CBSE Class 10 Mathematics Exam 2025 Most Repeated Questions

1

In ΔABC, altitude AD and CE intersect each other at the point P. Prove that

(i) ΔΑΡΕ ~ ΔCPD

(ii) AP x PD = CP x PE

(iii) ΔADB ~ ΔСЕВ

(iv) AB × CE = BC X AD

2

Assertion (A): The point (0, 4) lies on y-axis.

Reason(R): The x-coordinate of a point on y-axis is zero

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(c) Assertions (A) is true but reason (R) is false.

(d) Assertions (A) is false but reason (R) is true.

3

The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card

(i) of spades

(ii) of black king

(iii) of clubs

(iv) of jacks

4

5

Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. The difference between their 4th terms is

(a) 1

(b) -7

(c) 7

(d) 9

6

The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card

(i) of spades

(ii) of the black king

(iii) of clubs

(iv) of jacks

7

It is proposed to build a new circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park is

(a) 10m

(b) 15m

(c) 20m

(d) 24m

8

What is the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis?

(a) 1:2

(b) 2:1

(c) 2:5

(d) 5:2

9

The nature of roots of the quadratic equation 9×2 – 6x – 2 = 0 is:

(a) No real roots

(b) 2 equal real roots

(c) 2 distinct real roots

(d) More than 2 real roots

10

A point (x,y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?

(a) 0

(b) 1

(c) 2

(d) infinitely many

1

If sides AB, BC and median AD of ΔАВС are proportional to the corresponding sides PQ, QR and median PM of PQR, show that ΔABC ~ ΔPQR.

2

Prove that (2+√3)/5 is an irrational number, given that √3 is an irrational number.

3

As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]

4

The wheel of a motorcycle is of radius 35 cm. How many revolutions are required to travel a distance of 11 m?

5

A bird is sitting on the top of an 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of the flying bird. (Use √3 = 1.732)

6

A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes will the policeman catch the thief?

7

Solving the given pair of LE by substitution or Elimination Method. (Specific type: Solve: 99x y + 101 = 499, 101x + 99y = 501)

8

If -3 is a root of the quadratic equation 2x² + px - 15 = 0, while the quadratic equation x² - 4px + k = 0 has equal roots. Find the value of k.

9

Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with the same speeds as before, they would have met in 8 hours. Find their walking speeds.

10

What is the probability that a leap year selected randomly will have 53 Sundays (Or other days)?