List of practice Questions

Do all the parts:
(a) Given that HCF (99, 153) = 9, find the value of LCM (99, 153).

If \( 2\cos^2 45^\circ - 1 = \cos \theta \), then find the value of \( \theta \).

The distance between the points (4, y) and (12, 3) is 10 units. Find the value of \( y \).

Find the relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points (3, 6) and (-3, 4).

The radius of the base of a right circular cone is 3.5 cm and height is 12 cm. Find the volume of the cone.

Find the zeroes of the quadratic polynomial \( x^2 + 12 + 7x \) and verify the relationship between the zeroes and the coefficients.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

The value of \( (\sec A + \tan A)(1 - \sin A) \) will be:

In a triangle \( ABC \), \( \angle C = 90^\circ \) and \( \tan A = \dfrac{1}{\sqrt{3}} \). The value of \( \sin A \cos B + \cos A \sin B \) will be:

The length of the minute hand of a clock is \( r \) cm. The area of the sector swept by the minute hand in one minute will be:

The whole surface area of a solid hemisphere of diameter \( \dfrac{1}{2} \, \text{cm} \) will be:

The mean and median of a frequency distribution are 26.1 and 25.8 respectively. The value of mode for the distribution will be:

The measure of central tendency is:

The nature of the roots of the equation \( 2x^2 - 5x + 4 = 0 \) will be:

Two triangles are said to be similar to each other:

If \( \sin \theta = \cos \theta \), \( 0^\circ \leq \theta \leq 90^\circ \), then the value of \( \theta \) will be:

The value of \( \dfrac{\sin 15^\circ}{\cos 75^\circ} \) will be:

If \( \sin \theta - \cos \theta = 0 \), then the value of \( \sin^4 \theta + \cos^4 \theta \) will be:

If LCM of 26, 156 is 156, then the value of HCF will be:

Which one of the following is a pair of co-prime numbers?

The distance between the points (5, 0) and (-12, 0) will be:

The least number which when divided by 35, 56 and 91 leaves the same remainder 7 in each case will be:

The sum of first 15 multiples of 8 will be:

If one root of quadratic equation \( x^2 + 2x - p = 0 \) is \(-2\), then the value of \( p \) will be:

The coordinates of the point on the x-axis and equidistant from the points (5, -2) and (-3, 2) will be: