List of top Questions asked in CBSE Class X

If tan (A + B) = \(\sqrt3\) and tan (A - B) = \(\frac{1}{\sqrt3}\); 0°\( <\) (A + B) \(≤\) 90° ; A > B, find A and B
Choose the correct option and justify your choice: \(\frac{2\ tan\ 30°}{1 - tan^2 30°} =\)
Choose the correct option and justify your choice: sin 2A = 2 sin A is true when A =
Choose the correct option and justify your choice: \(\frac{1 - tan^2 45°}{1 + tan^2 45°} =\)
Choose the correct option and justify your choice: \(\frac{2\ tan\  30°}{1 + tan^2 30°} =\)

Evaluate the following. 
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan245° + cos230° - sin260°
(iii) \(\frac{cos 45°}{sec 30°+cosec30°}\)


(iv) \(\frac{sin\ 30°+tan\ 45°cosec\ 60°}{sec\ 30°+cos\ 60°+cot\ 45°}\)


(v) \(\frac{5cos^260°+4sec^230°-tan^245°}{sin^230°+cos^230°}\)

If \(cot\  \theta = \frac{7}{8},\) evaluate:

(i) \(\frac{(1 + sin\  \theta)(1 – sin θ)}{(1+cos θ)(1-cos θ)}\)

(ii) \(cot^2\) \(θ\)

The graphs of \(y = p(x)\) are given in Fig. 2.10 below, for some polynomials \(p(x)\) . Find the number of zeroes of \(p(x)\), in each case
(I)
(ii)
(iii)
(iv)
(v)
(vi)
Prove that \(3 + 2\sqrt 5\) is irrational.
Prove that \(\sqrt 5\) is irrational.
There is a circular path around a sports field. Sonia takes \(18\) minutes to drive one round of the field, while Ravi takes \(12\) minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
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.