List of practice Questions

The maximum number of tangents drawn from an external point to a circle will be
The distance of point (7, 3) from y-axis will be
If $\csc \theta = 2$, then find the value of $\cot \theta + \dfrac{\sin \theta}{1 + \cos \theta}$.
Prove that the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Show that the linear equations $3x - y = 2$ and $9x - 3y = 6$ have many solutions.
The angle of elevation of the top of a 10-metre high building from a point P on the earth is 30°. There is a flag on top of the building. The angle of elevation of the top of the flag from point P is 45°. Find the length of the flag.
The sum of the digits of a two-digit number is 9. If the digits of the number be interchanged then the new number is 27 more than the original number. Find the number.
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 \[ \frac{AD}{AB} = \frac{AE}{AC} \]
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.
If $\sin \theta - \cos \theta = 0$ then the value of $\sin^4 \theta + \cos^4 \theta$ 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 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
Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be
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
Total surface area of a solid hemisphere with radius $r$ 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 perimeter of a triangle whose vertices are (0, 4), (0, 0), and (3, 0) will be
If $3 \tan A = 4$ then the value of $\sec A$ will be
If $\tan \alpha + \cot \alpha = 5$, then the value of $\tan^2 \alpha + \cot^2 \alpha$ will be
If $\sin \theta = \csc \theta$ and $0 \leq \theta \leq \dfrac{\pi}{2}$, then the value of $\theta$ will be
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.