List of top Mathematics Questions asked in CBSE Class X

The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. Find the height of the tower and the length of the original shadow. (use \(\sqrt{ 3}\) = 1.73)
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (use \(\sqrt{ 3}\) = 1.73)
In two concentric circles, the radii \(OA = r\) cm and \(OQ = 6\) cm, as shown in the figure. Chord $CD$ of the larger circle is a tangent to the smaller circle at $Q$. $PA$ is tangent to the larger circle. If $PA$ = $16$ cm and $OP = 20$ cm, find the length of $CD$.
Problem Figure
Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they first beep together at 12 noon, at what time will they beep again together next time?
In the given figure, two tangents PT and QT are drawn to a circle with centre O from an external point T. Prove that \(\angle\) PQT = \(2\angle\) OPQ.
Problem Figure
The greater of two supplementary angles exceeds the smaller by \(18^\circ\). Find the measures of these two angles.
Find the co-ordinates of the points of trisection of the line segment joining the points \((-2, 2)\) and \((7, -4)\).
A bag contains 4 red, 5 white, and some yellow balls. If the probability of drawing a red ball at random is \(\frac{1}{5}\), then find the probability of drawing a yellow ball at random.
Evaluate: \(\sin A \cos B + \cos A \sin B\); if \(A = 30^\circ\) and \(B = 45^\circ\).
A juice glass is cylindrical in shape with a hemispherical raised-up portion at the bottom. The inner diameter of the glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use π = 3.14)
A solid is in the form of a cylinder with hemispherical ends of the same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.
Show that \(11 \times 19 \times 23 + 3 \times 11\) is not a prime number.
Prove that \(6 - 4\sqrt{5}\) is an irrational number, given that \(\sqrt{5}\) is an irrational number.
Problem Figure
Assertion (A): If the PA and PB are tangents drawn to a circle with center O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.
Assertion (A): Zeroes of a polynomial \(p(x) = x^2 − 2x − 3\) are -1 and 3.
Reason (R): The graph of polynomial \(p(x) = x^2 − 2x − 3\) intersects the x-axis at (-1, 0) and (3, 0).
\(D\) is a point on the side \(BC\) of \(\triangle ABC\) such that \(\angle ADC = \angle BAC\). Show that:
\(AC^2 = BC \times DC\)
Problem Figure
Check whether the point \((-4, 3)\) lies on both the lines represented by the linear equations:
\(x + y + 1 = 0 \quad \text{and} \quad x - y = 1\)
Solve the following pair of linear equations for \(x\) and \(y\) algebraically:
\(x + 2y = 9 \quad \text{and} \quad y - 2x = 2\)
The diameter of a circle is of length 6 cm. If one end of the diameter is \((-4, 0)\), the other end on \(x\)-axis is at:
The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is:
If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is:
The radius of a sphere is \(\frac{7}{2}\) cm. The volume of the sphere is:
Two dice are rolled together. The probability of getting a doublet is:
The value of \(k\) for which the pair of linear equations \(5x + 2y - 7 = 0\) and \(2x + ky + 1 = 0\) don't have a solution, is:
The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is: