List of top Questions asked in CBSE Class X

Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = \(\frac{3}{7}\) AB and P lies on the line segment AB.

Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B ?

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units?

If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

Find the coordinates of the points of trisection of the line segment joining (4, − 1) and (− 2, − 3).

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of \(\frac 14\) m and a tread of \(\frac 12\) m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace.

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

Which term of the AP: 121, 117, 113, ..... is its first negative term?

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.

A triangle ABC is circumscribed a circle of radius 4 cm — **Fig. 10.14**

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

For the following APs, write the first term and the common difference:
(i) 3, 1, − 1, − 3 …
(ii) − 5, − 1, 3, 7 …
(iii) \(\frac{1}{3}, \frac{5}{3},\frac{9}{3},\frac{13}{3}\) ,…
(iv) 0.6, 1.7, 2.8, 3.9 …

In which of the following situations, does the list of numbers involved make as arithmetic progression and why?
(1) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.
(2) The amount of air present in a cylinder when a vacuum pump removes \(\frac{1}{4}\) of the air remaining in the cylinder at a time.
(3) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.
(4) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.