List of top Questions asked in CBSE Class X- 2026

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

38(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:

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

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

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 \(\Delta DBA \sim \Delta DAC\)

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

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 \(\frac{MN}{QR} = \frac{1}{4}\).

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.

If \(\sin \theta = \frac{1}{\sqrt{11}}\text{, then } \cot \theta\) equals

In the given figure, \(DE \parallel BC\). If \(AD : AB = 1 : 3\) and \(AE = 2.5\text{ cm}\), then \(AC\) equals

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

In the given figure, \(\Delta ODC \sim \Delta OBA\). If \(\angle BOC = 110^\circ\), \(\angle ODC = 45^\circ\) and \(AB = 2 CD\), then find (i) \(m\angle OAB\) (ii) \(OB : OD\).

The distance between the points \(P(-4, 5)\) and \(Q(-1, 2)\) is

If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) 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. To find the number of calories burned per minute on each machine, answer the following :

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

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are \(60^\circ\) and \(30^\circ\) respectively. Find the height of the poles and the distance of the point from the poles.

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 (cylinderical). 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 :

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

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 :

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

Find mean and mode of the following data :

Prove that \(\sqrt{2}\) is an irrational number.

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

(a)(i) Prove that \(\triangle\)DBA \(\sim\) \(\triangle\)DAC

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

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

Chord AB of a circle subtends an angle of \(120^\circ\) at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.