HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Find the middle terms in the expansion of

`(3x + x^2/2)^8`

Find the middle terms in the expansion of

`(2x^2 - 3/x^3)^10`

Find the term independent of x in the expansion of

`(x^2 - 2/(3x))^9`

Find the term independent of x in the expansion of

`(x - 2/x^2)^15`

Find the term independent of x in the expansion of

`(2x^2 + 1/x)^12`

Prove that the term independent of x in the expansion of `(x + 1/x)^(2n)` is `(1*3*5...(2n - 1)2^n)/(n!)`.

Show that the middle term in the expansion of is (1 + x)²ⁿ is `(1*3*5...(2n - 1)2^nx^n)/(n!)`

Find the Co-efficient of x¹¹ in the expansion of `(x + 2/x^2)^17`

The middle term in the expansion of `(x + 1/x)^10` is

The constant term in the expansion of `(x + 2/x)^6` is

The last term in the expansion of (3 + √2 )⁸ is:

Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:

Sum of the binomial coefficients is

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.

The parabola y² = kx passes through the point (4, -2). Find its latus rectum and focus.

Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y² – 8y – 8x + 24 = 0.

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

y² = 20x

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x² = 8y

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x² = - 16y

The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ `1/5`x² – 6x + 100. Show that the average variable cost curve is a parabola. Also, find the output and the average cost at the vertex of the parabola.