List of top Mathematics Questions asked in CBSE Class X

The area (in \(\text{cm}^2\)) of a sector of a circle of radius 14 cm cut off by an arc of length 22 cm is :

The minute hand of a clock is 21 cm long. The distance covered by the tip of minute hand from 2:10 pm to 2:25 pm is :

The ratio in which the x-axis divides the line segment joining the points A\(-8, 4\) and B\(-6, -2\) is :

In \(\Delta\)ABC, P is a point on AB and Q is a point on AC such that PQ \(\parallel\) BC. If AP : PB = 3 : 2, then PQ : BC is equal to :

If in two triangles ABC and DEF, \(\frac{AB}{EF} = \frac{BC}{DE} = \frac{CA}{DF}\); then :

If two tangents inclined at an angle of \(60^\circ\) are drawn from an external point to a circle of radius 6 cm, then the length of each tangent is :

The fourth vertex D of a parallelogram ABCD whose three vertices are A\(-4, 1\), B\(4, 5\) and C\(6, 1\) is :

The nth term of an A.P. is \(3n + 2\). The common difference is :

If \(x = \sqrt{3}\) is a solution of the equation \(ax^2 + \sqrt{3}x - 12 = 0\), then :

The value of k for which the pair of linear equations \(kx - 3y = 5\), \(4x - 6y = 10\) has infinitely many solutions, is :

If \(\alpha\) and \(\beta\) are two zeroes of the quadratic polynomial \(p(x) = x^2 - 11x + 30\), then \(\frac{1}{\alpha} + \frac{1}{\beta}\) is equal to :

The product of the H.C.F. and L.C.M. of two numbers 50 and 20 is :

Three coins are tossed together. The probability of getting exactly two tails is

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

There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:

36(i) What is the total height of a mushroom ?

Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. Based on above information, answer the following questions:

38(i) Represent the above situation in terms of a pair of linear equations in two variables.

Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :

In the given figure, \(\Delta ABC\) is a right-angled triangle with \(\angle A = 90^\circ\). AD is perpendicular to BC.

35(a)(i) Prove that \(\Delta DBA \sim \Delta DAC\)

In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions:

37(i) Find \(m\angle AOP\).

Find the H.C.F. and L.C.M. of 408 and 312.

Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).

If 14th term of an A.P. is 4 and its 15th term is zero, then its first term is

In the given figure, two triangles ABC and PQR are shown such that \(\angle A = \angle P\) and \(\angle C = \angle R\). If \(AD \perp BC\) and \(PS \perp QR\), then prove that (i) \(\Delta ADB \sim \Delta PSQ\) (ii) \(AD \times QS = BD \times PS\).

Prove that : \(\sqrt{\frac{1 - \cos A}{1 + \cos A}} = \frac{\tan A}{\sec A + 1}\).

In the given figure, PQ is a tangent to a circle with centre \(O(-5, 3)\). If coordinates of P and Q are \((3, 1)\) and \((0, 6)\) respectively, then using distance formula, show that \(PQ \perp OQ\).