List of top Questions asked in CBSE Class X

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
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.
In the given figure, AB \(||\) DE and BD \(||\) EF. Prove that \(DC^2 = CF \times AC\).
AB || DE and BD || EF. Prove that DC2 = CF ×AC
Three friends plan to go for a morning walk. They step off together and their steps measures 48 cm, 52 cm and 56 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ten times?
Prove that \(\left(1 + \frac{1}{\tan^2 \theta}\right) \left(1 + \frac{1}{\cot^2 \theta}\right) = \frac{1}{\sin^2 \theta - \sin^4 \theta}\).
Find the zeroes of the polynomial \(p(x) = 3x^2 + x - 10\) and verify the relationship between zeroes and its coefficients.
The sum of a number and its reciprocal is \(\frac{13}{6}\). Find the number.
Two poles of equal heights are standing opposite each other on either side of the road which is 85 m wide. From a point between them on the road, the angles of elevation of the top of the poles are \(60^\circ\) and \(30^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. (Use \(\sqrt{3} = 1.73\))
Solve the following pair of linear equations by graphical method : \(2x + y = 9\) and \(x - 2y = 2\).