(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

Find: The sub-triplicate ratio of 216: 343

Find: The reciprocal ratio of 8: 15.

The work done by (x – 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio of 3: 10. Find the value of x.

Solve for x: `(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (3x + 5)/(5x - 6)`.

If (a – x) : (b – x) be the duplicate ratio of a: b show that:
`(1)/x = (1)/a + (1)/b.`

If a: b with a ≠ b is the duplicate ratio of a + c: b + c, show that c² = ab.

If a : b = 5 : 3, show that (5a + 8b) : (6a – 7b) = 49 : 9.

If `a/b = c/d = e/f`, Prove that each of these ratios is equal to `(a + c + e)/(b + d + f)`.

If `a/(b + c) = b/(c + a) = c/(a + b)`, show that each ratio is equal to `(1)/(2) or -1`.

If x and y be unequal and x: y is the duplicate ratio of (x + z) and (y + z) prove that z is mean proportional between x and y.

If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` then show that (b - c)x + (c - a)y + (a - b) z = 0.

If p + r = 2q and `(1)/q + (1)/s = (2)/r`, then prove that p : q = r : s.

Take a point O on the plane at the paper. With O as center draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.

Draw a circle at a radius of 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.

Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.

Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60°, and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.

Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.

Draw a circle of radius 3 cm. Construct a square about the circle.

Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.

Draw a circle of radius 4 cm. Take a point P outside the circle without using the center at the circle. Draw two tangents to the circle from point P.