English Medium इयत्ता १० - CBSE Question Bank Solutions

If P and Q are two points whose coordinates are (at² ,2at) and (a/t² , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.

If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex

Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circum radius

If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.

Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle

If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.

Express the number as a product of its prime factor:

140

Find the LCM and HCF of the following integers by applying the prime factorisation method.

12, 15 and 21

Given that HCF (306, 657) = 9, find LCM (306, 657).

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in the following.

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).

Find the distance between the following pairs of points:

(2, 3), (4, 1)