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

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is an odd natural number}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is a positive multiple of 3}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is a prime number}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is a natural number divisible by 3 and 5}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is a perfect square}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is perfect cube}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x + 5 = 8}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : 2x + 5 = 9}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x ≥ 7}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x ∈ N and 2x + 1 > 10}

If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.

Given the ellipse with equation 9x² + 25y² = 225, find the eccentricity and foci.

(3x + 5)(1 + tan x)

(sec x – 1)(sec x + 1)

If X and Y are two sets such that X ∪Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩Y have?

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

If S and T Are Two Sets Such that S Has 21 Elements, T Has 32 Elements, and S ∩ T Has 11 Elements, How Many Elements Does S ∪ T Have?

If X and Y are two sets such that X has 40 elements, X ∪Y has 60 elements and X ∩Y has 10 elements, how many elements does Y have?

In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea?