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

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)|`

Evaluate the Following limit:

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

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)|`

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.

Without expanding evaluate the following determinant.

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

Following tale gives income (X) and expenditure (Y) of 25 families:

Find Marginal frequency distributions of income and expenditure.

Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159, etc. for X and 35-39, 40-44, etc. for Y. Find marginal frequency distributions.

(152, 40) (160, 54) (163, 52) (150, 35) (154, 36) (160, 49) (166, 54) (157, 38) (159, 43) (153, 48) (152, 41) (158, 51) (155, 44) (156, 47) (156, 43) (166, 53) (160, 50) (151, 39) (153, 50) (158, 46)

Sketch the graph which represents the solution set for the following inequation.
x > 5

Sketch the graph which represents the solution set for the following inequation.
x ≥ 5

Sketch the graph which represents the solution set for the following inequation.
x < 3

Sketch the graph which represents the solution set for the following inequation.
x ≤ 3

Sketch the graph which represents the solution set for the following inequation.
– 4 < x < 3

Sketch the graph which represents the solution set for the following inequation.
– 2 ≤ x < 2.5

Sketch the graph which represents the solution set for the following inequation.
– 3 ≤ x ≤ 1

Sketch the graph which represents the solution set for the following inequation.
|x| < 4

Sketch the graph which represents the solution set for the following inequation.
|x| ≥ 3.5