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The value of g ^(1//3) , 9 ^( 1//27)……. upto 'oo, is -

The roots of x^(4) - 12x^(3) + 34x^(2) - 12x + 1 = 0are

Solve the following linear programming problems graphically : Minimise : Z = 3x + 5y subject to constraints -2x+y le 4, x+y ge 3, x-2y le 2, x, y ge 0.

Which scatterplot shows a nonlinear positive association ? (Note : A positive association between two variables is one in which higher values of one variable correspond to higher values of the other variable.)

Which one of the following statements can be informed from the table ?

If int_(-(1)/(2))^(1/2)cosx.log((1+x)/(1-x))dx=k.log2, then k =

If P(A)=2/5,P(B)1/3,P(AnnB)=1/5"then find"P(barA|barB).

If the circles (x-a)^(2)+(y-b)^(2)=r^(2), (x-b)^(2)+(y-a)^(2)=r^(2) touch each other then the point of contact is

If the normal at any point P of the ellipse (x^(2))/(16)+(y^(2))/(9) =1 meets the coordinate axes at M and N respectively, then |PM|: |PN| equals

Integrate the following functions e^x(1/x - 1/x^2)

The normal form of the line x+y+1=0 is

Match the item of list-I with those of List-II Then, which of the following is correct ?

Find the sum of all 3-digit natural numbers which contain at least one odd digit and at least one even digit

Verify Property 2 for Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

If 4-3y+7 = 0 is a tangent ot the circle repesented by x^(2) + y^(2) -6x + 4y - 12 = 0 , then find its point of contact.

The product of lengths of perpendicular from any point on the hyperola x^(2)-y^(2)=16 to its asymptotes is

If logx=z, then the value ofx^(2)(d^(2)y)/(dx^(2)) is -

~p vv ~q is logically equivalent to

A right solid circular cylinder of given volume will have the least total surface area when

If int(1 - tan 3x)^(2) dx = (1)/(3)[tan 3x+logf(x)] + C then f(x) is given by

Write the component statement "57 is divisible by 2 or 3" compound statements and check whether the compound statement is true or false.

Let ** be a binary operation on the set Q of rational numbers as follows : a "*" b = (ab)/(4) Find which of the binary operations are commutative and which are associative.

Let P(n): 1+1/4+1/9 +….+(1)/(n^2) lt 2- (1)/(n), is true

"Evaluate "Delta ={:|( 0 , sin alpha ,-cos alpha ) ,( -sin alpha , 0 , sin beta ),( cos alpha , -sin beta, 0)|:}

underset(-pi//4)overset(pi//4)int (dx)/(1+cos 2x) is equal to

Match the following.{:("I) "(i)^i=,"a) "ipi//2),("II) "log_ei=,"b) "ipi//2+logpi//2),("III) "log(logi)=,"c) "sqrt2),("IV "sqrti+sqrt(-i)=,e^(-pi//2)):}

int_(1)^(2) (1)/(2(1+x^(4)))dx

int(x^(2)+1)/(x(x^(2)-1))dx=....

Evalute the following integrals intx log (1 + x) dx

If int (4e^(x) + 6e^(-x))/(9e^(x) - 4e^(-x))dx = Ax + B log (9x^(x) - 4e^(-x) ) + Cthen

int_(0)^(oo)[(2)/(e^(x))]dx=

If the line (x-4)/(1) = (y-2)/(1) = (z+k)/(2) lies in the plane 2x -4y + z =7 then k =........

Two consecutive numbers from 1,2,3 …., n are removed.The arithmetic mean of the remaining numbers is 105/4 . The removed numbers

Let A(0,6,6), B(6,6,0) and C(6,0,6) are three points and point D is moving on the line x+z-3=0=y. If G is centroid of DeltaABC, then minimum value of GD is

int(dx)/((x^2-1)sqrt(x^2+1))=

A point P is movingin a plane such that the difference of its distances from two fixedpoints in the same plane is a constant. The path traced by the point P is a/an

(i) What is the second term in the expansion of (1 + x)^(n)? (ii) Write the 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n). (iii) If the coefficients of 2^(nd), 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) are in A.P, then show that n^(2) - 9n + 14 = 0.

(d)/(dx) tan^(-1) (sec x- tan x)- Find

If circle x^(2)+y^(2)+2gx+2fy+c=0(c gt 0) touches both the coordinate axes and lies in the third quadrant then the length of thechord intercepted by the circle on the line x+y+sqrt (c )=0 is

If x, y, z arein A.P., then the value of |{:(p + 2, p+3,p+4),(p+3,p+4,p+5),(p+ 2x,p+2y,p+2z):}| equals to

Find the area of quadrilateral formed by 3x ^(2) + y ^(2) - 4xy + 6x - 4y + 3=0 and x ^(2) + 4y ^(2) - 4xy + 6x + 12y + 9=0

If x satisfies the equation x^2-2xcostheta+1=2costheta,then the value of x^n+1//x^n is

What is the smallest possible natural number 'n' for which the equation x^(2)-nx + 2014=0has integer roots.

int x^(2) sin^(2)x dx =

If a=Sigma_(n=0)^(oo) (x^(3x))/(3n)!,b=Sigma_(n=1)^(oo)(x^(3n-2))/(3n-2!) and C= Sigma_(n=1)^(oo)(x^(3n-1))/(3n-1!) then the value of a^(3)+b^(3)+C^(3)-3abc is

A = ((2.1,2.5,3.7),(-2.1,5.9,3.8),(0,-2.9,-3)),B=((cosalpha,sinalpha,0),(sin alpha,cosalpha,0),(0,0,-1)) ,C=((cos alpha,sinalpha,0),(-sin alpha,cos alpha,0),(0,0,1)) thensum_(k=0)^(oo)(1)/(3^(k))tr(A(BC)^(k))=________

When 9​th term of A.P is divided by its 2​nd term then quotient is 5 and when 13​th term is divided by 6​thterm then quotient is 2 and Remainder is 5 then find first term of A.P. :-

Is the number set {0.2,-0.5,0.9,0.4} determining a probability distribution ?

When 9th term of A.P is divided by its 2nd term then quotient is 5 and when 13th term is divided by 6thterm then quotient is 2 and Remainder is 5 then find first term of A.P. :-