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The sum of the fourth powers of the roots of the equation x^(3)+x+1=0 is

The value of |{:(2008,2009),(2010,2011):}| is …..

The sum of roots of equation 4cos^(3) (Pi + x) – 4cos^(2)(Pi – x) + cos(Pi + x) – 1 = 0 in the interval [0,320] is p Pi. Then p is equal to :-

If the maxtrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is a skewsymmetric matrix , find the values of a,b,andc.

d /dx (log ( sqrt(x+ sqrt( x^(2) + a^(2) ))))=

If n is a natural number, then [7 ^(2n)+2^(3(n-1)), 3 ^(n=-1)] is always a multiple of-

int(dx)/(2sin2x-3)=

Prove the following : 8sin^4(1/2theta)-8sin^2(1/2theta)+1=cos2theta

If n and r are two positive integers such that nger,"then "^(n)C_(r-1)+""^(n)C_(r)=

If P, Q, R are the mid-point of the sides AB, BC and CA of Delta ABC respectively, then PC-BQ=

If A=[{:(4,3),(2,5):}], find x and y such that A^(2)+xA+yI_(2)=O_(2). Hence, find A^(-1).

Express "tan"^(-1)(cosx)/(1-sinx),(-3pi)/2ltxlt(pi)/2 in the simplest form.

Let f(x)=x^(2), g(x)="cos" x and alpha,beta (alpha lt beta) be the roots of the equation 18x^(2)-19pi x+pi^(2)=0. Then the area bounded by the curves u="fog"(x), the ordinates x=alpha, x=beta and the X-asis is

A insurancecompanyinsured2000scooterdrivers, 4000cardriversand6000truckdirvers .The probabilityof anaccidentare 0.01 , 0.03and 0.15respectivelyone of theinsuredpersonsmeetswith an accident. Whatis theprobabilitythathe isscooterdiriver?

Find the vertex, focus, equation of directrix and axis, of parabolas 3x^(2)-9x+5y

int (sin^(-1) x)/(sqrt(1 - x^2)) dx.

The symmetrical form of the line x - y + 2z = 5, 3x + y + z = 7 is

A chord is drawn through the focus of the parabola y^(2)=6x such that its distance from the vertex of this parabola is (sqrt5)/(2) , then its slope can be

Which of the followingis NOT equivalent to (P^^ ~ q) rarr r

Match the statements given in List I with the values given in List II.

If n=10 , sum_(i=1)^(10) x_(i)=60 and sum_(i=1)^(10) x_(i)^(2)=1000 then find s.d

Evaluate the following define integrals as limit of sums : lim_(n rarr oo) sum_(i=1)^(n) (i)/(n^(2)+i^(2))

(d)/(dx) [ 2 cot^(-1) ((sqrt(1+ sin x) + sqrt(1-sin x))/(sqrt(1+ sin x) - sqrt(1-sin x)))]=

Let a_(n)=(10^(n))/(n!) for n = 1, 2, 3,… then the greatest value of n for which a_(n) is the greatest is

Using the combined method find all roots of the equation f(x) -= x^(3)- 5x+1 =0accurate to three decimal places.

If d is the distance between the point of intersection of the lines x^(2)+4xy+ky^(2)-4x-10y+3=0 and the origin and p is the product of the perpendicular distances from the origin to these lines, then d^(2)-20p^(2)=

Find number of integral values of k for which the line3x + 4y - k = 0 , lies between the circlesx^2 + y^2 - 2x - 2y + 1 = 0 andx^2 + y^2 - 18 x - 12 y + 113 = 0, without cutting a chord on either of circle.

Differentiate cos (tan sqrt(x+ 1))

If (sin A-sinC)/(cosC-cosA)=cotB then angles A,B,C arein

int(cos3xcos2x+sin3xsin2x)/(1-cos^2)dx

Let f(x) = 4x^(2)-4ax+a^(2)-2a+2 and the global minimum value of f(x) for x in [0,2] is equal to 3 The values of a for which f(x) is monotonic for x in [0,2]

Area bounded by x ^(2) y ^(2)+ y ^(4)-x ^(2)-5y ^(2)+4=0 is equal to :

Out of 12 persons sitting at a round table three persons are chosen at random. The probability that no two of them are consecutive is

Find the Principle values of the following : tan^(-1)(1/sqrt(3))

A family of curves whose equation is general solution of a differential equation having order 1 and degree 3, is (g, a, c are arbitrary constants)

Integration of some particular functions : int(2x+3)/(3x^(2)+4x+5)dx= plog|3x^(2)+4x+5|+q tan^(-1) ((3x+2)/(sqrt(11)))+c then p^(2)+q^(2)=....

Evaluate the following integrals: int_0^1 dx/sqrt(1-x^2)

If either vector veca=vec0orvecb=vec0,, then veca*vecb=0.But the converes need not be true . Justify your answer with an example.

int_(0)^(pi//2) (Sec x)/(Sec x + Cosec x) dx=

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

If x^(4)(1+y)=1y," then "(dy)/(dx)=

Which of the following is not logically equivalent to the proposition? " A real number is either rational or irrational."

State with reason whether following functions have inverse : h: {2,3,4,5} rarr {7,9,11,13} with h{(2,7),(3,9),(4,11),(5,13)}

Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre of the sphere passing through the points O, A, B, C if OS=x, then

If alpha, beta, gamma are roots ofx^(3) + px^(2) + qx + r = 0then sum alpha^(3) beta^(3) =

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).