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

Answer the following:

If a, b, c are in G.P. and ax² + 2bx + c = 0 and px² + 2qx + r = 0 have common roots then verify that pb² – 2qba + ra² = 0

Answer the following:

If p, q, r, s are in G.P., show that (p² + q² + r²) (q² + r² + s²) = (pq + qr + rs)²   

Answer the following:

If p, q, r, s are in G.P., show that (pⁿ + qⁿ), (qⁿ + rⁿ) , (rⁿ + sⁿ) are also in G.P.

Answer the following:

Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`

Evaluate: 8!

Evaluate: 10!

Evaluate: 10! – 6!

Evaluate: (10 – 6)!

Compute: `(12!)/(6!)`

Compute: `(12/6)!`

Compute: (3 × 2)!

Compute: 3! × 2!

Compute: `(9!)/(3!  6!)`

Compute: `(6! - 4!)/(4!)`

Compute: `(8!)/(6! - 4!)`

Compute: `(8!)/((6 - 4)!)`

Write in terms of factorial.

5 × 6 × 7 × 8 × 9 × 10

Write in terms of factorial.

3 × 6 × 9 × 12 × 15

Write in terms of factorial.

6 × 7 × 8 × 9

Write in terms of factorial.

5 × 10 × 15 × 20