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List of top Mathematics Questions

Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.

Find mean of the following frequency table:

Prove that $\dfrac{1+\sec\theta}{\sec\theta}=\dfrac{\sin^2\theta}{1-\cos\theta}$.

Prove that $7\sqrt{5}$ is an irrational number.

The modal class of the following table will be:
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-5 & 5 \\ \hline 5-10 & 8 \\ \hline 10-15 & 12 \\ \hline 15-20 & 10 \\ \hline 20-25 & 7 \\ \hline \end{array} \]

If $\sin \theta = \cos \theta$, $0 \leq \theta \leq 90^\circ$, then the value of $\theta$ will be:

Median class of the following frequency distribution will be:
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-10 & 7 \\ \hline 10-20 & 12 \\ \hline 20-30 & 18 \\ \hline 30-40 & 15 \\ \hline 40-50 & 10 \\ \hline 50-60 & 3 \\ \hline \end{array} \]

In the figure, the value of $\angle P$ will be:

The length of a tangent of a circle of radius $3 \,\text{cm}$ drawn from a point at a distance of $5 \,\text{cm}$ from the centre will be:

For a polynomial $f(x)$, the graph of $y=f(x)$ is given. The number of zeroes of $f(x)$ in the graph will be:

The sum of a two-digit number and the number obtained by reversing the digits is $88$. If the digits of the number differ by $4$, find the number. How many such numbers are there?

The length of a rectangular field is $9$ m more than twice its width. If the area of the field is $810\ \text{m}^2$, find the length and width of the field.

In the figure, $DE \parallel AC$ and $DF \parallel AE$. Prove that $\dfrac{BF}{FE} = \dfrac{BE}{EC}$.

A solid is a cone standing on a hemisphere with both radii $2$ cm and the slant height of the cone $=2\sqrt{2}$ cm. Find the volume of the solid. (Use $\pi=3.14$)

The shadow of a tower on level ground is $30\ \text{m}$ longer when the sun's altitude is $30^\circ$ than when it is $60^\circ$. Find the height of the tower. (Use $\sqrt{3}=1.732$.)

The following table shows the literacy rate (in percent) of 35 cities. Find the mean literacy rate.
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Literacy rate (in \%)} & 45-55 & 55-65 & 65-75 & 75-85 & 85-95 \\ \hline \text{Number of cities} & 3 & 10 & 11 & 8 & 3 \\ \hline \end{array}\]

If $\left(\frac{1-i}{1+i}\right)^{n/2} = -1$, where $i = \sqrt{-1}$, one possible value of n is

If the system of linear equations
x + my + az = 0
2x + ay + mz = 0
ax + 2y - z = 0
with m and a as non-zero constants, admits a non-trivial solution, then which one of the following conditions is correct?

In Cartesian coordinates, consider the functions $u(x, y) = \frac{1{2}(x^2 - y^2)$ and $v(x,y) = xy$. If $(r, \theta)$ are the polar coordinates, the Jacobian determinant $|\frac{\partial(u,v)}{\partial(r,\theta)}|$ is}

Given a function $f(x, y) = \frac{x}{a}e^y + \frac{y}{b}e^x$, where $x = at$ and $y = bt$ (a and b are non-zero constants), the value of $\frac{df}{dt}$ at $t = 0$ is

Which one of the following figures represents the vector field $\mathbf{A} = y\hat{i}$?
($\hat{i}$ is the unit vector along the x-direction)

Two point-particles having masses $m_1$ and $m_2$ approach each other in perpendicular directions with speeds $v_1$ and $v_2$, respectively, as shown in the figure below. After an elastic collision, they move away from each other in perpendicular directions with speeds $v'_1$ and $v'_2$, respectively.
The ratio $\frac{v'_1}{v_1}$ is