List of top Mathematics Questions asked in CBSE Class X

Prove that $\sqrt{3}$ is an irrational number.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
Find the smallest number that is divisible by each of 8, 9, and 10.
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them
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 the area of a sector is one-twelfth that of a complete circle, then the angle of the sector is :
Assertion (A): The area of canvas cloth required to just cover a heap of rice in the form of a cone of diameter 14 m and height 24 m is $175\pi$ sq.m.
Reason (R): The curved surface area of a cone of radius $r$ and slant height $l$ is $\pi r l$.
Two friends were born in the year 2000. The probability that they have the same birthday is :
Marks : Below 10Below 20Below 30Below 40Below 50
Number of Students : 312275775
For the above distribution, the modal class 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 :
The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :
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 :
If tan A = 3 cot A, then the measure of the angle A is :
$(\sec \theta + \tan \theta)(1 - \sin \theta)$ is equal to:
The perpendicular bisector of the line segment joining the points A(–1, 3) and B(2, 4) cuts the y-axis at :
The probability of getting a sum of 8, when two dice are thrown simultaneously, is :
The solution of the pair of linear equations: \[ \frac{2x}{3} - \frac{y}{2} = -\frac{1}{6} \quad \text{and} \quad \frac{x}{2} + \frac{2y}{3} = 3 \] is:
The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :
Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. Find the height of the tower and the length of the original shadow. (use \(\sqrt{ 3}\) = 1.73)
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (use \(\sqrt{ 3}\) = 1.73)
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.