List of practice Questions

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:
A die is thrown once. Find the probability of getting: (i) A prime number. (ii) A number lying between 2 and 6.
If the sum of the first 8 terms of an A.P. is 64 and the sum of its first 17 terms is 289, then find the first term and the common difference of the progression.
A spherical glass vessel has a cylindrical neck 7 cm long and diameter 2 cm, while the diameter of the spherical part is 8.4 cm. Find how much water can be filled in the vessel.
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
The angles of depression of the top and bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building.
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3 : 1 internally.
Find the values of \( y \) for which the distance between the points (5, -3) and (13, y) is 10 units.
Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.
Solve the following pair of linear equations:
\( 0.2x + 0.3y = 1.3 \) and \( 0.4x - 0.5y = -0.7 \).
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
D is a point on the side BC of a triangle ABC such that \( \angle ADC = \angle BAC \). Prove that \( CA^2 = CB \times CD \).