List of practice Questions

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.
BL and CM are medians of a triangle ABC, right-angled at A. Prove that \( 4(BL^2 + CM^2) = 5BC^2 \).
Solve: \[ \frac{4}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 3 \] \[ \frac{8}{\sqrt{x}} - \frac{9}{\sqrt{y}} = 1 \]
A motor boat, whose speed is 18 km/hour in still water, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill up the container, at the rate of Rs. 40 per litre. (Use \( \pi = 3.14 \))
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around the well in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
The decimal expansion of the rational number $\dfrac{17}{2^2 \times 5}$ will terminate after how many places of decimal?