List of top Mathematics Questions asked in CBSE Class X

Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

Nidhi received simple interest of ₹1,200 when she invested ₹x at 6% per annum and ₹y at 5% per annum for 1 year. Had she invested ₹x at 3% per annum and ₹y at 8% per annum for that year, she would have received simple interest of ₹1,260.Find the values of x and y.

In the adjoining figure, $PQ \parallel XY \parallel BC$, $AP=2\ \text{cm}, PX=1.5\ \text{cm}, BX=4\ \text{cm}$. If $QY=0.75\ \text{cm}$, then $AQ+CY =$

In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

Solve the following pair of equations algebraically:
\[ 101x + 102y = 304 \quad \text{(i)}\\ 102x + 101y = 305 \quad \text{(ii)} \]

Find the nature of roots of the equation $3x^2 - 4\sqrt{3}x + 4 = 0$.

A drone is flying at a height of $h$ metres. At an instant it observes the angle of elevation of the top of an industrial turbine as $60^\circ$ and the angle of depression of the foot of the turbine as $30^\circ$. If the height of the turbine is $200\, \text{metres}$, find the value of $h$ and the distance of the drone from the turbine.
(Use $\sqrt{3} = 1.73$)

Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

Find the smallest value of $p$ for which the quadratic equation $x^2 - 2(p + 1)x + p^2 = 0$ has real roots. Hence, find the roots of the equation so obtained.

In $\triangle ABC, DE || BC$. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is

Find the sum of first 20 terms of an A.P. whose n$^{th}$ term is given by $a_n = 5 + 2n$. Can 52 be a term of this A.P. ?

There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.