CBSE EXAMINATION PAPER-2025

The Olympic symbol comprising five interlocking rings represents the union of the five continents of the world and the meeting of athletes from all over the world at the Olympic games. In order to spread awareness about Olympic games, students of Class-X took part in various activities organised by the school. One such group of students made 5 circular rings

in the school lawn with the help of ropes. Each circular ring required 44 m of rope.

Also, in the shaded regions as shown in the figure, students made rangoli showcasing various sports and games. It is given that ΔOAB is an equilateral triangle and all unshaded regions are congruent.

Based on above information, answer the following questions :

Cable cars at hill stations are one of the major tourist attractions. On a hill station, the length of cable car ride from base point to top most point on the hill is 5000 m. Poles are

installed at equal intervals on the way to provide support to the cables on which car moves. The distance of first pole from base point is 200 m and subsequent poles are installed at equal interval of 150 m. Further, the distance of last pole from the top is 300 m.

Based on above information, answer the following questions using Arithmetic Progression :

A drone was used to facilitate movement of an ambulance on the

straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be 30° at a particular instant.

Based on above information, answer the following questions :

If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) — LCM (x, y)] is equal to :

(1 + √3)²-(1-√3)² is :

The value of 'a' for which ax²+ x+a=0 has equal and positive roots is:

The number of red balls in a bag is 10 more than the number of black balls. if the probability of drawing a red ball at random from this bag is 3/5, then the total number of balls in the bag is :

tan 2 A = 3 tan A is true, when the measures of ∠ A is :

A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of 60° with the ground, the height of the pole is :

On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the wood. The maximum number of depressions that can be formed is :

The cumulative frequency for calculating median is obtained by adding the frequencies of all the :

If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is :

In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the circles is O. If AB =2 r and OP =r, then the radius of larger circle is :

A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is :

E and F are points on the sides AB and AC respectively of a ΔABC such that AE/EB=AF/FC=1/2. Which of the following relation is true ?

A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most 10 is :

Assertion (A) : Tangents drawn at the end points of a diameter of a circle are always parallel to each other.

Reason (R) : The lengths of tangents drawn to a circle from a point outside the circle are always equal.

Solve the following system of equations algebraically: 30x+44y =10; 40x+55y =13

A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the length of his shadow after 3 seconds.

In parallelogram ABCD, side AD is produced to E and BE intersects CD at F. Prove that ΔABE ~ ΔCFB.

Find the coordinates of the point C which lies on the line AB produced such that AC = 2BC, where coordinates of points A and B are (- 1, 7) and (4, — 3) respectively.

Find value of x for which (sin A + cosec A)² + (cos A + sec A)² = x + tan² A + cot² A.

Prove that √2 is an irrational number.

P(x,y), Q(-2, -3), and R(2, 3) are vertices of a right triangle PQR right angled at P. Find the relationship between x and y. Hence, find all possible values of x for which y =2.

Prove that cos A + sin A -1 / cos A- sinA+1=cosec A -cot A

Let x and y be two distinct prime numbers and p = x² y³, q = xy⁴, r =x⁵ y². Find the HCF and LCM of p, q and r. Further check if HCF(p, q, r) × LCM(p, q, r) = p × q × r or not.

If cotθ+cosθ = p and cotθ—cosθ =q,

prove that p² — q² = 4√pq

The corresponding sides of ΔABC and Δ PQR are in the ratio 3 : 5. AD⊥BC and PS⊥QR as shown in the following figures :

(i) Prove that ΔADC ~ ΔPSR

(ii) If AD =4 cm, find the length of PS.

(iii) Using (ii) find ar (ΔABC) : ar (PQΔR)

State basic proportionality theorem. Use it to prove the following: If three parallel lines l, m, n are intersected by transversals p and q as shown in the adjoining figure, then AB/BC = DE/EF.

wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one depression, face 2 has two depressions and so on. The sum of number of hemispherical depressions on opposite faces is always 7. If the edge of the cubical die measures 5 cm

and each hemispherical depression is of diameter 1.4 cm, find the total surface area of the die so formed.

The following table shows the number of patients of different age group who were discharged from the hospital in a particular month :

Find the ‘mean’ and the ‘mode’ of the above data.