List of practice Questions

The roots of the quadratic equation \( px^2 - qx + r = 0, \, p \neq 0 \) are:
If \( x = -1 \) is a common root of both the equations \( 2x^2 + 3x + p = 0 \) and \( qx^2 - qx + 4 = 0 \), then the value of \( p + q \) is:
The length, breadth, and height of a cuboid are 15 m, 6 m, and 5 m, respectively. Then the lateral surface area of the cuboid is:
The distance covered by a wheel of radius 14 cm in 5 revolutions is:
If the area of a circle is equal to the area of a square, then the ratio of their perimeters is:
Which of the following is a quadratic equation?
If one root of the quadratic equation \( x^2 + 2kx + 4 = 0 \) is \( 2 \), then the value of \( k \) is:
If \( (x + 3) \) is a factor of \( ax^2 + x + 1 \), then the value of \( a \) is:
The area of a circle is \( 49\pi \) square cm. Then its diameter is:
\( \tan 5^\circ \cdot \tan 25^\circ \cdot \tan 30^\circ \cdot \tan 65^\circ \cdot \tan 85^\circ \) is:
\( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \) is:
\( \frac{\csc 42^\circ \cdot \cos 37^\circ}{\sec 48^\circ \cdot \sin 53^\circ} \) is:
\( \sqrt{2} \left(\sin \frac{\pi}{4} + \cos \frac{\pi}{4} \right) \) is:
If \( a \cos \theta + b \sin \theta = 4 \) and \( a \sin \theta - b \cos \theta = 3 \), then the value of \( a^2 + b^2 \) is:
The ratio of the areas of two circles is \( x^2 : y^2 \). Then the ratio of their radii is:
If \( \sin(20^\circ + \theta) = \cos 30^\circ \), then the value of \( \theta \) is:
If in \( \triangle ABC \), \( \angle C = 90^\circ \), then \( \sin(A + B) \) is:
\( \sec^2 23^\circ - \tan^2 23^\circ + 2 \) is:
If \( x \cos \theta = 1 \), \( \tan \theta = y \), then the value of \( x^2 - y^2 \) is:
If \( \tan \theta = \frac{3}{4} \), then \( \sin \theta \) is:
\( \frac{1 + \cos A}{1 - \cos A} \) is equal to:
If an equilateral triangle \( \triangle ABC \) has one side of 12 cm, and another equilateral triangle \( \triangle DEF \) has one side of 6 cm, then what is the ratio of their areas?
In \( \triangle ABC \) and \( \triangle PQR \), which are similar triangles, \( AD \) is perpendicular to \( BC \) and \( PT \) is perpendicular to \( QR \). If \( AD = 9 \) cm and \( PT = 7 \) cm, then the ratio of the areas of triangles \( ABC \) and \( PQR \) is:
If one side of an equilateral triangle is 12 cm, then its height is:
The distance between two parallel tangents of a circle is 10 cm. Then the radius of the circle is: