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Evaluate the following determinants. [[1,omega],[-omega,omega]]

Find the volume of the spherical cap of height h cut of feom a sphere of radius r.

Find int(x^(2)+x+1dx)/((x+2)(x^(2)+1))

If lamda be the number of 3-digit numbers are o the form xyz with x lt y, z lt y and x ne0, the value of (lamda)/(30) is

For which value of x, function f(x)=(40)/(3x^(4)+8x^(3)-18x^(2)+60) has maximum and minimum ?

|(2bc-a^(2),c^(2),b^(2)),(c^(2),2ca-b^(2),a^(2)),(b^(2),a^(2),2abc-c^(2))|=

Minimise Z=3x+2y subject to the constraints, x+yge8 3x+5yle15 xge0, yge0

bar(a)=hati+hatj+hatk,bar(b)=hati+3hatj+5hatk and bar( c )=7hati+9hatj+11hatk are vectors. The area of the parallelogram whose diagonals are bar(a)+bar(b) and bar(b)+bar( c ) is …………..

State whether the following statements are true or false. Justify For an arbitary binary operation ** on N, a**a=a AA a in N

The order of the differential equation(d^(2)y)/(dx^(2)) - 5 (dy)/(dx) + 6y = 0 is

The probability that a police inspector Ravi will catch a thief in a day is 1/4 and the probability he will catch a robber in that day is 1/5 and the probability that he will catch both a thief and a robber in a dy is 1/15 then what is the probability that Ravi will catch at least 1 mischief?

If A,B,C are the maximum heights reched when three stones projected vertically upwards moves according to the law s= 128t -16t^2,s=48t-16t^2,s=80t-16t^2 respectively then the descending order of A,B,C is

If a leap year is having 53 sundays then find the probability that leap year contains 52 Mondays only.

Evaluate : int(x+2)/(sqrt((x-2)(x-3)))dx.

Without using graph paper, draw the graph of the function f(x)=sin""(1)/(x) and determine from the graph whether lim_(xto0)f(x) exsits or not.

Determine the area of parallelogram whose adjacent sides are the vector 2hati+hatj+3hatk, hati-hatj

Reduce the matrix [[2,0,3],[1,-1,-2],[4,1,0]] to the identity matrix by elementary row transformation, show also it is non singular.

Assertion (A) : The area bounded by y^(2)=8x and x^(2)=8y is (64)/(3) sq. units. Reason ( R ) : The area bounded by y^(2)=4ax and x^(2)=4by is (16ab)/(3) sq. units. The correct answer is

If the vectors hat(i)+hat(j)+2hat(k),-hat(i)+2hat(k)and2hat(i)+xhat(j)-yhat(k) are mutually orthogonal, then the values of x, y, z are

Let f and g be continuous function on alexleb and set p(x)=max{f(x),g(x)} and q(x)="min"{f(x),g(x), then the area bounded by the curves y=p(x),y=q(x) and the ordinates x=a and x=b is given by

A is the orthocentre of DeltaABC and D is reflection point of A w.r.t. perpendicualrbisectorof BC, then orthocenterof DeltaDBC is :

If l, m, n be there real numbers proportional to the direction cosinesof L, then p+m^2+n^2=1.

If a hyperbola has one focus at the origin and its eccentricity is sqrt2. One of the directrices is x+y+1=0,Then equation its asymptotes are

Choose the correct answer int(sin^(2)x-cos^(2)x)/(sin^(2)xcos^(2)x)dx is equal to

Find AB, if A=[(0,-1),(0,2)] and B=[(3,5),(0,0)].

A plane makes 2,1,-2 intercepts on co-ordinate axes. Its distance from the origin is

If x+y le 50, 3x+y le 90, x ge 0, y ge 0 then the maximum value of f=4x+y is

int(1)/(sqrt(7-6x-x^(2)))dx=

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

Ifx^(y) * y^(x) = (x + y) ^(5) , " find " (dy)/( dx)

The maximum number of normals to hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 from an external point is

If (x + 3i)/(2 + iy) = 1 - i then the value of (5x - 7y)^(2) =

If any tangent to the ellipse 25x^(2)+9y^2=225 meets the coordinate axes at A and B such that OA = OB then , the length AB is equal to (where , O is the origin)

Obtain the general solution of the following differential equations.dy/dx(x^2+1)(y^2+1)

Prove that the number of selections of n things from two sets of n identical things and n other distinct things is (n+2)2^(n-1)

Mean deviation of first three odd numbers from mean is

Derive the formula for the shortest distance between skew lines vec(r)=vec(a)+lambdavec(b) " and " vec(r)=vec(a)_(2)+lambdavec(b_(2)) in vector form.

Smaller area enclosed by the circlex^(2) + y^(2) = 4 and the line x + y = 2 is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The function f(x) is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f(x), is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f'(10), is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f(1), is

The optimal value of the objective function is attained at the points ……..

Which of the following graphs best describes the velocity of the woman on her walk ?

One of the closest points on the curve x^(2) - y^(2) = 4 to the point (6,0) is

State whether the following statements are true or false. Justify For an arbitary binary operation on N, aa=a AA a in N