ICSE ICSE Class 7 - CISCE Question Bank Solutions for Mathematics

Simplify, giving Solution with positive index

`(1/("4ab"^2"c"))^2 div (3/(2"a"^2"bc"^2))^4`

Simplify, giving Solution with positive index

`((5"x"^7)^3 . (10"x"^2)^2)/(2"x"^6)^7 = (5^3 "x"^(7xx3) . 10^2 . "x"^(2xx2))/(2^7. "x"^(6xx7))`

Simplify, giving Solution with positive index

`((7 "p"^2 "q"^9 "r"^5)^2 (4 "pqr")^3)/(14 "p"^6 "q"^10 "r"^4)^2`

Simplify and express the Solution in the positive exponent form:

`((-3)^3 xx 2^6)/(6 xx 2^3)`

Simplify and express the Solution in the positive exponent form:

`((2^3)^5 xx 5^4)/(4^3 xx 5^2)`

Simplify and express the Solution in the positive exponent form:

`(36 xx (-6)^2 xx 3^6)/(12^3 xx 3^5)`

Simplify and express the Solution in the positive exponent form:

`- 128/2187`

Simplify and express the Solution in the positive exponent form:

`("a"^-7 xx "b"^-7 xx "c"^5 xx "d"^4)/("a"^3 xx "b"^-5 xx "c"^-3 xx "d"^8)`

Simplify and express the Solution in the positive exponent form:

`("a"^3 "b"^(-5))^-2 = "a"^(3 xx -2) "b"^(-5 xx -2)`

Evaluate: `(2^2)^0 + 2^-4 div 2^-6 + (1/2)^-3`

Evaluate: `5^"n" xx 25^("n" - 1) div (5^("n" -1) xx 25^("n" - 1))`

If m = -2 and n = 2; find the values of m² + n² - 2mn.

If m² = -2 and n = 2; find the values of: mⁿ + n^m

If m² = -2 and n = 2; find the values of: 6m^-3 + 4n² 

If m² = -2 and n = 2; find the values of: 2n³ – 3m 

A can do a piece of work in 6 days and B can do it in 8 days. How long will they take to complete it together?

A and B working together can do a piece of work in 10 days B alone can do the same work in 15 days. How long will A alone take to do the same work?

A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in:

1. one day
2. 2 days

What part of work will be left, after they have worked together for 2 days?

A and B take 6 hours and 9 hours respectively to complete a work. A works for 1 hour and then B works for two hours.
(i) How much work is done in these 3 hours?
(ii) How much work is still left?

A, B and C can do a piece of work in 12, 15 and 20 days respectively. How long will they take to do it working together?