List of top Mathematics Questions

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

The graph of y = f(x) is given.
The number of zeroes of f(x) is :

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 \(\sin \theta = a/b\), then \(\cos \theta\) is equal to :

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

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is \(10\sqrt{3}\) m away from the base of the tower, 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 :

The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is :

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.