English Medium कक्षा १० - CBSE Important Questions

In an A.P., if S5 + S7 = 167 and S₁₀₌235, then find the A.P., where Sn denotes the sum of its first n terms.

Find the 9^th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185

Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

What value is generated in the above situation?

Find the sum of first 15 multiples of 8.

Find how many integers between 200 and 500 are divisible by 8.

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^th terms.

Find the sum of first 8 multiples of 3

Find a and b so that the numbers a, 7, b, 23 are in A.P.

Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n = 5 – 2n.

Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.

Reason (R): The sum of first n odd natural numbers is n².

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 distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

If a≠b≠0, prove that the points (a, a²), (b, b²) (0, 0) will not be collinear.

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k

Find the distance of a point P(x, y) from the origin.

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides