HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions

Answer the following:

Find the term independent of x in the in expansion of `(1 - x^2) (x + 2/x)^6`

Answer the following:

(a + bx) (1 − x)⁶ = 3 − 20x + cx² + ..... then find a, b, c

Answer the following:

The 3^rd term of (1 + x)ⁿ is 36x². Find 5^th term

Answer the following:

Suppose (1 + kx)ⁿ = 1 − 12x + 60x² − .... find k and n.

If (x − 1, y + 4) = (1, 2) find the values of x and y

If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y

If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B

If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P

Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)

Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)

Express {(x, y) / x² + y² = 100, where x, y ∈ W} as a set of ordered pairs

Let A = {6, 8} and B = {1, 3, 5}
Show that R₁ = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R₂ = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation

Write the relation in the Roster Form. State its domain and range

R₁ = {(a, a²)/a is prime number less than 15}

Write the relation in the Roster Form. State its domain and range

R₂ = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`

Write the relation in the Roster Form. State its domain and range

R₃ = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₄ = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}

Write the relation in the Roster Form. State its domain and range

R₅ = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₆ = {(a, b)/a ∈ N, a < 6 and b = 4}

Write the relation in the Roster Form. State its domain and range

R₇ = {(a, b)/a, b ∈ N, a + b = 6}

Write the relation in the Roster Form. State its domain and range

R₈ = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}