List of top Mathematics Questions asked in CBSE X

The solution of the pair of linear equations: \[ \frac{2x}{3} - \frac{y}{2} = -\frac{1}{6} \quad \text{and} \quad \frac{x}{2} + \frac{2y}{3} = 3 \] is:
The LCM of 24, 36 and 60 in terms of their prime factors is :
The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
The probability of getting a sum of 8, when two dice are thrown simultaneously, is :
A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.
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
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)
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)
Prove that: \((\cot \theta - \csc \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}.\)
Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
How many terms of the $A.P.$ $27, 24, 21, . . .$ must be taken so that their sum is 105? Which term of the A.P. is zero?
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
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.
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Evaluate: \(\sin A \cos B + \cos A \sin B\); if \(A = 30^\circ\) and \(B = 45^\circ\).
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.
Find the co-ordinates of the points of trisection of the line segment joining the points \((-2, 2)\) and \((7, -4)\).
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?
The greater of two supplementary angles exceeds the smaller by \(18^\circ\). Find the measures of these two angles.
Solve the following pair of linear equations for \(x\) and \(y\) algebraically:
\(x + 2y = 9 \quad \text{and} \quad y - 2x = 2\)
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.
Check whether the point \((-4, 3)\) lies on both the lines represented by the linear equations:
\(x + y + 1 = 0 \quad \text{and} \quad x - y = 1\)
If one of the zeroes of the quadratic polynomial \((\alpha - 1)x^2 + \alpha x + 1\) is \(-3\), then the value of \(\alpha\) is: