CBSE EXAMINATION PAPER-2025

A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs. One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure.

Based on the above given information, answer the following questions :

Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be 60°. Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be 45°.

Based on the above given information, answer the following questions :

If α and β are the zeroes of polynomial 3x² + 6x + k such that α + β + αβ =-2/3, then the value of k is:

If x = 1 and y = 2 is a solution of the pair of linear equations 2x - 3y + a = 0 and 2x + 3y - b = 0, then:

The mid-point of the line segment joining the points P(-4, 5) and Q(4, 6) lies on:

If θ is an acute angle and 7+ 4 sin θ = 9, then the value of θ is:

The value of tan²θ - (1/cosθ x secθ) is:

If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n -7 m is:

The tangents drawn at the extremities of the diameter of a circle are always:

If (−1)ⁿ + (−1)⁸ = 0, then n is:

Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:

Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is:

A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:

Which of the following is a rational number between √3 and √5?

If a sector of a circle has an area of 40π sq. units and a central angle of 72°, the radius of the circle is:

In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠POB = 115°, then ∠APO is equal to:

A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30° to the horizontal. The length of the string is:

A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/π cm. The angle subtended by the arc at the centre of the circle is:

Assertion (A) : The probability of selecting a number at random from the numbers 1 to 20 is 1.

Reason (R): For any event E, if P(E) = 1, then E is called a sure event.

Assertion (A) : If we join two hemispheres of same radius along their bases, then we get a sphere.

Reason(R): Total Surface Area of a sphere of radius r is 3πr².

If x cos 60° + y cos 0° + sin 30° -cot 45° = 5, then find the value of x + 2y.

Evaluate: tan²60°/ sin²60° + cos² 30°

Find the zeroes of the polynomial p(x) = x² +4/3x-4/3.

The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of a, if the circle passes through the point (11,-9) and has diameter 10√2 units.

If Δ ABC~ ΔPQR in which AB = 6 cm, BC = 4 cm, AC = 8 cm and PR = 6 cm, then find the length of( PQ + QR).

In the given figure, QR/QS= QT/PR and ∠1 = ∠2, show that ∆PQS~ ∆TQR.

A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his distances from the points A and B on the ground are 10 m (PA and PB are tangents to the circle). Find the radius of the circular ground.

Prove that: sin A + cos A / sin A-cos A + sin A - cos A / sin A + cos A=2/2 sin² A-1

Prove that 1/√5 is an irrational number.

A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains 1408 / 21m³ of air, find the height of the cylindrical part. (Use π = 22/7)

The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that DF x EF = FB x FA.

In Δ ABC, if AD ⊥ BC and AD²= BD x DC then prove that ∠BAC = 90°.

Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.