List of top Questions asked in CBSE Class X- 2026

Which of the following statements is not always true?

The pair of linear equations \( \frac{3x}{2} + \frac{5y}{3} = 7 \) and \( 9x + 10y = 14 \), is :

An ice-cream cone of radius r and height h is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then h : 2r equals

If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

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 $\pi = 3.14$)

For any natural number $n$, $6^n$ ends with the digit :

In the given figure, \(DE \parallel BC\). If \(\frac{AD}{DB} = \frac{1}{3}\) and \(AC = 6\) cm, then length AE is

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.

Assertion (A) : The probability that a leap year has 53 Mondays is \(\frac{2}{7}\).
Reason (R) : The probability that a non-leap year has 53 Mondays is \(\frac{5}{7}\).

Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is

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

Equation of another line parallel to the line represented by $2x - 6y = 7$ is :

In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions :

(i) Find m\(\angle\)AOP.

In the given figure, PA and PB are tangents to a circle centred at O. If \(\angle AOB = 130^\circ\), then \(\angle APB\) is equal to :

S is any point on the side QR of a \(\Delta PQR\) such that \(\angle PSR = \angle QPR\). Prove that \(\frac{QR}{RP} = \frac{RP}{RS}\).

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

If PQ and PR are tangents to the circle with centre O and radius 4 cm such that \(\angle QPR = 90^\circ\), then the length OP is

If \(\alpha\) and \(\beta\) are two zeroes of the quadratic polynomial \(p(x) = x^2 - 11x + 30\), then \(\frac{1}{\alpha} + \frac{1}{\beta}\) is equal to :

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

The natural number 1 is :

Find the H.C.F. and L.C.M. of 1530 and 2040.

ABCD is a rectangle of dimensions 80 cm \(\times\) 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width x cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of x.

If $a_n$ represents $n^{\text{th}}$ term of the A.P. $-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots$ then value of $a_{16} - a_{12}$ is

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is

PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is