List of top Mathematics Questions asked in CBSE Class X

Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
Find the zeroes of the polynomial $f(t) = t^2 + 4\sqrt{3}t - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 2500 per month, find the monthly income of each
If $\triangle ABC \sim \triangle DEF$ and $AB = 4$ cm, $DE = 6$ cm, $EF = 9$ cm, and $FD = 12$ cm, find the perimeter of $\triangle ABC$.
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
Prove that $\sqrt{3}$ is an irrational number.
If $\tan \theta + \sec \theta = m$, then prove that $\sec \theta = \frac{m^2 + 1}{2m}$.
If $\sin A = \frac{3}{5}$ and $\cos B = \frac{12}{13}$, then find the value of $(\tan A + \tan B)$.
Assertion (A): The sum of the first fifteen terms of the AP $21, 18, 15, 12, \dots$ is zero.
Reason (R): The sum of the first $n$ terms of an AP with first term $a$ and common difference $d$ is given by: \[ S_n = \frac{n}{2} \left[ a + (n - 1) d \right]. \]
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Find the smallest number that is divisible by each of 8, 9, and 10.
The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :
A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is :
Two friends were born in the year 2000. The probability that they have the same birthday is :
In a $\triangle ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $BD = CE$. If $\angle B = \angle C$, then show that $DE \parallel BC$.
If the area of a sector is one-twelfth that of a complete circle, then the angle of the sector is :
If tan A = 3 cot A, then the measure of the angle A is :
$(\sec \theta + \tan \theta)(1 - \sin \theta)$ is equal to:
A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:
A line l intersects the sides PQ and PR of a \(\triangle\) PQR at L and M respectively such that LM || QR. If PL = 5·7 cm, PQ = 15·2 cm and MR = 5·5 cm, then the length of PM (in cm) is :
If in triangles $ABC$ and $PQR$, $\frac{AB}{QR} = \frac{BC}{PR}$, then they will be similar, when:
If two tangents inclined at an angle of 60º are drawn to a circle of radius 5 cm, then the length of each tangent is :
The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :