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

Evaluate the following :

`lim_(x -> pi/6) [(2 - sqrt(3)cosx - sinx)/(6x - pi)^2]`

Evaluate the following :

`lim_(x -> "a") [(sin(sqrt(x)) - sin(sqrt("a")))/(x - "a")]`

Evaluate the following:

`lim_(x -> pi/2) [(cos3x + 3cosx)/(2x - pi)^3]`

Evaluate the following :

`lim_(x -> 0)[((1 - x)^5 - 1)/((1 - x)^3 - 1)]`

Evaluate the following :

`lim_(x -> 1) [(2^(2x - 2) - 2^x + 1)/(sin^2 (x - 1))]`

Evaluate the following :

`lim_(x -> 1) [(4^(x -  1) - 2^x + 1)/(x - 1)^2]`

Evaluate the following :

`lim_(x -> 1) [(sqrt(x) - 1)/logx]`

Differentiate the following w.r.t.x. :

y = x³ log x

Differentiate the following w.r.t.x. :

y = e^x logx

Differentiate the following w.r.t.x. :

y = `x^(3/2)  "e"^xlogx`

Differentiate the following w.r.t.x. :

y = log e^_x3 log x³ 

Differentiate the following w.r.t.x. :

y = `x^2sqrt(x) + x^4logx`

Differentiate the following w.r.t.x. :

y = (x³ – 2) tan x – x cos x + 7^x. x⁷

Differentiate the following w.r.t.x. :

y = `(x log x)/(x + log x)`

Find the trigonometric functions of 120°.

Find the value of x³-x^{2 ,} if x=2+3i

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

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

Examine the consistency of the following equation:

2x − y + 3 = 0, 3x + y − 2 = 0, 11x + 2y − 3 = 0

Examine the consistency of the following equation:

2x + 3y − 4 = 0, x + 2y = 3, 3x + 4y + 5 = 0