List of top Mathematics Questions asked in CBSE Class X

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 :

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 \(m\angle AOP\).

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 ?

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

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.

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 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) \(AD \times QS = BD \times PS\).

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

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

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 \(PQ \perp OQ\).

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

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

\(17 \times 11 \times 13 + 11\) is

The distance between the points \(P(-2, 5)\) and \(Q(5, -2)\) is

PQ is tangent to the circle with centre O such that OP = 2OQ. m\(\angle\)OPQ is

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:

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

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:

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

If H.C.F. of \(135x^2\) and \(189x^3\) is 108, then find the value of x.

Prove that : \(\tan^2 \theta + \cot^2 \theta + 2 = \sec^2 \theta \csc^2 \theta\)

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

34(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:

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

ABCD is a rectangle of dimensions 80 cm \(\times\) 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width x cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of x.

Points \(P(6, 0)\), \(Q(2, 8)\) and \(R(-2, 4)\) are vertices of \(\Delta PQR\). It is given that \(MN \parallel QR\) such that \(\frac{PM}{MQ} = \frac{1}{3}\). Using distance formula and ratio formula, show that \(\frac{MN}{QR} = \frac{1}{4}\).

If \(\frac{-20}{9}, \frac{-2}{9}, \frac{16}{9}, \ldots\) are in A.P., then next term of the sequence is