List of top Questions asked in CBSE Class X

The following distribution shows the marks of 230 students in a particular subject. If the median marks are 46, then find the values of $x$ and $y$.

Marks	Number of Students
10 -- 20	12
20 -- 30	30
30 -- 40	$x$
40 -- 50	65
50 -- 60	$y$
60 -- 70	25
70 -- 80	18

From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$

If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to third side. State and prove the converse of the above statement.

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 the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

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

If the points $A(6, 1)$, $B(p, 2)$, $C(9, 4)$ and $D(7, q)$ are the vertices of a parallelogram $ABCD$, then find the values of $p$ and $q$. Hence, check whether $ABCD$ is a rectangle or not.

Find the zeroes of the polynomial $p(x) = 3x^2 - 4x - 4$. Hence, write a polynomial whose each of the zeroes is 2 more than the zeroes of $p(x)$.

Prove that $\sqrt{5}$ is an irrational number.

The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

P is a point on the side BC of $\triangle ABC$ such that $\angle APC = \angle BAC$. Prove that $AC^2 = BC \cdot CP$.

Use the identity: $\sin^2A + \cos^2A = 1$ to prove that $\tan^2A + 1 = \sec^2A$. Hence, find the value of $\tan A$, when $\sec A = \dfrac{5}{3}$ where A is an acute angle.

In a pair of supplementary angles, the greater angle exceeds the smaller by $50^\circ$. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

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

The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of a project, a student constructed an inclinometer and wishes to find the height of the Statue of Unity using it. He noted the following observations from two places:
Situation – I: The angle of elevation of the top of Statue from Place A, which is $80\sqrt{3}$ m away from the base of the Statue, is found to be $60^\circ$.
Situation – II: The angle of elevation of the top of the Statue from a Place B, which is 40 m above the ground, is found to be $30^\circ$ and the total height of the statue including the base is given to be 240 m.
Based on the given information, answer the following: