List of top Questions asked in Maharashtra Class X Board

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

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.

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.

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 \[ S = (q + r - 2p) \times \frac{(p + r)}{2(q - p)} \]

Solve the following simultaneous equations: \[ x + y = 4 \quad \text{and} \quad 2x - y = 2 \]

Write the following equation in the form \(ax^2 + bx + c = 0\), then write the values of \(a, b, c\):
\[ 2y = 10 - y^2 \]

Write an A.P. whose first term is \(a = 10\) and common difference \(d = 5\).

Out of the following equations, which one is not a quadratic equation?

For the given A.P. \(a = 3.5, \, d = 0\), find \(t_n = \, ?\)

Find the common difference of the following A.P.: \[ 2, \, 4, \, 6, \, 8, \ldots \]

On a certain article, if the rate of CGST is 9%, then what is the rate of SGST?

If one coin is tossed, write the sample space ‘S’.

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.

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. ($\pi = 3.14$)

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?

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

To draw the graph of \(4x + 5y = 19\), find \(y\) when \(x = 1\):

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.

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

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.