HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following Limit.

`lim_(x->1)[(x^3-1)/(x^2+5x-6)]`

Find the value of `sqrt(-3) xx sqrt(-6)`

Evaluate the following limit:

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

Simplify the following and express in the form a+ib:

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`

Evaluate the following limit:

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

Evaluate the following Limit:

`lim_(x->1)[(x^3-1)/(x^2+5x-6)]`

Simplify the following and express in the form a + ib.

`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`

Simplify the following and express in the form a+ib.

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`

Evaluate the following limit:

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

Evaluate the following limit:

`\underset{x->2}{lim} [(x^7 + x^5 + 160)/(x^3 +8)]`

Evaluate the following Limit.

`lim_(x->1)[(x^3 - 1)/(x^2 + 5x - 6)]`

Evaluate the following limit:

`lim_(x ->1)[(x^3 - 1)/(x^2 + 5x - 6)]`

Evaluate the following:

i³⁵

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

Calculate D₆ and P₈₅ for the following data:
79, 82, 36, 38, 51, 72, 68, 70, 64, 63.

The daily wages (in Rs.) of 15 laboures are as follows:
230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250
Calculate D₈ and P₉₀.

Calculate 2^nd decide and 65^th percentile for the following:

From the following data calculate the rent of 15^th, 65^th and 92^nd house.

The following frequency distribution shows the weight of students in a class:

(a) Find the percentage of students whose weight is more than 50 kg.
(b) If the weight column provided is of mid values then find the percentage of students whose weight is more than 50 kg.

Calculate D₄ and P₄₈ from the following data: