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Integrate the functions 1/(x+xlogx)

The proposition (p ^^ q) ^^ ( p to~ q)is

If a flagstaff 6 metres high placed on the top of a tower throws a shadow of 2 sqrt(3) metres along the ground then the angle (in degrees) that the sun makes with the ground is

A(1, 3) and C(5, 1) are two oppositevertices of a rectangleABCD. If the slope of BD is 2, then the coordinates of B can be :

A plane P = 0 passes through the line of intersection of the planes x+y+z+3=0 and x-y+z-2=0. If the plane P divides the ratio 2:1internally and the equation of the plane is ax-2y+bz=c where a, b, c in N, then the value of 3a+4b-5c is equal to

Evalute the following integrals int "tanh"^(-1)x dx or R

Find p if vectors veca=2hati-hatj+phatk and vecb=hati-2hatj+hatk are perpendicular.

Find the area of the region enclosed by the loop of the curve x= (t)/(3) (6-t), y = (t^(2))/(8) (6-t)

1 + (1+2)/(2!) + (1+2+3)/(3!) + (1+2+3+4)/(4!) + ......oo

Let A = [-1,1] . Then , discuss whether the following functions defined on A are one - one , onto or bijective. f(x) =x/2

If omega is a complex cube root unity then sin { (omega^(10) + omega^(23)) pi - (pi)/(4)} equals

Evaluate the integral underset(0)overset(1)int sin^(-1) ((2x)/(1+x^(2)))dx

If intsqrt(x/(a^(3)-x^(3)))dx = g(x)+c, then g(x) is equal to

Solve system of linear equations ,using matrix methodx-y+2z=73x+ 4y-5z=-5 2x-y+3z=12

Evalute the following integrals int (sec^(2) x - cos x + x^(2)) dx

The value of 'b' such that the solution of x = by (dy)/(dx) represents a family of circles with centre origin is

If int_(0)^(1)(2^(t)dt)/(t+3)=A and int_(a-1)^(a)(2^(t)dt)/(t+b-1)=2^(a-b)A, then b is equal to

Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](dx)/(dy) = 1(x ne 0).

Four cards are drawn at random from a pack of 52 playing cards, one of them is King other is Queen, third is Jack and fourth is Ace. If the probability is K/(.^(52)C_(4)), then K is

y=int cos[2tan^(-1)sqrt((1-x)/(1+x))]dx is an equation of a family of

If normal chords on any two points on the rectangular hyperbola xy = c^(2) meet at R, then show that point R does not xy = c^(2) .

If h(x) = 3f(x^(2)/3)+f(3-x^2) for allx in (-3,4), where f(x)gt 0 for all x in (-3,4). Find the intervals of increase and decrease of h(x).

Show that the family of curves for which the slope of the tangent at any point (x,y) on its (x^(2) + y^(2))/(2xy) , is given by x^(2) - y^(2) = cx.

If r is a unit vector satisfying r xx a =b , |a|=2 and |b| = sqrt3, theone such r =

Find the number of 4 digited numbers that can be formed by using the digit 0,2,3,5,7,8 which are divisble by 4

Integral part of (7 + 5sqrt2)^(2n+1)is (n in N)

Find the number of 4 digited numbers that can be formed by using the digit 0,2,3,5,7,8 which are divisble by 3

If thesum of thetwo rootsofx^3+px^2 +qx +r=0 is zerothenpq=

If int (sin 2x-cos2x)dx=(1)/(sqrt(2))sin(2x-a)+b then .....

The tangent to the curve y^(2)-xy+9=0 is vertical when ……………… .

Prove that :int_(0)^(pi) (x^(2)cos x)/((1+sin x)^(2))dx =pi (2-pi)

A commontangent to the circle x^(2) +y^(2) =16 and an ellipse(x^(2) )/( 49) +(y^(2))/( 4) = 1is

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the hyperbola. 9x^2 - 16y^2 = 144

Find the absolute maximum value and the absolute minimum value of the functions f(x)=sinx+cosx,x in [0,pi].

On an average nine out of 10 ships that have departed at A reach B safely. The probability that out of five ships that have departed at A atleast four will reach B safely is

Ilf the circle x^(2)+y^(2)=2 and x^(2)+y^(2)_4x-4y+lamda=0 have exactly three real common tangents then lamda=

Considerf: R ^+to [4 ,oo]given byf(x)=x^2+ 4show thatf is f invertiblewith the inversef^(-1)ofgivenbyf^(-1)(y)= sqrt(y-4)whereR^+is setof allnon - negativerealnumbers .

Number of normals drawn through the point (8, 4) to the parabola y^(2)= 2x

If a_r is the coefficient of x^r in the expansion of (1+x)^n then a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1))=

If a,b,c are non-coplanar vectors and lambda is a real number, then the vectors a + 2b + 3c, lambda b + 4c and (2 lambda - 1) c are non coplanar for

Two equal circles of largest radii have following property: (i) They intersect each other orthogonally, (ii) They touch both the curves 4(y+2) = x^(2) and 4(2-y) =x^(2) in the region x in [-2 sqrt(2),2sqrt(2)]. Then radius of this circle is

Total number of electron present in 48 g Mg^(2+) are :-

A certain polynomial,P, has a degree of 2. Polynomial P has zeroes of 2 and -3 and a gt 0 when the function of polynomial P is written in the form of y=ax^2+bx+c. Given this information, which of the following could be the graph of polynomial P?

Integrate the functions (cosx)/(sqrt(4-sin^(2)x))