List of top Mathematics Questions

In the given figure, \(PA\) is a tangent from an external point \(P\) to a circle with centre \(O\). If \(\angle POB = 125^{\circ}\), then \(\angle APO\) is equal to :

Shown in the given figure is a circle with centre \(O\). The area of the minor sector is \(7 \text{ cm}^{2}\). Area of circle is :

In the given figure, \(O\) is the centre of circle. \(XYZ\) is an arc of the circle subtending an angle of \(45^{\circ}\) at the centre. If the radius of the circle is 32 cm, then the length of the arc \(XYZ\) is :

The radius of a sphere (in cm) whose volume is \(36 \pi \text{ cm}^{3}\), 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 :

The natural number 2 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 \(\frac{5}{7}\).

Do the points \(P (1, 0)\), \(Q (- 5, 0)\) and \(R (- 2, 5)\) form a triangle ? If so, name the type of triangle formed.

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

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.

Find a quadratic polynomial whose zeroes are \((5 - 2\sqrt{3})\) and \((5 + 2\sqrt{3})\).

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 :