List of practice Questions

Draw a line segment of length 76 cm and divide it in the ratio 3:4. Write the measures of both the two parts.
If \( \cos \theta = \frac{4}{5} \), find the value of \( \sin \theta \cos \theta + \tan^2 \theta \).
Find the value of \( f \) from the following frequency table if 25 is the mean of marks obtained by the students:
The dimensions of a metallic solid cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \). It is melted and recast into cubes of dimension 2 m. Thus the number of cubes so formed will be:
The mean of the following table will be:
If the arithmetic mean and mode of the given data are 28 and 16 respectively, the median will be:
The modal class of the following frequency distribution will be:
The median class of the following frequency distribution will be:
Prove that \( \sqrt{3} \) is an irrational number.
Two cubes each of volume 64 cm\(^3\) are joined end to end to form a cuboid. Find the total surface area of the resulting cuboid.
In \( \triangle ABC \) if \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm, and \( BC = 6 \) cm, then measure of \( \angle B \) will be:
Areas of two similar triangles are in the ratio $16 : 25$. The ratio of corresponding sides of the triangles will be:
In the figure, \( AB = 3 \) cm, \( AC = 6 \) cm, \( BD = 2 \) cm and \( CD = 4 \) cm. The ratio of \( \angle BAD \) and \( \angle CAD \) will be:
The value of $\frac{\sin 31^\circ}{\cos 59^\circ}$ will be:
In the figure, the angles of depressions of point O as seen from points A and P are:
If the circumference and the area of a circle are numerically equal, the radius of the circle will be:
The sum of powers of prime factors of the factorization of the number 144 will be:
Given that LCM of \( (132, 288) = 3168 \), then HCF of \( (132, 288) \) will be:
If the roots of the quadratic equation $3x^2 - 12x + m = 0$ are equal, the value of $m$ will be:
The sum of the roots of the equation \( 5x^2 - 3x + 2 = 0 \) will be:
The simultaneous equations $x + 2y = 70$ and $2x + \lambda y = 35$ have no solution if $\lambda$ will be:
Point \( P \left( \frac{a}{8}, 4 \right) \) is the mid-point of the line segment joining the points \( A(-4, 2) \) and \( B(5, 6) \). The value of \( a \) will be:
In the given figure, if $PQ : BC = 1 : 3$, then the ratio of $AP : PB$ will be:
Find the mean of the following frequency distribution:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then prove that the two triangles are similar.