List of top Mathematics Questions

Radio station tower built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’. (Assuming standard height/angle data from such figures: Base OP = 36m, $\angle AOP = 30^\circ$, $\angle BOP = 45^\circ$).

(i) Length of wire from O to top of B.
(ii) Length of wire from O to top of A.
(iii) (a) Distance AB. OR
(iii) (b) Area of \(\triangle OPB\).}

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 mm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors.

(i) What is the radius of circle?
(ii) What is the circumference of the brooch?
(iii) (a) What is the total length of silver wire required? OR
(iii) (b) What is the area of each sector of the brooch?}

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

The common difference of the AP : \(\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots\) is :

If \(\Delta ABC\) and \(\Delta DEF\) are similar such that \(2 AB = DE\) and \(BC = 8\) cm, then \(EF\) is equal to :

The mid-point of the line segment joining the points \((5, -4)\) and \((6, 4)\) lies on :

Given that \(\sin \theta = \frac{a}{b}\), then \(\cos \theta\) is equal to :

If \(\cos A = \frac{1}{2}\), then the value of \(\sin^{2} A + 2 \cos^{2} A\) is :

The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle of \(30^{\circ}\) with the ground. The height of the kite above the ground is :

If \(TP\) and \(TQ\) are two tangents to a circle with centre \(O\) from an external point \(T\) so that \(\angle POQ = 120^{\circ}\), then \(\angle PTQ\) is equal to :

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 HCF of 960 and 432 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: \(AB=4, BC=6, AC=y, XY=x, YZ=7.2, XZ=6\))