List of top Mathematics Questions asked in CBSE X

Explain why \(7 × 11 × 13 + 13\) and  \(7 × 6 × 5 × 4 × 3 × 2 × 1 + 5\) are composite numbers.
Given that HCF \((306, 657) = 9\) , find LCM \((306, 657)\).
Find the LCM and HCF of the following integers by applying the prime factorisation method. 
  1. \(12, 15\) and 
  2.  \(17, 23\) and 
  3. \(8, 9\) and \(25\)
If \(∠\) A  and \(∠\) B are acute angles such that cos A = cos B, then show that
\(∠ A = ∠ B\).
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
  1. \(26\) and \(91\)
  2. \(510\) \(\)and \(92\)
  3. \(336\) and \(54\)
Express each number as a product of its prime factors: 
  1. \(140\) 
  2. \(156\) 
  3. \(3825\) 
  4. \(5005\) 
  5. \(7429\)
Find the sum of the following APs:
  1. \(2, 7, 12, .......,\) to \(10\) terms.
  2. \(–37, –33, –29,.......,\) to \(12\) terms.
  3. \(0.6, 1.7, 2.8, ......., \)to \(100\) terms.
  4. \(\frac {1}{15}, \frac {1}{12}, \frac {1}{10}, .......,\) to \(11\) terms.

To conduct Sports Day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. Niharika runs \(\frac{1}{4}\)th the distance AD on the 2nd line and posts a green flag. Preet runs \(\frac{1}{5}\)th the distance AD on the eighth line and posts a red flag. What is the distance between both flags? If Rashmi has to post a blue flag halfway between the line segment joining the two flags, where should she post her flag?
If Rashmi has to post a blue flag halfway between the line segment joining the two flags

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.
A small terrace at a football ground comprises of 15 steps each of which is 50 m
Fig. 5.8