List of top Mathematics Questions asked in CBSE Class X

In \(\Delta ABC\), \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\) and \(EC = x - 1\), then find the value of \(x\).

In the figure given, \(\Delta ABC \sim \Delta XYZ\), then find the values of \(x\) and \(y\). (Given: \(AB=4, BC=6, AC=y, XY=x, YZ=7.2, XZ=6\))

If \(x = h + a\cos\theta, y = k + b\sin\theta\), then prove that : \(\left(\frac{x-h}{a}\right)^2 + \left(\frac{y-k}{b}\right)^2 = 1\).

Prove that : \(\frac{\tan A}{1 + \sec A} - \frac{\tan A}{1 - \sec A} = 2\csc A\).

In the given figure, \(\Delta ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle \(ABC\).

In the given figure, if a circle touches the side \(QR\) of \(\Delta PQR\) at \(S\) and extended sides \(PQ\) and \(PR\) at \(M\) and \(N\) respectively, then prove that : \(PM = \frac{1}{2}(PQ + QR + PR)\).

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio \(8 : 5\), then find the ratio between the radius of their bases to their height.

Two different coins are tossed simultaneously. What is the probability of getting :
(i) at least one head ?
(ii) at most one tail ?
(iii) a head and a tail ?

Prove that \(\sqrt{3}\) is an irrational number.

Find the ratio in which the \(x\)-axis divides the line segment joining the points \((6, 5)\) and \((-4, -1)\). Also find the point of intersection.

State and prove Basic Proportionality Theorem.

In the given figure, CM and RN are respectively the medians of $\Delta ABC$ and $\Delta PQR$. If $\Delta ABC \sim \Delta PQR$, then prove that : (i) $\Delta AMC \sim \Delta PNR$, (ii) $\Delta CMB \sim \Delta RNQ$.

The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data :

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

Draw the graph of the pair of linear equations $x - y + 2 = 0$ and $4x - y - 4 = 0$. Calculate the area of the triangle formed by the lines so drawn and the $x$-axis.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

The sum of the areas of two squares is 640 $m^2$. If the difference in their perimeters is 64 m, find the sides of the two squares.

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

The HCF of \(2^2 \cdot 3^3\) and \(3^2 \cdot 2^3\) is :

A letter is selected from the letters of the word FEBRUARY. The probability that it is a vowel is :

Which of the following numbers will not end with 0 for any natural number \(n\)?

The system of linear equations \(px + qy = r\) and \(p_1x + q_1y = r_1\) has a unique solution, if :

Which of the equations among the following is/are quadratic equation(s)? \(q_1 : x^2 + x = (x+1)^2\), \(q_2 : x-1 = x^2 - 1\), \(q_3 : x = x^2\), \(q_4 : \sqrt{x} = x^2 \sqrt{x+1}\)

The discriminant of the quadratic equation \(ax^2 + x + a = 0\) is :

The distance between points (3, 0) and (0, -3) is :