HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following quadratic equation.

x² − (5 − i) x + (18 + i) = 0

Solve the following quadratic equation.

(2 + i)x² − (5 − i) x + 2(1 − i) = 0

Find the value of x³ − x² + x + 46, if x = 2 + 3i

Find the value of 2x³ − 11x² + 44x + 27, if x = `25/(3 - 4"i")`

Find the value of x³ + x² − x + 22, if x = `5/(1 - 2"i")`

Find the value of x⁴ + 9x³ + 35x² − x + 4, if x = `-5+sqrt(-4)`

Find the value of 2x⁴ + 5x³ + 7x² − x + 41, if x = `-2 - sqrt(3)"i"`

Find the sum to n terms 3 + 33 + 333 + 3333 + …

Find the sum to n terms 8 + 88 + 888 + 8888 + ...

Find the sum to n terms 0.4 + 0.44 + 0.444 + ...

Find the sum to n terms 0.7 + 0.77 + 0.777 + ...

Find S_n of the following arithmetico - geometric sequence: 

2, 4x, 6x², 8x³, 10x⁴, …

Find S_n of the following arithmetico - geometric sequence: 

1, 4x, 7x², 10x³, 13x⁴, …

Find S_n of the following arithmetico - geometric sequence:

1, 2 × 3, 3 × 9, 4 × 27, 5 × 81, …

Find S_n of the following arithmetico - geometric sequence:

3, 12, 36, 96, 240, …

Find the sum to infinity of the following arithmetico - geometric sequence:

`1, 2/4, 3/16, 4/64, ...`

Find the sum to infinity of the following arithmetico - geometric sequence:

`3, 6/5, 9/25, 12/125, 15/625, ...`

Find the sum to infinity of the following arithmetico - geometric sequence:

`1, -4/3, 7/9, -10/27 ...`

Find the sum `sum_("r" = 1)^"n" ("r" + 1)(2"r" - 1)`

Find `sum_("r" = 1)^"n"(3"r"^2 - 2"r" + 1)`