List of practice Questions

The system of linear equations \( 2x - 3y = 5 \) and \( 4x - 6y = 7 \) has:
If straight lines \( 4x + py = 16 \) and \( 2x + 9y = 15 \) are parallel, then what is the value of \( p \)?
If \( \sin \theta = \sqrt{2} \cos \theta \), then the value of \( \sec \theta \) is:
Evaluate \( 3 \tan^2 60^\circ \):
Evaluate \( 3 \tan^2 60^\circ \):
If \( A \), \( B \), and \( C \) are angles of a triangle ABC, then the value of \( \csc \left( \frac{A + B}{2} \right) \) is:
If the radius of a circle becomes \( k \) times, then the ratio of the areas of the previous and new circles is:
What is the total perimeter of a semicircle whose radius is \( k \)?
In \( L_2 \) form of 0.375, the form of \( q \) is:
The H.C.F. of two numbers is 15 and L.C.M. is 105. If one of the numbers is 5, then the other number is:
In division algorithm \( a = bq + r \), \( b = 43 \), \( q = 31 \) and \( r = 32 \), the value of \( a \) will be:
If \( q \) is a positive integer, which of the following is an even positive integer?
Which of the following has a terminating decimal expansion?
What is the reciprocal of \( \sin \theta \times \cot \theta \)?
Evaluate \( \cot 12^\circ \cdot \cot 38^\circ \cdot \cot 52^\circ \cdot \cot 60^\circ \cdot \cot 78^\circ \):
The ratio of volumes of two cubes is \( 1 : 64 \). The ratio of their total surface area is:
Two circular cylinders of equal volume have their heights in the ratio \( 1 : 2 \). The ratio of their radii is:
If the curved surface area of a cylinder is 1760 cm² and its diameter is 28 cm, then its height is:
If \( O \) is the center and \( R \) is the radius of a circle and \( \angle AOB = \theta \), then the length of arc \( AB \) is:
If \( l \) is the slant height of a cone and \( r \) is the radius of its base, then the total surface area of the cone is:
The ratio of volumes of two spheres is \( 125 : 27 \). The ratio of their surface areas is:
A sphere of radius 8 cm is melted to form a cone of height 32 cm. The radius of the base of the cone is:
If the length of any chord of a circle is equal to the radius of the circle, then the angle subtended by the chord at the centre is:
\( TP \) and \( TQ \) are two tangents drawn from an external point \( T \) to a circle whose center is \( O \) such that \( \angle POQ = 120^\circ \). Then the value of \( \angle OTP \) is:
If \( \tan 2A = \cot(A - 18^\circ) \), where \( 2A \) is an acute angle, then the value of \( A \) is: