List of top Questions asked in CBSE Class X- 2026

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Assertion (A) : H.C.F. ($36\text{ m}^2, 18\text{ m}$) = $18\text{ m}$, where m is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

The area of a sector of a circle of radius $10\text{ cm}$ is $\frac{55}{3}\text{ cm}^2$. The value of central angle is

A camping tent in hemispherical shape of radius $1.4\text{ m}$, has a door opening of area $0.50\text{ m}^2$. Outer surface area of the tent is

The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, is

Which of the following can not be the probability of an event ?

Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

If sum and product of zeroes of a polynomial are ($-3$) and ($-2$) respectively, then a polynomial is

A wire is attached from a point $A$ on the ground to the top of a pole $BC$, making an angle of elevation as $60^\circ$. If $AB = 5\sqrt{3}\text{ m}$, then length of the wire is

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius $10\text{ cm}$. Curved surface area of the cavity carved out is (use $\pi = 3.14$)

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x - a}{h} = u\right)$. It was found that $\bar{x} = 64$, $h = 5$ and $a = 62.5$. The value of $\bar{u}$ is

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

For an acute angle $\theta$, if $\cos \theta = \frac{1}{8}$, then $\frac{8\sec\theta + 1}{8\sec\theta - 1}$ equals

Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is

The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

In the given figure, $PQ \parallel YZ$ such that $XP : PY = 2 : 3$. If $PQ = 5\text{ cm}$, then $YZ$ equals

In an A.P., if $a_{14} - a_8 = 24$, then the common difference of the A.P. is

In the given figure, $PQ$ is tangent to the circle with centre $O$. $S$ is a point on the circle such that $\angle SQT = 55^\circ$. The $m\angle QPS$ is

Devansh proved that $\Delta ABC \sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C = \angle R$, then which of the following was proved true?

A circle of diameter $20\text{ cm}$ is equally divided into five sectors. Find the area and perimeter of one of the sectors.

The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Solve the system of linear equations: $x = 4$ and $3x - 2y = 6$ graphically.

Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$