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

Evaluate the following limit :

`lim_(Deltax -> 0) [((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)]`

Evaluate the following limit :

`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`

Evaluate the following limit :

`lim_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`

Evaluate the following limit :

`lim_(y -> 1/2) [(1 - 8y^3)/(y - 4y^3)]`

Evaluate the following limit :

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

Evaluate the following limit:

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

Evaluate the following limit :

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

Evaluate the following limit :

`lim_(x -> "a")[1/(x^2 - 3"a"x + 2"a"^2) + 1/(2x^2 - 3"a"x + "a"^2)]`

Select the correct answer from the given alternatives.

`lim_(x -> 2) ((x^4 - 16)/(x^2 - 5x + 6))` =

Select the correct answer from the given alternatives.

`lim_(x -> -2)((x^7 + 128)/(x^3 + 8))` =

Select the correct answer from the given alternatives.

`lim_(x -> 3) (1/(x^2 - 11x + 24) + 1/(x^2 - x - 6))` = 

Select the correct answer from the given alternatives.

`lim_(x -> 5) ((sqrt(x + 4) - 3)/(sqrt(3x - 11) - 2))` =

Differentiate the following w.r.t.x :

y = `x^(4/3) + "e"^x - sinx`

Differentiate the following w.r.t.x :

y = `sqrt(x) + tan x - x^3`

Differentiate the following w.r.t.x :

y = `log x - "cosec"  x + 5^x - 3/(x^(3/2))`

Differentiate the following w.r.t.x :

y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`

Differentiate the following w.r.t.x :

y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`

Differentiate the following w.r.t.x :

y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`

Select the correct answer from the given alternative:

If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`

Select the correct answer from the given alternative:

If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =