducts : [[a,b],[c,d]][[0,1],[1,0]]

The parabola y=px^(2)+px+q is symmetrical about the line

Evaluate the following:lim_(xto0) cos(sin x)

Find the Principle values of the following : tan^(-1)(-1)

The solution of the differential equation (1-x^(2)).(dy)/(dx)+xy=(x-x^(3))y^((1)/(2)), is(AA|x| lt1)sqrt(9y)=-f(x)=c(1-x^2)^((1)/(4)), where c is an arbitrary constant and f((1)/(2))=(3)/(4). Then f(x) is

A fair die is rolled. Consider the events A={1,3,5}, B={2,3} and C={2,3,4,5}. Find (i) P(AnnB),P(AuuB) (ii) P(A//B),P(B//A) (iii) P(A//C),P(C//A) (iv) P(B//C),P(C//B)

IFDelta= | (1,5,6),(0,1,7),(0,0,1)| and Delta ' =|(1,0,1),(3,0,3),(4,6,100)| then

I :If(a alpha+b)^2+ (a beta= b)^(-2)=1wherealpha, betaare therootsof ax^2 + bx+c=0 thenac ( ac+ 2)=b^2 II :the valueof 'a' forwhichonerootof the quadraticequation(a^2 -5a+3) x^2 + (3a-1)x+2=0istwiceaslargeasthequadraticequation

{:(" "Lt),(n rarr oo):} ((n!)/(n^(n)))^(1/n)=

The value of sqrt24.99 is

int sec^((2)/(3))x dx=

If the sum of the first n terms of a series be 5n^(2) + 2n, then its second term is

If 2x-y ge 2, x -2y le 2, x+y le 5, x ge 0, y gt 0 then the minimum value of f=x-y is

A circle of radius r passes through the origin and meets the axes at A and B. The locus of the centroid of triangleOAB" is"

If A and B are mutually exclusive events with P(B)ne 1thenP(A| bar B) is equal to {HerebarB is the complement of the event B)

Integration of a binomialdifferential int3sqrt(1+4sqrt(x))/(sqrt(x))dx.

Which of the graphs is not a graph of functions ?

Which of the following graph of potential energy represents the unimolecular elimination reaction ?

In a B School there are 15 teachers who teach marketing or finance. Of these, 8 teach finance and 4 teach both marketing and finance. How many teach marketing but not finance?

Simplify the following((costheta-isintheta)^7)/((sin2theta-icos2theta)^4)

If X and Y are two non-empty sets, where f:XtoY is function defined such that f(C)={f(x):x inC}andf'(D)={x:f(x)inD} for DsubeYfor any AsubeXandBsubeY, then :

The volume (in ml) of 0.5 M NaOH required for the complete reaction with 150 ml of 1.5M H_(3)PO_(3) solution is

int_(- (pi)/(6) )^((pi)/(6) ) sin^(5) x cos^(2) x dx = …......

If (x^(4))/((x-1)(x-2))=x^(2)+3x+7+(A)/(x-2)+(B)/(x-1) then A=

If the tangent and the normal to a rectangular hyperbola xy = c^(2) , at apoint , cuts off intercepts a_(1)" and " a_(2) on the x- axis and b_(1) b_(2) on the y- axis, then a_(1)a_(2) + b_(1) b_(2) is equal to

Find the area of the region enclosed by the given curves .y=cos x , y=1 -(2x)/(pi)

If the latus rectum through one focum subtends a right angle at the farther vertex of the hyperbola then its eccentricity is

Consider the equaitonof line abarz + abarz+ abarz + b=0, whereb is arealparameterand a isfixed non-zero complex number. The interceptof line on imaginary axis is givenby