List of top Questions asked in CBSE Class X

Prove that $\sqrt{5}$ is an irrational number.
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 $p(x)$.
Check whether the following pair of equations is consistent or not. If consistent, solve graphically:
\[ x + 3y = 6\\ 3y - 2x = -12 \]
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.

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 $\sin 2\theta$.

Verify that \(\sin 2A = \frac{2 \tan A}{1 + \tan^2 A}\) for \(A = 30^\circ\).

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 \(y\).

MarksNumber of Students
10 -- 2012
20 -- 3030
30 -- 40\(x\)
40 -- 5065
50 -- 60\(y\)
60 -- 7025
70 -- 8018
In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to
In two concentric circles centred at O
Three coins are tossed together. The probability that exactly one coin shows head, is
The volume of air in a hollow cylinder is 450 cm\(^3\). A cone of same height and radius as that of cylinder is kept inside it. The volume of empty space in the cylinder is
The volume of air in a hollow cylinder is 450 cm
In \(\triangle ABC, \angle B = 90^\circ\). If \( \frac{AB}{AC} = \frac{1}{2} \), then cos C is equal to
15th term of the A.P. \( \frac{13}{3}, \frac{9}{3}, \frac{5}{3}, \dots \) is

If probability of happening of an event is 57%, then probability of non-happening of the event is

A quadratic polynomial having zeroes 0 and -2, is
To calculate mean of a grouped data, Rahul used assumed mean method. He used \( d = (x - A) \), where A is assumed mean. Then \( \bar{x} \) is equal to
If the sum of first n terms of an A.P. is given by \( S_n = \frac{n}{2}(3n+1) \), then the first term of the A.P. is
In the given figure, PA is tangent to a circle with centre O. If \(\angle APO = 30^\circ\) and OA = 2.5 cm, then OP is equal to
PA is tangent to a circle with centre O
Two dice are rolled together. The probability of getting an outcome (a, b) such that b = 2a, is
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is
If radius of base is 4 cm and slant height of the cone is 6 cm
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
△ABC,DE||BC. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1)
The value of k for which the system of equations \(3x - 7y = 1\) and \(kx + 14y = 6\) is inconsistent, is
The line \(2x - 3y = 6\) intersects x-axis at
Assertion (A) : \(\triangle ABC \sim \triangle PQR\) such that \(\angle A = 65^\circ\), \(\angle C = 60^\circ\). Hence \(\angle Q = 55^\circ\).
Reason (R) : Sum of all angles of a triangle is \(180^\circ\).
Assertion (A) : \((a + \sqrt{b})(a - \sqrt{b})\) is a rational number, where a and b are positive integers.
Reason (R) : Product of two irrationals is always rational.
Find the nature of roots of the equation \(3x^2 - 4\sqrt{3}x + 4 = 0\).