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

The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P. the first term is 25, n^th term is –17 and the sum of n terms is 132. Find n and the common difference.

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P. Also, find the sum of first 20 terms of A.P.

Find the sum of all multiples of 7 lying between 300 and 700.

The sum of n natural numbers is 5n² + 4n. Find its 8^th term.

The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5 cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C. 

In each of the given figures; PA = PB and QA = QB. 

i.
ii.

Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.

Construct a right angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4.5 cm. Draw bisector of angle PQR and let it meets PR at point T. Prove that T is equidistant from PQ and QR. 

In parallelogram ABCD, side AB is greater than side BC and P is a point in AC such that PB bisects angle B. Prove that P is equidistant from AB and BC. 

In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. Prove that:

1. Point A is equidistant from all the three sides of the triangle.
2. AM bisects angle LMN. 

Use ruler and compasses only for this question.

1. Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
2. Construct the locus of points inside the triangle which are equidistant from BA and BC.
3. Construct the locus of points inside the triangle which are equidistant from B and C.
4. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that: 

F is equidistant from A and B.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that: 

F is equidistant from AB and AC.

The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD. 

Draw a line AB = 6 cm. Draw the locus of all the points which are equidistant from A and B. 

Draw an angle ABC = 75°. Draw the locus of all the points equidistant from AB and BC.

Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5 cm. Find a point P equidistant from AB and BC; and also equidistant from A and B.