List of practice Questions

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?
The H.C.F. of two consecutive odd numbers is
tan 5° · tan 25° · tan 30° · tan 65° · tan 85° =
cos 38° · cos 52° - sin 38° · sin 52° =
\[ \frac{\text{cosec} 42^\circ}{\sec 48^\circ} \times \frac{\cos 37^\circ}{\sin 53^\circ} = \]
\( \sqrt{2} \left( \sin \frac{\pi}{4} + \cos \frac{\pi}{4} \right) =\)
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 simplest form of \( 0.\overline{3} + 0.\overline{4} \) is
If \( 156 = 2^x \times 3^y \times 13^z \), then \( x + y + z = ? \)
\( \sqrt{10} \times \sqrt{15} \) is
In the form of \( \frac{p}{2^n \times 5^m} \), \( 0.105 \) can be written as
If H.C.F. of two numbers = 25 and L.C.M = 50, then the product of the numbers will be
If in division algorithm \( a = bq + r \), \( b = 61 \), \( q = 27 \), and \( r = 32 \), what is the value of \( a \)?
If \( q \) is a positive integer, which of the following is an odd positive integer?
If the ratio of corresponding sides of two similar triangles is 5:6, then the ratio of their perimeters is
In \( \triangle ABC \), \( AB = 6\sqrt{3} \, \text{cm}, AC = 12 \, \text{cm}, \) and \( BC = 6 \, \text{cm} \), then \( \angle B \) is
If one side of an equilateral triangle \( ABC \) is 12 cm and one side of equilateral triangle \( DEF \) is 6 cm, then the ratio of areas of \( \frac{\triangle ABC}{\triangle DEF} \) is:
If \( \triangle ABC \) and \( \triangle PQR \) are similar triangles in which \( AD \) is perpendicular from vertex \( A \) to \( BC \) and \( PT \) is perpendicular from vertex \( P \) to \( QR \), \( AD = 9 \, \text{cm} \) and \( PT = 7 \, \text{cm} \), then the ratio of areas of triangle \( \triangle AB \) and triangle \( \triangle PQR \) is
If one side of an equilateral triangle is 12 cm, then its height is
\( \sqrt{\frac{64}{81}} + \sqrt{\frac{16}{9}} \) is
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a/an
If the sum of the first \( n \) terms of an A.P. is \( (5n - n^2) \), then the common difference of the A.P. is
If \( P \left( \frac{a}{2}, 4 \right) \) is the midpoint of the line segment joining the points \( A (-6, 5) \) and \( B (-2, 3) \), then the value of \( a \) is
If three points are collinear, then what is the area of the triangle made by them?