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

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

(A – B)² = A² – 2A . B + B²

Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.  

The bisectors of angles A and B of a scalene triangle ABC meet at O.

1. What is the point O called?
2. OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
3. What is the relation between angle ACO and angle BCO?

1. Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
2. Find its in centre and mark it I.
3. With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle. 

Construct a circle, inscribing an equilateral triangle with side 5.6 cm. 

Draw a circle circumscribing a regular hexagon with side 5 cm. 

Draw an inscribing circle of a regular hexagon of side 5.8 cm.

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent. 

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.

1. Construct a circle circumscribing the triangle ABC.
2. Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. 

If `(y- x)/x = 3/8` , find the value of  `y /x`

Two numbers are in the ratio 2 : 3. If 5 is added to each number, the ratio becomes 5 : 7. Find the numbers.

Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the numbers.

The ratio between the number of boys and the number of girls in a class is 4:3 . If there were 20 more boys and 12 less girls, the ratio would have been 2:1. Find the total number of students in
the class.

Find the compound ratio of :
3 : 5 and 8 : 15

Find the reciprocal ratio of 5 : 8

If 3x + 4 : x + 5 is the duplicate ratio of 8 : 15, find x.

If 4x + 4 : 9x – 10 is the triplicate ratio of 4 : 5, find x.

If `(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` prove that each of theseccc `2/(m+n)`provided  a + b + c ≠ 0

Two numbers are in the ratio 5:7. If 3 is subtracted from each of them, the ratio between them becomes 2:3. Find the numbers.

If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – B + C