List of top Mathematics Questions asked in CBSE Class X

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :

\(ABCD\) is a parallelogram such that \(AF = 7 \text{ cm}\), \(FB = 3 \text{ cm}\) and \(EF = 4 \text{ cm}\), length \(FD\) equals

Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).

Find the coordinates of the points of trisection of the line segment joining the points \( A(-1, 4) \) and \( B(-3, -2) \).

If \( \frac{\sec \alpha}{\text{cosec} \beta} = p \) and \( \frac{\tan \alpha}{\text{cosec} \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. Find the modal age and median age of the policy holders.

The natural number 1 is :

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle OAB = 15^\circ \), then \( \angle APB \) equals :

How many zeroes does p(x) = (x $-$ 2)(x + 3) have ?

From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \( 45^\circ \). The height (in metres) of the tower is :

If \( 2 \sin A = 1 \), then the value of \( \tan A + \cot A \) is :

Given cot \(\theta\) = 3, the value of cos \(\theta\) is :

The distance of the point \( A(4a, 3a) \) from x-axis is :

A chord of a circle, of radius 14 cm, subtends an angle of \(60^{\circ}\) at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

If \(a_n\) represents \(n^{\text{th}}\) term of the A.P. \(-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots\) then value of \(a_{16} - a_{12}\) is

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

In an A.P., \(15^{th}\) term exceeds the \(8^{th}\) term by 21. If sum of first 10 terms is 55, then form the A.P.

Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \( x - 5y = 6; 2x - 10y = 12 \)

If \(\sin x = p\), then prove that : (i) \(\cot x = \frac{\sqrt{1 - p^2}}{p}\) (ii) \(\frac{1 + \tan^2 x}{1 + \cot^2 x} = \frac{p^2}{1 - p^2}\)

The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.