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

Evaluate the following limit :

`lim_(y -> 0) [(sqrt("a" + y) - sqrt("a"))/(ysqrt("a" + y))]`

Evaluate the following limit :

`lim_(x -> 0)[(sqrt(x^2 + 9) - sqrt(2x^2 + 9))/(sqrt(3x^2 + 4) - sqrt(2x^2 + 4))]`

Evaluate the following limit :

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

Evaluate the Following limit :

`lim_(x -> 0) [(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 - x))]`

Evaluate the Following limit :

`lim_(x -> 4) [(x^2 + x - 20)/(sqrt(3x + 4) - 4)]`

Evaluate the Following limit :

`lim_(z -> 4) [(3 - sqrt(5 + z))/(1 - sqrt(5 - z))]`

Evaluate the Following limit :

`lim_(x -> 0)[3/(xsqrt(9  - x)) - 1/x]`

Evaluate the following :

`lim_(x -> 0)[x]` ([*] is a greatest integer function.)

Evaluate the following :

If f(r) = πr² then find `lim_("h" -> 0) [("f"("r" + "h") - "f"("r"))/"h"]`

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

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

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

y = `(sqrt(x) + 5)/(sqrt(x) - 5)`

By using properties of determinant prove that

`|(x+ y,y+z, z+x ),(z, x,y),(1,1,1)|` = 0 

Evaluate the following limit:

`lim_(x->0)[(sqrt(6 + x + x^2) - sqrt6)/ (x)]`

Evaluate the following limit:

`lim_(x -> 0)[(sqrt(6 + x + x^2) - sqrt6)/x]`

Convert the following angle into radian:

85°

Convert the following angle into radian:

250°

Convert the following angle into radian:

−132°

Convert the following angles into radian:

65°30′

Convert the following angles into radian:

75°30′

Convert the following angles into radian:

40° 48′