List of practice Questions

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:
If two circles touch each other externally, then what is the number of common tangents?
From an external point \( P \), two tangents \( PA \) and \( PB \) are drawn to a circle. If \( PA = 6 \) cm, then \( PB \) is:
If three points are collinear then what is the area of the triangle formed by them?
If \( A(-1,0) \), \( B(5,-2) \), and \( C(8,2) \) are the vertices of a triangle \( \triangle ABC \), then the coordinates of its centroid are:
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = 10 \) cm, \( AC = 14 \) cm, \( BC = 6 \) cm, then the value of \( DC \) is: