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

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number

Answer the following:

Show that z = `5/((1 - "i")(2 - "i")(3 - "i"))` is purely imaginary number.

Expand: `(sqrt(3) + sqrt(2))^4`

Expand: `(sqrt(5) - sqrt(2))^5`

Expand: (2x² + 3)⁴ 

Expand: `(2x - 1/x)^6`

Find the value of `(sqrt(3) + 1)^4- (sqrt(3) - 1)^4`.

Find the value of `(2 + sqrt(5))^5 + (2 - sqrt(5))^5`

Prove that `(sqrt(3) + sqrt(2))^6 + (sqrt(3) - sqrt(2))^6` = 970

Prove that `(sqrt(5) + 1)^5 - (sqrt(5) - 1)^5` = 352

Using binomial theorem, find the value of (102)⁴ 

Using binomial theorem, find the value of (1.1)⁵ 

Using binomial theorem, find the value of (9.9)³ 

Using binomial theorem, find the value of (0.9)⁴ 

Without expanding, find the value of (x + 1)⁴ − 4(x + 1)³ (x − 1) + 6 (x + 1)² (x − 1)² − 4(x + 1) (x − 1)³ + (x − 1)⁴

Without expanding, find the value of (2x − 1)⁴ + 4(2x − 1)³ (3 − 2x) + 6(2x − 1)² (3 − 2x)² + 4(2x − 1)¹ (3 − 2x)³ + (3 − 2x)⁴ 

Find the value of (1.02)⁶, correct upto four places of decimal

Find the value of (1.01)⁵, correct up to three places of decimals.

Find the value of (0.9)⁶, correct upto four places of decimal

If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respective, then verify that [A – (B ∪ C)] = [(A – B) ∩ (A – C)]