List of top Mathematics Questions

If $\csc \theta = 2$, then find the value of $\cot \theta + \dfrac{\sin \theta}{1 + \cos \theta}$.

Find the coordinates of the point which divides the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 2 : 3.

The mean and median of a frequency table are 30 and 35 respectively. Then its mode will be

If an event occurs certainly, then its probability will be

Find the LCM and HCF of 2520 and 10530 by prime factorization method.

If a line intersects the sides AB and AC at D and E respectively in a triangle ABC and it is parallel to the side BC, then prove that \[ \frac{AD}{AB} = \frac{AE}{AC} \]

The diameter of a solid pipe is 4 cm whose length is 20 cm. Then the volume of the metal used in the pipe will be

The length of tangent from a point Q to a circle is 24 cm and the distance of Q from the centre of circle is 25 cm. Then radius of the circle will be

If $\sin \theta - \cos \theta = 0$ then the value of $\sin^4 \theta + \cos^4 \theta$ will be

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then $\angle POA$ will be

Total surface area of a solid hemisphere with radius $r$ will be

Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be

If $\tan \alpha + \cot \alpha = 5$, then the value of $\tan^2 \alpha + \cot^2 \alpha$ will be

If $3 \tan A = 4$ then the value of $\sec A$ will be

If $\sin \theta = \csc \theta$ and $0 \leq \theta \leq \dfrac{\pi}{2}$, then the value of $\theta$ will be

The perimeter of a triangle whose vertices are (0, 4), (0, 0), and (3, 0) will be

10th term of the sequence $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, \dots$ will be

If in $\triangle ABC$ and $\triangle DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then they will be similar if

The shape of the graph of a quadratic equation $y = ax^2 + bx + c$, $a \neq 0$, will be

If the equation $x^2 - 4x + a = 0$ has no real roots, then

Rational number will be

In the system of equations $\dfrac{x}{a} = \dfrac{y}{b}$, $ax + by = a^2 + b^2$, value of y will be

Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and the diameter of the cylinder is 7 cm. Find the weight of the solid if the weight of \(1 \, \text{cm}^3\) of the metal is \(4.5 \, \text{g}\).

A chord of a circle of radius 15 cm subtends an angle of \(60^\circ\) at the centre of the circle. Find the area of the corresponding minor segment. \((\pi = 3.14, \, \sqrt{3} = 1.73)\)

The angle of elevation of the top of a tower from the top of a house whose height is 15 m is \(30^\circ\). Also, the angle of elevation of the top of the tower from the ground of the same house is \(60^\circ\). Find the height of the tower and the distance of the tower from the house.