List of top Mathematics Questions asked in CBSE X

The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.
The interior of a building is in the form of a cylinder of base radius 12 m and height 3×5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building.
Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]
From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.
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.
Calculate the mean of the following data :
Class :4 – 67 – 910 – 1213 – 15
Frequency :54910
The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]
A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle
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 $\tan \theta + \sec \theta = m$, 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 $(\tan A + \tan B)$.
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 $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
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
Find the smallest number that is divisible by each of 8, 9, and 10.
If $\triangle ABC \sim \triangle DEF$ and $AB = 4$ cm, $DE = 6$ cm, $EF = 9$ cm, and $FD = 12$ cm, find the perimeter of $\triangle ABC$.
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 a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
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 $\pi r l$.
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: \[ S_n = \frac{n}{2} \left[ a + (n - 1) d \right]. \]
Two friends were born in the year 2000. The probability that they have the same birthday is :