Secondary School (English Medium) (5 to 8) Class 8 - CBSE Question Bank Solutions

Factorise the following expression.

a²b + a²c + ab + ac + b²c + c²b

Factorise the following expression.

2ax² + 4axy + 3bx² + 2ay² + 6bxy + 3by² 

For a fixed base, if the exponent decreases by 1, the number becomes ______.

The multiplicative inverse of 10^–100 is ______.

The multiplicative inverse of `(- 5/9)^-99` is ______.

The multiplicative inverse of 10¹⁰ is ______.

The multiplicative inverse of (– 4)^–2 is (4)^–2.

The multiplicative inverse of `(3/2)^2` is not equal to `(2/3)^-2`.

The expression for 4^–3 as a power with the base 2 is 2⁶.

Express 3^–5 × 3^–4 as a power of 3 with positive exponent.

Express 16^–2 as a power with the base 2.

The cells of a bacteria double itself every hour. How many cells will there be after 8 hours, if initially we start with 1 cell. Express the answer in powers.

Predicting the ones digit, copy and complete this table and answer the questions that follow.

1. Describe patterns you see in the ones digits of the powers.
2. Predict the ones digit in the following:
   1. 4¹²
   2. 9²⁰
   3. 3¹⁷
   4. 5¹⁰⁰
   5. 10⁵⁰⁰
3. Predict the ones digit in the following:
   1. 31¹⁰
   2. 12¹⁰
   3. 17²¹
   4. 29¹⁰ 

Which quantities in the previous question vary inversely with each other?

Which of the following vary inversely with each other?

If two quantities p and q vary inversely with each other, then ______

If xy = 10, then x and y vary ______ with each other.

When two quantities x and y are in ______ proportion or vary ______ they are written as `x  oo  1/y`.

Both x and y are said to vary ______ with each other if for some positive number k, xy = k.

Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant.