List of top Mathematics Questions asked in CBSE Class X

A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as \(60^{\circ}\). If \(AB = 5\sqrt{3}\) m, then length of the wire is

Using the conditions from 32(b), prove that \(PR = 2AP\).

Prove that \(2 + 3\sqrt{5}\) is an irrational number given that \(\sqrt{5}\) is an irrational number.

In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :

Find mean and mode of the following frequency distribution :

PQ is tangent to a circle with centre O. If \(OQ = a\), \(OP = a + 2\) and \(PQ = 2b\), then relation between \(a\) and \(b\) is

If \(2\tan A = 3\), then value of \(\sec A\) equals

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))

Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)

A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.

Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).

An ice-cream cone of radius \(r\) and height \(h\) is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then \(h : 2r\) equals

Solve the linear equations \(3x + y = 14\) and \(y = 2\) graphically.

Assertion (A) : The mean of first 'n' natural numbers is \( \frac{n - 1}{2} \).
Reason (R) : The sum of first 'n' natural numbers is \( \frac{n(n + 1)}{2} \).

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.

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.

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 :

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