List of top Mathematics Questions asked in Maharashtra Class X Board

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

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.

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

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

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 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.

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

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

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.

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

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:

Co-ordinates of origin are:

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.

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

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:
\[ \begin{array}{|c|c|} \hline \text{No. of Mangoes} & \text{No. of Trees (f)} \\ \hline 50 - 100 & 33 \\ 100 - 150 & 30 \\ 150 - 200 & 90 \\ 200 - 250 & 80 \\ 250 - 300 & 17 \\ \hline \end{array} \]

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

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.

Solve the following simultaneous equations using Cramer’s Rule: \[ 4m + 6n = 54 \quad \text{and} \quad 3m + 2n = 28 \]

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

A two-digit number is formed with digits 2, 3, 5, 7, 9 without repetition. Find the probability of the following events:
Event A: The number formed is an odd number.
Event B: The number formed is a multiple of 5.