List of practice Questions

The sum of the digits of a two-digit number is 9. If the digits of the number are interchanged, then the new number will exceed the original number by 27. Find the number.
Construct \( \triangle ABC \) in which \( BC = 6 \, \text{cm} \), \( AB = 3 \, \text{cm} \), and \( \angle ABC = 45^\circ \). Construct a similar triangle \( A'B'C' \) whose corresponding sides are \( \frac{3}{4} \) of the sides of \( \triangle ABC \). Write the steps of construction in brief.
In the figure, if \( BD \perp AC \) and \( CE \perp AB \), prove that \( \triangle AEC \sim \triangle ADB \).
Find the arithmetic mean from the following frequency table:
Find the mode of the following data:
Which one of the following is not a measure of central tendency?
The arithmetic mean of natural numbers 1 to 9 will be:
In a given frequency distribution, if the mean is 15 and the median is 16, then its mode will be:
Median of the first 10 natural numbers will be:
Prove that \(5 + \sqrt{3}\) is an irrational number.
If \( \cos A = \frac{\sqrt{3}}{2} \), then find the value of \( \sin 2A \).
Prove that the twice of the volume of a cylinder is equal to the product of its radius of base and curved surface.
If the corresponding sides of two similar triangles are in the ratio 3:5, the ratio of their areas will be:
If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the triangle will be:
The perimeter of two similar triangles are 10 cm and 15 cm respectively, find the ratio of their areas.
If \( \tan \theta = \frac{8}{15} \), then the value of \( \csc \theta \) will be:
If \( 2 \cos 3\theta = 1 \), then the value of \( \theta \) will be:
The circumferences of two circles are in the ratio 3:2, then the ratio of their areas will be:
If two hemispheres of equal radius \( r \) are joined by their bases, then the curved surface area of this new solid will be:
For what value of ‘m’, pair of equations \( x - 2y = 3 \) and \( 3x + my = 1 \) will have a unique solution?
The solution of \( 2x + 3y = 18 \); \( x - 2y = 2 \) will be:
For which value of \( k \), there will be an infinite number of solutions for the pair of linear equations \( x + ky = 1 \) and \( kx + y = k^2 \)?
If \( \frac{1}{x^2 - 2} = \frac{1}{7} \), then the value of \( x \) will be:
The centre \( (2, -3) \) of a circle has diameter as AB. The coordinate of B is \( (1, 4) \). The coordinate of A will be:
If roots of the equation \( 3x^2 - 12x + k = 0 \) are equal, then the value of \( k \) will be: