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

Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.

The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`

The relation g is defined by  g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a relation from A to B

Justify your answer in case.

Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`

Express the given complex number in the form a + ib: i^–39

Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`

Express the given complex number in the form a + ib:

`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`

Express the given complex number in the form a + ib: `(1/3 + 3i)^3`

Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`

Evaluate: `[i^18 + (1/i)^25]^3`

If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a² + b² = `(x^2 + 1)^2/(2x + 1)^2`

Let z₁ = 2 – i, z₂ = –2 + i. Find Re`((z_1z_2)/barz_1)`

Let z₁ = 2 – i, z₂ = –2 + i. Find `"Im"(1/(z_1barz_1))`

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?