List of top Mathematics Questions asked in CBSE X

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{cos A - sin A + 1})}{\text{(cos A + sin A + 1)}} = \text{cosec A + cot A}\), using the identity cosec2 A = 1 + cot2 A.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(1 + \text{sec A})}{\text{sec A}} = \frac{\text{sin² A}}{(\text{1 - cos A})}\) [Hint: Simplify LHS and RHS separately]
Choose the correct option. Justify your choice. \(\frac{(1 + \text{tan}^2 A)}{(1 +\text{ cot}^ 2 A)}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{tan θ}}{(\text{1 - cot θ})} + \frac{\text{cot θ}}{(\text{1 - tan θ})} = 1 + \text{secθ cosecθ}\) [Hint: Write the expression in terms of \(\text{sin θ}\) and \(\text{cos θ}\)]
Prove the following identities, where the angles involved are acute angles for which the expressions are defined: \(\frac{\text{cos A}}{(1 + \text{sin A})} + \frac{(1 +\text{ sin A})}{\text{cos A }}=\text{ 2 sec A}\)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\( (\text{cosec θ}-\text{cot θ})²=\frac{(1-\text{cos θ})}{(1 +\text{cos θ})}\)
Choose the correct option. Justify your choice. (sec A + tan A) (1 - sin A)
Choose the correct option. Justify your choice. \((1+\text{tan θ+sec θ}) (1+\text{cot θ - cosec θ}) =\)
Choose the correct option. Justify your choice. 9 sec2A - 9 tan2A =
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A
Write all the other trigonometric ratios of \(∠\) A in terms of sec A
State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin \(\text{θ}\) increases as \(\text{θ}\) increases.
(iii) The value of cos \(\text{θ}\) increases as \(\text{θ}\) increases.
(iv) sin \(\text{θ}\) = cos \(\text{θ}\) for all values of \(\text{θ}\).
(v) cot A is not defined for A = 0°

In a classroom, 4 friends are seated at points A, B, C and D. 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 the distance formula, find which of them is correct.
In a classroom, 4 friends are seated at points A, B, C and D.

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 the following are irrationals :
  1.   \(\dfrac{1}{\sqrt 2}\) 
  2. \(7\sqrt 5\) 
  3. \(6 + \sqrt 2\)
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?