CBSE EXAMINATION PAPER-2024

Ryan, from a very young age, was fascinated by the twinkling of stars

and the vastness of space. He always dreamt of becoming an astronaut

one day. So he started to sketch his own rocket designs on the graph

sheet. One such design is given below :

Based on the above, answer the following questions :

Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize.

While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following questions to help the players in spotting the clues:

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals. 500 mL milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.

Based on the above given information, answer the following questions

If ax + by = a² – b² and bx + ay = 0, then the value of x + y is:

The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:

If a polynomial p(x) is given by p(x) = x² – 5x + 6, then the value of p(1) + p(4) is:

If the discriminant of the quadratic equation 3x² – 2x + c = 0 is 16, then the value of c is:

The area of the sector of a circle of radius 12 cm is 60π cm². The central angle of this sector is:

If the difference of mode and median of a data is 24, then the difference of its median and mean is:

If sin θ = 1, then the value of (1/2 sin(θ/2)) is:

Two lines are given to be parallel. The equation of one of these lines is 5x – 3y = 2. The equation of the second line can be:

In ∆ABC, DE || BC.(as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is:

In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of ∠BAC is:

The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is:

For an event E, if P(E) + P(E)̅= q, then the value of q² – 4 is:

In the given figure, QR is a common tangent to two circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is:

Assertion (A) : Mid-point of a line segment divides the line segment in the ratio 1: 1.

Reason (R): The ratio in which the point (-3, k) divides the line segment joining the points (- 5, 4) and (- 2,3)is 1: 2.

Assertion (A) : If the circumference of a circle is 176 cm, then its radius is 28 cm.

Reason (R): Circumference = 21 x radius of a circle.

Evaluate: 5 cos²60° + 4 sec²30°- tan²45° /sin²30° +sin²60°

If sin (A – B) = 1/2, cos (A + B) = 1/2; 0 < A + B ≤ 90°, A > B; find ∠A and ∠B.

Prove that sin θ - cos θ+1 / sin θ + cos θ -1 = 1 / sec θ - tan θ

Three coins are tossed simultaneously. What is the probability of getting

(i) at least one head?

(ii) exactly two tails?

(iii) at most one tail?

A box contains 90 discs numbered 1 to 90. Find the probability that the disc bears

(i) a 2-digit number less than 40.

(ii) a number divisible by 5 and greater than 50.

(iii) a perfect square number.

Rehana went to a bank to withdraw ₹ 2,000 She asked the cashier to

give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.

If α and β are zeroes of the polynomial x² + x – 2, find the value of α /β + β / α.

Prove that 2-√3 / 5 is an irrational number, given that √3 is irrational.

The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode and mean of the data given above.