List of top Mathematics Questions

Eliminate $\theta$ if $x = r \cos \theta$ and $y = r \sin \theta$.

The radii of the circular ends of a frustum are 14 cm and 6 cm respectively, and its height is 6 cm. Find its curved surface area. ($\pi = 3.14$)

Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q.

In $\triangle ABC$, seg $DE \parallel BC$. If $2A(\triangle ADE) = A(\triangle DBCE)$, find $AB : AD$ and show that $BC = \sqrt{3 \, DE$.}

An ice-cream pot has a right circular cylindrical shape. The radius of the base is 12 cm and the height is 7 cm. This pot is completely filled with ice-cream. The entire ice-cream is given to students in the form of right circular cones having diameter 4 cm and height 3.5 cm. If each student is given one cone, how many students can be served?

In $\triangle ABC$, seg $AP$ is a median. If $BC = 18$, and $AB^2 + AC^2 = 260$, find $AP$.

Find the length of the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

Show that points A($-1, -1$), B($0, 1$), and C($1, 3$) are collinear.

A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is $45^\circ$. Find the height of the temple.

Find the distance between the points $O(0, 0)$ and $P(3, 4)$.

In $\triangle RST$, $\angle S = 90^\circ$, $\angle T = 30^\circ$, and $RT = 12$ cm, then find $RS$.

Show that, $\cot \theta + \tan \theta = \csc \theta \times \sec \theta$

If the radius of a circle is 5 cm, then find the length of the longest chord of the circle.

Find the surface area of a sphere of radius 7 cm.

Co-ordinates of origin are:

If $a$, $b$, $c$ are sides of a triangle and $a^2 + b^2 = c^2$, name the type of triangle:

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 4, EB = 10, and CE = 8, then find ED:

If the radius of the base of a cone is 7 cm and the height is 24 cm, find its slant height:

A survey was conducted for 180 people in a city. 70 ate Pizza, 60 ate Burgers, and 50 ate Chips. Draw a pie diagram for the given information.

The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.

Show the following data by a frequency polygon:
\[ \begin{array}{|c|c|} \hline \text{Electricity Bill (₹)} & \text{Families (f)} \\ \hline 200 - 400 & 240 \\ 400 - 600 & 300 \\ 600 - 800 & 450 \\ 800 - 1000 & 350 \\ 1000 - 1200 & 160 \\ \hline \end{array} \]

Draw the graph of the equation \(x + 2y = 4\). Find the area of the triangle formed by the line intersecting the X-axis and Y-axis.

If the first term of an A.P. is \(p\), second term is \(q\), and last term is \(r\), then show that the sum of all terms is \[ S = (q + r - 2p) \times \frac{(p + r)}{2(q - p)} \]

The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data:
\[ \begin{array}{|c|c|} \hline \text{No. of Mangoes} & \text{No. of Trees (f)} \\ \hline 50 - 100 & 33 \\ 100 - 150 & 30 \\ 150 - 200 & 90 \\ 200 - 250 & 80 \\ 250 - 300 & 17 \\ \hline \end{array} \]

Solve the following quadratic equation by formula method: \[ x^2 + 10x + 2 = 0 \]