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

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 ______.

If P(n): “49ⁿ + 16ⁿ + k is divisible by 64 for n ∈ N” is true, then the least negative integral value of k is ______.

If z₁ and z₂ both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.

State true or false for the following:

If a complex number coincides with its conjugate, then the number must lie on imaginary axis.

Match the statements of column A and B.

If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).

If a = cosθ + isinθ, find the value of `(1 + "a")/(1 - "a")`.

State True or False for the following:

The order relation is defined on the set of complex numbers.