List of practice Questions

What is the nature of roots of the quadratic equation \( 6x^2 - 3x + 5 = 0 \)?
If one root of the quadratic equation \( x^2 + x - 20 = 0 \) is \( 4 \), then the other root is:
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 + 6x + 5 = 0 \), then the value of \( \alpha^2 + \beta^2 \) is:
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?