HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following :

`lim_(x -> ∞) [sqrt(x^4 + 4x^2) - x^2]`

Evaluate the following :

`lim_(x -> ∞) [((3x^2 + 4)(4x^2 - 6)(5x^2 + 2))/(4x^6 + 2x^4 - 1)]`

Evaluate the following :

`lim_(x -> ∞) [((3x - 4)^3 (4x + 3)^4)/(3x + 2)^7]`

Evaluate the following :

`lim_(x -> ∞) [sqrt(x)(sqrt(x + 1) - sqrt(x))]`

Evaluate the following :

`lim_(x -> ∞) [((2x - 1)^20 (3x - 1)^30)/(2x + 1)^50]`

Evaluate the following :

`lim_(x -> ∞) [(sqrt(x^2 + 5) - sqrt(x^2 - 3))/(sqrt(x^2 + 3) - sqrt(x^2 + 1))]`

Select the correct answer from the given alternatives.

`lim_(x -> ∞) [((2x + 3)^7 (x - 5)^3)/(2x - 5)^10]` =

Evaluate the following : 

`lim_(x -> ∞) [((2x + 1)^2*(7x - 3)^3)/(5x + 2)^5]`

Evaluate the following :

`lim_(x -> ∞) [(8x^2 + 5x + 3)/(2x^2 - 7x - 5)]^((4x + 3)/(8x - 1))`

If f(x) is a quadratic polynomial such that f(0) = 3, f'(2) = 2 and f'(3) = 12 then find f(x)

If f(x) = a sin x – b cos x, `"f'"(pi/4) = sqrt(2) and "f'"(pi/6)` = 2, then find f(x)

If f(2) = 4, f′(2) = 1 then find `lim_(x -> 2) [(x"f"(2) - 2"f"(x))/(x - 2)]`

Prove the following identity:

`(1 - sec theta + tan theta)/(1 + sec theta - tan theta) = (sec theta + tan theta - 1)/(sec theta + tan theta + 1)`

Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.

Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

If A = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.

If A = `[(7,1), (2,5)]` and B = `[(1,2), (3,-1)]` then verify that |AB| = |A|  |B|.

Find the value of `sin  (19pi^"c")/3`.

Find the value of :

cos 1140°

Find the values of:

`cot  (25pi^"c")/3`