English Medium कक्षा १० - CBSE Important Questions for Mathematics

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Three numbers in A.P. have the sum of 30. What is its middle term?

If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

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

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.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.

Using distance formula, find which of them is correct.

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.

Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.

The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.

Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?

Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?

For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?

The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?

Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?

If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is