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

Factorise the expression and divide them as directed:

(3x⁴ – 1875) ÷ (3x² – 75)

The sum of first n natural numbers is given by the expression `n^2/2 + n/2`. Factorise this expression.

The sum of (x + 5) observations is x⁴ – 625. Find the mean of the observations.

The base of a parallelogram is (2x + 3 units) and the corresponding height is (2x – 3 units). Find the area of the parallelogram in terms of x. What will be the area of parallelogram of x = 30 units?

The radius of a circle is 7ab – 7bc – 14ac. Find the circumference of the circle. `(pi = 22/7)`

Verify the following:

(ab + bc)(ab – bc) + (bc + ca)(bc – ca) + (ca + ab)(ca – ab) = 0

Verify the following:

(a + b + c)(a² + b² + c² – ab – bc – ca) = a³ + b³ + c³ – 3abc

Verify the following:

(p – q)(p² + pq + q²) = p³ – q³

Verify the following:

(m + n)(m² – mn + n²) = m³ + n³

Verify the following:

(a² – b²)(a² + b²) + (b² – c²)(b² + c²) + (c² – a²) + (c² + a²) = 0

Verify the following:

`((3p)/7 + 7/(6p))^2 - (3/7p  + 7/(6p))^2 = 2`

Find the value of a, if 8a = 35² – 27² 

Find the value of a, if 9a = 76² – 67²

Find the value of a, if pqa = (3p + q)² – (3p – q)²

Find the value of a, if pq²a = (4pq + 3q)² – (4pq – 3q)² 

Find the value of `(6.25 xx 6.25 - 1.75 xx 1.75)/(4.5)`

Find the value of `(198 xx 198 - 102 xx 102)/96`

The product of two expressions is x⁵ + x³ + x. If one of them is x² + x + 1, find the other.