Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

For all sets A, B and C is (A ∩ B) ∪ C = A ∩ (B ∪ C)? Justify your statement.

Use the properties of sets to prove that for all the sets A and B 

A – (A ∩ B) = A – B

For all sets A, B, and C

Is (A – B) ∩ (C – B) = (A ∩ C) – B? Justify your answer.

Let A, B and C be sets. Then show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Let P be the set of prime numbers and let S = {t | 2^t – 1 is a prime}. Prove that S ⊂ P.

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the largest possible number that could have passed all three examination?

The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to ______.

For all sets A, B and C, show that (A – B) ∩ (A – C) = A – (B ∪ C)

For the hyperbola 9x² – 16y² = 144, find the vertices, foci and eccentricity

Find the equation of the ellipse which passes through the point (–3, 1) and has eccentricity `sqrt(2)/5`, with x-axis as its major axis and centre at the origin.

If e is the eccentricity of the ellipse `x^2/a^2 + y^2/b^2` = 1 (a < b), then ______.

Find the derivative of f(x) = ax + b, where a and b are non-zero constants, by first principle

Find the derivative of f(x) = ax² + bx + c, where a, b and c are none-zero constant, by first principle.

Find the derivative of f(x) = x³, by first principle.

Find the derivative of f(x) = `1/x` by first principle.

Find the derivative of f(x) = sin x, by first principle.

Find the derivative of `cosx/(1 + sinx)`

`(x^4 + x^3 + x^2 + 1)/x`

`(x + 1/x)^3`

`(3x + 4)/(5x^2 - 7x + 9)`