List of top Mathematics Questions

Number of ways of arranging 5 officers in 4 rooms.
If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).
Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is \((α,β,\frac{6}{7}),\) then 98(α + β)2 is equal to___.

Find the Mean from the Following Table

Given data:

\[ \begin{array}{|c|c|} \hline \text{Class-interval} & \text{Frequency (f)} \\ \hline 0-10 & 3 \\ 10-20 & 10 \\ 20-30 & 11 \\ 30-40 & 9 \\ 40-50 & 7 \\ \hline \end{array} \]

From the following data, the modal class of the table will be:

\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency (f)} & 11 & 21 & 23 & 14 & 5 \\ \hline \end{array} \]

The mean of the following table will be: 

Class-interval0-22-44-66-88-10
Frequency (f)31547
If \( \tan(A + B) = 1 \) and \( \tan(A - B) = \frac{1}{\sqrt{3}} \), \( 0^\circ \leq A + B \leq 90^\circ \), find the values of \( A \) and \( B \).
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.
Divide a 10 cm line segment in the ratio 3:2.
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.
If \( BL \) and \( CM \) are medians of a right triangle \( ABC \) whose \( \angle A = 90^\circ \), then prove that: \( 4(BL^2 + CM^2) = 6 BC^2 \).
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.
Find the mean of the following data:
Prove that the points \( (3, 2) \), \( (-2, -3) \), and \( (2, 3) \) are vertices of a right angled triangle.
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.
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 \( \pi = \frac{22}{7} \))
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.
Do the equations \( x + 2y - 4 = 0 \) and \( 2x + 4y - 12 = 0 \) represent two parallel lines? Express this by geometrical method.
In the figure \( OA \cdot OB = OC \cdot OD \), then prove that \( \angle A = \angle C \) and \( \angle B = \angle D \).
The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:
Prove that \( \sqrt{2} \) is not a rational number.
In \( \triangle PQR \), \( \angle Q = 90^\circ \), if \( \tan P = \frac{1}{\sqrt{3}} \), then find the value of \( \sin P \cos R + \cos P \sin R \).
If the arithmetic mean of 7, 13, 20, 17, and \( 3x \) is 18, then the value of \( x \) will be: