English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.

If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.

If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.

Consider the number 6ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 6ⁿ is divisible by 7.

Consider the number 12ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 12ⁿ ends with the digital zero.

Find the distance between two points

(i) P(–6, 7) and Q(–1, –5)

(ii) R(a + b, a – b) and S(a – b, –a – b)

(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.

Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area

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:

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