HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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°

Evaluate the following : 

sin 30° × cos 45° × tan 360°

If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`

Eliminate θ from the following: 

x = 3secθ , y = 4tanθ

Eliminate θ from the following : 

x = 6cosecθ, y = 8cotθ

Eliminate θ from the following :

x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ

Eliminate θ from the following :

x = 5 + 6cosecθ, y = 3 + 8cotθ

Eliminate θ from the following:

2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ

Find the acute angle θ such that 2 cos²θ = 3 sin θ.

Find the acute angle θ such that 5tan²θ + 3 = 9secθ.

Find sinθ such that 3cosθ + 4sinθ = 4

If cosecθ + cotθ = 5, then evaluate secθ.

If cotθ = `3/4` and π < θ < `(3pi)/2` then find the value of 4cosecθ + 5cosθ.

Prove the following identities:

`(1 + tan^2 "A") + (1 + 1/tan^2"A") = 1/(sin^2 "A" - sin^4"A")`

Prove the following identities: 

(cos²A – 1) (cot²A + 1) = −1

Prove the following identities:

(sinθ + sec θ)² + (cosθ + cosec θ)² = (1 + cosecθ sec θ)²