Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Let S = {x | x is a positive multiple of 3 less than 100}
P = {x | x is a prime number less than 20}. Then n(S) + n(P) is ______.

The set {x ∈ R : 1 ≤ x < 2} can be written as ______.

If A and B are any two sets, then A – B is equal to ______.

State True or False for the following statement.

Let sets R and T be defined as
R = {x ∈ Z | x is divisible by 2}
T = {x ∈ Z | x is divisible by 6}. Then T ⊂ R

Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.

Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.

Is the following relation a function? Justify your answer

R₁ = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`

Is the following relation a function? Justify your answer

R₂ = {(x, |x |) | x is a real number}

Given R = {(x, y) : x, y ∈ W, x² + y² = 25}. Find the domain and Range of R.

If R₁ = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R₁.

If R₂ = {(x, y) | x and y are integers and x² + y² = 64} is a relation. Then find R₂.

If R₃ = {(x, x) | x is a real number} is a relation. Then find domain and range of R₃.

Is the given relation a function? Give reasons for your answer.

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}

Is the given relation a function? Give reasons for your answer.

f = {(x, x) | x is a real number}

Is the given relation a function? Give reasons for your answer.

g = `"n", 1/"n" |"n"` is a positive integer

Is the given relation a function? Give reasons for your answer.

s = {(n, n²) | n is a positive integer}

Is the given relation a function? Give reasons for your answer.

t = {(x, 3) | x is a real number

Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.

Define the sequence a₁, a₂, a₃ ... as follows:
a₁ = 2, a_n = 5 a_n–1, for all natural numbers n ≥ 2.

Write the first four terms of the sequence.

If P(n) : “2.4²ⁿ⁺¹ + 3³ⁿ⁺¹ is divisible by λ for all n ∈ N” is true, then the value of λ is ______.