Without expanding, evaluate the determinants :
`|(2,3,4),(5,6,8),(6x,9x,12x)|`

Without expanding evaluate the determinant |(41,1,5),(79,7,9),(29,5,3)|

Find the minor of elements 6 in the determinants Delta = {:[( 1,2,3),(4,5,6),(7,8,9)]:}

Evaluate the definite integrals int_(1)^(2)(4x^(3)-5x^(2)+6x+9)dx

Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x+9x+8x+11 x+15| is, p. 1 If one of the roots of the equation |7 6x^2-13 2x^2-13 2x^2-13 3 7|=0i sx+2, then sum of all other five roots is, q. -6 The value of |sqrt(6)2i3+sqrt(6)sqrt(12)sqrt(3)+sqrt(8)i3sqrt(2)+sqrt(6)isqrt(18)sqrt(2)+sqrt(12)isqrt(27)+2i| is, r. 2 If f(theta)=|cos^2thetacosthetas intheta-s inthetacosthetasin^2thetacosthetas intheta-costheta0|=t h e nf(pi//3) , s. -2

Using the property of determinants and without expanding {:[( 2,7,65),( 3,8,75),( 5,9,86) ]:} = 0

Find the derivative of x^(5)(3-6x^(-9))

A square is inscribed in the circle x^2+y^2-2x+4y-93=0 with its sides parallel to the coordinate axes. The coordinates of its vertices are (-6,-9),(-6,5),(8,-9),(8,5) (-6,-9),(-6,-5),(8,-9),(8,5) (-6,-9),(-6,5),(8,9),(8,5) (-6,-9),(-6,5),(8,-9),(8,-5)

Integrate the function 1/(9x^(2)+6x+5)

Find the non-zero values of x satisfying the matrix equation x[(2x, 2), (3, x)], 2[(8, 5x), (4, 4x)]=2[(x^(2)+8, 24), (10, 6x)]

Find absolute maximum and minimum values of a function f given by f(x) =12x^((4)/(3))-6x^((1)/(3)),x in [-1,1]