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

Evaluate the following Limits: `lim_(x -> "a") ((x + 2)^(5/3) - ("a" + 2)^(5/3))/(x - "a")`

Evaluate the following Limit:

`lim_(x -> 0) ((1 + x)^"n" - 1)/x`

Examine whether the function is continuous at the points indicated against them :

f(x) `{:( = (x^2 + 18x - 19)/(x - 1)",",  "for"  x ≠ 1),(= 20",",  "for"  x = 1):}}` at x = 1

Evaluate the following:

i³⁵

Evaluate the following :

`i^35`

Evaluate the following limits: `lim_(x ->3) [sqrt(x + 6)/x]`

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 :

`"i"^35`

Without expanding determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`

Without expanding determinants find the value of `|(10,57,107), (12, 64, 124), (15, 78, 153)|`

Without expanding evaluate the following determinant.

`|(1, a, a + c),(1, b, c + a),(1, c, a + b)|`

Find the value of `(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`

Without expanding determinants find the value of  `|(10,57,107),(12,64,124),(15,78,153)|`

Evaluate the following:

i³⁵

Find the value of `(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`

Without expanding determinants find the value of `|(10,57,107),(12,64,124),(15,78,153)|`

By using properties of determinant prove that `|(x + y, y+z, z +x),(z,x,y),(1,1,1)| =0`

Evaluate the following:

i³⁵ 

Evaluate the following :

`i^35`