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

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

Evaluate the following :

`i^35`

Without expanding evaluate the following determinant:

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

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 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)[((root(3)(x)-root(3)(7))(root(3)(x)+root(3)(7)))/(x-7)]`

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

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:

i³⁵

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:

i³⁵ 

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

Evaluate the following limits: `lim_(x -> 5)[(x^3 - 125)/(x^5 - 3125)]`

Evaluate the following limit:

`lim_(x->7)[((root(3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x - 7)]`