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

Find the sub-triplicate ratio of 216 : 343

Find the reciprocal ratio of 3 : 5

Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-duplicate ratio of 36 : 49.

Find the value of x, if: (2x + 3) : (5x – 38) is the duplicate ratio of `sqrt(5) : sqrt(6)`.

Find the value of x, if: (2x + 1) : (3x + 13) is the sub-duplicate ratio of 9 : 25.

Find the value of x, if: (3x – 7) : (4x + 3) is the sub-triplicate ratio of 8 : 27.

What quantity must be added to each term of the ratio x : y so that it may become equal to c : d?

A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 84 kg?

If 15(2x² – y²) = 7xy, find x : y; if x and y both are positive.

If `a/b = c/d`, show that: `(a + b) : (c + d) = sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`

if `x/a = y/b = z/c` prove that `(ax - by)/((a + b)(x - y)) + (by - cz)/((b + c)(y - z)) + (cz - az)/((c + a)(z - x)) = 3`

There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How any more girls should be added to the council so that the ratio of the number of boys to the number of girls may be 9 : 5?

State, whether the following statement is true or false. If false, give a reason.

If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.

State, whether the following statement is true or false. If false, give a reason.

The matrices A_2 × 3 and B_2 × 3 are conformable for subtraction.

State, whether the following statement is true or false. If false, give a reason.

Transpose of a 2 × 1 matrix is a 2 × 1 matrix.

State, whether the following statement is true or false. If false, give a reason.

Transpose of a square matrix is a square matrix.

State, whether the following statement is true or false. If false, give a reason.

A column matrix has many columns and only one row.

Given : `[(x, y + 2),(3, z - 1)] = [(3, 1),(3, 2)]`; find x, y and z.

Solve for a, b and c; if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`

Solve for a, b and c; if `[(a, a - b),(b + c, 0)] = [(3, -1),(2, 0)]`