List of top Mathematics Questions asked in CBSE Class X

Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Given that \(\sqrt{5}\) is an irrational number, prove that \(3 + 2\sqrt{5}\) is also an irrational number.

For any natural number n, \( 5^n \) ends with the digit :

If \( \alpha, \beta \) are the zeroes of the quadratic polynomial \( px^2 + qx + r \), then find the value of \( \alpha^3\beta + \beta^3\alpha \).

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.

PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that OBGC is a parallelogram.

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Two dice are rolled together. The probability of getting an outcome \((x, y)\) where \(x>y\), is

A camping tent in hemispherical shape of radius \(1.4\) m, has a door opening of area \(0.50\) \(\text{m}^2\). Outer surface area of the tent is

Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is

The HCF of 960 and 432 is :

The value of x for which \( 2x, (x + 10) \) and \( (3x + 2) \) are the three consecutive terms of an A.P. is :

In the given figure, \(\Delta AHK \sim \Delta ABC\). If \(AK = 10 \text{ cm}\), \(BC = 3.5 \text{ cm}\) and \(HK = 7 \text{ cm}\), find the length of \(AC\).

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

The internal and external radii of a hollow hemisphere are \(5\sqrt{2} \text{ cm}\) and \(10 \text{ cm}\) respectively. A cone of height \(5\sqrt{7} \text{ cm}\) and radius \(5\sqrt{2} \text{ cm}\) is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of \(\pi\). (Use \(\sqrt{2} = 1.4\))

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.

The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :

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

If the HCF of 210 and 55 is expressed as \(210 \times 5 + 55m\), then find the value of \(m\).

In the given figure, \(AB \parallel DE\) and \(AC \parallel DF\). Show that \(\triangle ABC \sim \triangle DEF\). If \(BC = 10\) cm, \(EB = CF = 5\) cm and \(AB = 7\) cm, then find the length DE.