List of practice Questions

If the probability of occurrence of an event \( A \) is 0.35, then the probability of non-occurrence of \( A \) is:

In tossing of three coins, the number of possible outcomes is:

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Prove that:
\[ \frac{\sec^3 0}{\sec^2 0 -1} + \frac{\cosec^3 0}{\cosec^2 0 -1} = \sec 0 \cosec 0 ( \sec 0 + \cosec 0 ). \]

A 20 m deep well with a diameter of 7 m is dug, and the soil from digging is evenly spread out to form a platform of 22 m × 14 m. Find the height of the platform.

The angle of elevation of the top of a building from the foot of a tower is \( 30^\circ \), and the angle of elevation of the top of the tower from the foot of the building is \( 60^\circ \). If the tower is 50 m high, find the height of the building.

Construct a triangle with sides 4 cm, 5 cm, and 6 cm and then construct another triangle similar to it whose sides are \( \frac{2}{3} \) of the corresponding sides of the first triangle.

The median of 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22 is:

An isosceles triangle has \( AB = AC = 13 \) cm. If the length of the perpendicular from vertex \( A \) to \( BC \) is 5 cm, find the length of \( BC \).

Find the value of \( x \) for which the distance between the points \( P(x, 4) \) and \( Q(9,10) \) is 10 units.

In what ratio does the point \( (-1,6) \) divide the line segment joining the points \( (-3,10) \) and \( (6,-8) \)?

A ladder 15 m long makes an angle of \( 60^\circ \) with the wall. Find the height of the point on the wall where the ladder touches the wall.

The length of the minute hand of a clock is 15 cm. Find the area swept by it in 20 minutes.

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 9.

Draw the graph of the pair of linear equations \( 3x - 5y + 1 = 0 \) and \( 2x - y + 3 = 0 \) and solve them.

The area of a rectangular field is 260 square meters. If its length becomes 5 meters less and breadth 2 meters more, it becomes a square field. Find the length and breadth of the rectangular field.

If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term.

Find the sum of the first 22 terms of an A.P. in which the common difference is 7 and the 22nd term is 149.

Each side of an equilateral triangle \( ABC \) is \( a \). Prove that the altitude of the triangle is \( \frac{\sqrt{3}}{2} a \).

Find the discriminant of the quadratic equation \( 9x^2 - 6x + 1 = 0 \) and hence find the nature of the roots.

For what values of \( k \) does the quadratic equation \( (k+1)x^2 - 2(k-1)x + 1 = 0 \) have equal roots?

If the 3rd and 9th terms of an A.P. are 4 and -8 respectively, which term of this A.P. is zero?

For what value of \( k \), do the equations \( kx + y = 1 \) and \( (k+1)x + 2y = 3 \) have no solution?