List of top Mathematics Questions asked in CBSE Class X

The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
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.
$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
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 $\pi r l$.
Calculate the mean of the following data :
Class :4 – 67 – 910 – 1213 – 15
Frequency :54910
The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
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
Prove that: \((\cot \theta - \csc \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}.\)
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: \[ S_n = \frac{n}{2} \left[ a + (n - 1) d \right]. \]
The LCM of 24, 36 and 60 in terms of their prime factors 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 :
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
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.
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.
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 $\triangle PCD$.
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
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
Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]
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 $\tan \theta + \sec \theta = m$, 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 $(\tan A + \tan B)$.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.