HSC Commerce (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following limit:

`lim_(x->5)[(x^3-125)/(x^5-3125)]`

Show that `(-1+sqrt3i)^3` is a real number.

Evaluate the following limit:

`lim_(x->7)[((root3 x - root3 7)(root3 x + root3 7))/(x - 7)]`

By using properties of determinant prove that

`|(x + y,y + z,z + x),(z,x,y),(1,1,1)|= 0`

For the G.P. if a = `2/3` , t₆ = 162 , find r

For the G.P. If a = `2/3, t_6 = 162,` find r

Evaluate the following limit:

`lim_(z->2)[(z^2 - 5z+6)/(z^2-4)] `

Evaluate the following limit:

`lim_(x->0)[[sqrt(6+x+x^2) -sqrt6]/x]`

Verify whether the following sequence is G.P. If so, find t_n.

`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5), ...`

Evaluate the Following limit:

`\underset{x->7}{lim} [((root3(x) - root3(7)) (root3(x) + root3(7)))/(x-7)]`

For the G.P. if a = `2/3`, t₆ = 162, find r.

Evaluate the following limit:

`lim_(z -> 2)[(z^2 - 5z + 6)/(z^2 - 4)]`

Evaluate the following limit:

`lim_(x->3)[sqrt(x + 6)/x]`

Evaluate the following limit:

`lim_(x->5)[(x^3 -125)/(x^5 - 3125)]`

Evaluate the following limit:

`lim_(x ->7)[((root3x - root3(7))(root3x + root3(7)))/(x - 7)]`

Evaluate the following limit:

`lim_(x->-2)[(x^7 + x^5 + 160)/(x^3 + 8)]`

Find the various and S.D. for the following set of numbers.

7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6

Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129

Compute variance and standard deviation for the following data:

Compute the variance and S.D.