HSC Commerce: Marketing and Salesmanship 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

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

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 determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`

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)]`

By using properties of determinants, 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

Without expanding evaluate the following determinant.

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

Evaluate the Following limit:

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

Evaluate the following : 

`i^35`

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:

`\underset{x->3}{lim}[sqrt(x +6)/(x)]`

Evaluate the following limit:

`\underset{x->5}{lim}[(x^3 - 125)/(x^5 - 3125)]`

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 the determinant, find the value of `|(10,57,107),(12,64,124),(15,78,153)|`

Without expanding evaluate the following determinant.

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

Without expanding evaluate the following determinant.

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