List of practice Questions

Which of the following metals produces hydrogen gas with cold water?

The alkene in the following is:

Which of the following metals produces hydrogen gas with cold water?

Find the area of a sector whose angle is \( 30^\circ \) of a circle whose radius is 4 cm. Also, find the area of the corresponding major sector.

Divide a 10 cm line segment in the ratio 3:2.

If \( BL \) and \( CM \) are medians of a right triangle \( ABC \) whose \( \angle A = 90^\circ \), then prove that: \( 4(BL^2 + CM^2) = 6 BC^2 \).

Find the values of \( x \) and \( y \) from the following equations: \[ \frac{30}{x - y} + \frac{44}{x + y} = 10 \quad \text{and} \quad \frac{40}{x - y} + \frac{55}{x + y} = 13 \]

If 1 is subtracted from the numerator of a fraction, then it becomes \( \frac{1}{3} \), and if 8 is added to its denominator, then it becomes \( \frac{1}{4} \). Find that fraction.

To have a real and enlarged image of an object by a concave mirror, the position of the object should be:

The unit of the power of the lens is:

When a beam of white light falls on the surface of a triangular prism of glass, it splits, after emerging out from the prism, into various colours with different deviations. Which colour has maximum deviation?

If a copper rod whose diameter is 1 cm and length 8 cm is melted and recasted into another rod whose length is 18 cm, then find the width of the rod.

Find the mean of the following data:

Do the equations \( x + 2y - 4 = 0 \) and \( 2x + 4y - 12 = 0 \) represent two parallel lines? Express this by geometrical method.

The ratio of income of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them saves ₹ 2,000 per month, then find their monthly income.

Prove that the points \( (3, 2) \), \( (-2, -3) \), and \( (2, 3) \) are vertices of a right angled triangle.

In the figure \( OA \cdot OB = OC \cdot OD \), then prove that \( \angle A = \angle C \) and \( \angle B = \angle D \).

The angle of elevation of the top of a 10 m high building from a point \( P \) on the ground is 30°. There is a flag on the top of the building. The angle of elevation of the top of the flag from \( P \) is 45°. Then find the length of the flagpole and distance of point \( P \) from the building.

If the median of the following data is 525 and the sum of frequencies is 100, then find values of \( x \) and \( y \): % Frequency Table \[ \begin{array}{|c|c|} \hline Class Interval & Frequency
\hline 0 - 100 & 2
100 - 200 & 5
200 - 300 & x
300 - 400 & 12
400 - 500 & 17
500 - 600 & 20
600 - 700 & y
700 - 800 & 9
800 - 900 & 7
900 - 1000 & 4
\hline \end{array} \]

There is a frustum of a cone whose height is 45 cm. If the radii of its ends are 28 cm and 7 cm, find its volume, curved surface area, and total surface area. (Use \( \pi = \frac{22}{7} \))

If the arithmetic mean of 7, 13, 20, 17, and \( 3x \) is 18, then the value of \( x \) will be:

The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:

If ratio of sides of two similar triangles is 4:7, then ratio of their areas will be:

If the area and perimeter of a circle are numerically the same, then the radius of that circle will be:

Prove that \( \sqrt{2} \) is not a rational number.