English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

The distance between the points A(0, 6) and B(0, –2) is ______.

The distance of the point P(–6, 8) from the origin is ______.

The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.

∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).

Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).

Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.

A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).

Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).

Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?

What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?

Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.

Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.

If two positive integers a and b are written as a = x³ y² and b = xy³; x, y are prime numbers, then HCF (a, b) is ______.

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is ______.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.