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

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Prove that the common chord of two intersecting circles is bisected at right angles by the line of centres.

In Fig. ABCD is a quadrilateral in which AB = BC. E is the point of intersection of the right bisectors of AD and CD. Prove that BE bisects ∠ABC.

Find the locus of the centre of a circle of radius r touching externally a circle of radius R.

ΔPBC and ΔQBC are two isosceles triangles on the same base. Show that the line PQ is bisector of BC and is perpendicular to BC.

Find the locus of points which are equidistant from three non-collinear points.

Show that the locus of the centres of all circles passing through two given points A and B, is the perpendicular bisector of the line segment AB.

ΔPBC and ΔQBC are two isosceles triangles on the same base BC but on the opposite sides of line BC. Show that PQ bisects BC at right angles.

ΔPBC, ΔQBC and ΔRBC are three isosceles triangles on the same base BC. Show that P, Q and R are collinear.

In Fig. AB = AC, BD and CE are the bisectors of ∠ABC and ∠ACB respectively such that BD and CE intersect each other at O. AO produced meets BC at F. Prove that AF is the right bisector of BC.

Given: ∠BAC, a line intersects the arms of ∠BAC in P and Q. How will you locate a point on line segment PQ, which is equidistant from AB and AC? Does such a point always exist?

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

The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?

The mean monthly salary of 10 members of a group is Rs.1,445, one more member whose monthly salary is Rs.1,500 has joined the group. Find the mean monthly salary of 11 members of the group.

The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean.

The mean of 100 items was found to be 30. If at the time of calculation two items were wrongly taken as 32 and 12 instead of 23 and 11, find the correct mean.

If `bar"X"` is the mean of n observations x₁, x₂, x₃,..., x_n then the mean of `x_1/"a", x_2/"a", x_3/"a",...,x_"n"/"a" "is" bar"X"/"a"`, where a is an non-zero number.

i.e., if each observation is divided by a non-zero number, then the mean is also divided by it.

By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x² + 5x – 3.

Show that (x – 2) is a factor of 3x² – x – 10 Hence factorise 3x² – x – 10.

Show that (x – 1) is a factor of x³ – 5x² – x + 5 Hence factorise x³ – 5x² – x + 5.