List of top Mathematics Questions asked in CBSE Class X

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

The total surface area of a solid hemisphere of diameter ‘2d’ is :

If the mean and mode of a data are 12 and 21 respectively, then its median is :

A die is thrown once. Probability of getting a number other than 3 is :

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 \(\frac{5}{7}\).

Assertion (A) : The polynomial \(p(y) = y^2 + 4y + 3\) has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

If \(\alpha, \beta\) are the zeroes of the polynomial \(p(x) = x^2 - 3x - 1\), then find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\).

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

The coordinates of the centre of a circle are \((x - 7, 2x)\). Find the value(s) of ‘x’, if the circle passes through the point \((-9, 11)\) and has radius \(5\sqrt{2}\) units.

If \(\tan \theta = \frac{24}{7}\), then find the value of \(\sin \theta + \cos \theta\).

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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.

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, \(\triangle ABC\) 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.

Prove that : \(PM = \frac{1}{2} (PQ + QR + PR)\)

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use \(\pi = \frac{22}{7}\))

Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :
(i) same number appears on both the dice?
(ii) different number appears on both the dice?

Determine graphically, the coordinates of vertices of a triangle whose equations are \(2x - 3y + 6 = 0\); \(2x + 3y - 18 = 0\) and \(x = 0\). Also, find the area of this triangle.

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 areas of two squares is 640 m\(^2\). If the difference in perimeters is 64 m, find the sides.

State and prove Basic Proportionality Theorem.

In \(\triangle ABC \sim \triangle PQR\), CM and RN are medians. Prove \(\triangle AMC \sim \triangle PNR\) and \(\triangle CMB \sim \triangle RNQ\).