HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following limit :

`lim_(x -> 0) [((49)^x - 2(35)^x + (25)^x)/(sinx* log(1 + 2x))]`

Select the correct answer from the given alternatives.

`lim_(x -> 0) ((15^x - 3^x - 5^x + 1)/sin^2x)` =

Select the correct answer from the given alternatives.

`lim_(x -> 0) ((3 + 5x)/(3 - 4x))^(1/x)` =

Select the correct answer from the given alternatives.

`lim_(x -> 0) [(log(5 + x) - log(5 - x))/sinx]` =

Select the correct answer from the given alternatives.

`lim_(x -> pi/2) ((3^(cosx) - 1)/(pi/2 - x))` =

Select the correct answer from the given alternatives.

`lim_(x -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =

Select the correct answer from the given alternatives.

`lim_(x→0)[(3^(sinx) - 1)^3/((3^x - 1).tan x.log(1 + x))]` =

Select the correct answer from the given alternatives.

`lim_(x -> 3) [(5^(x - 3) - 4^(x - 3))/(sin(x - 3))]` =

Evaluate the following :

`lim_(x -> 0)[("e"^x + "e"^-x - 2)/(x*tanx)]`

Evaluate the following :

`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`

Evaluate the following :

`lim_(x -> 2) [(logx - log2)/(x - 2)]`

Evaluate the following :

`lim_(x -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`

Evaluate the following : 

`lim_(x -> 0) [((5^x - 1)^2)/((2^x - 1)log(1 + x))]`

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

y = `(x"e"^x)/(x + "e"^x)`

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

y = `(5"e"^x - 4)/(3"e"^x - 2)`

Evaluate the following limit :

`lim(x>2)[(z^2 -5z+6)/(z^2-4)]`

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.

Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find 

1. P (A ∩ B)
2. P (A ∪ B)
3. P (A | B)
4. P (B | A)

Evaluate the following:

sin 30° + cos 45° + tan 180°

Evaluate the following : 

cosec 45° + cot 45° + tan 0°