CBSE EXAMINATION PAPER-2024

A stable owner has four horses. He usually ties these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build a fence around the area so that each horse can graze.

Based on the above, answer the following questions :

Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student selfreliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.

From the above answer the following questions :

Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250.

Now, Mukta asked some questions as given below to the students :

The pair of linear equations x + 2y + 5 = 0 and –3x = 6y – 1 has

The common difference of the A.P.

1/2x, 1 – 4x / 2x, 1 – 8x / 2x, ... is:

The probability of guessing the correct answer to a certain test question is x/6. If the probability of not guessing the correct answer is 2/3, then the value of x is:

If a = 2² × 3ˣ, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM(a, b, c) = 3780, then x is equal to

The zeroes of the quadratic polynomial 2x² – 3x – 9 are:

From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is 60°. The height (in metres) of the tower is:

If cos θ = √3/2 and sin ∅ = 1/2, then tan(θ + ∅) is:

In the given figure, if PT is a tangent to a circle with centre O and ∠TPO = 35°, then the measure of ∠x is:

If the diagonals of a quadrilateral divide each other proportionally, then it is a:

In ∆ABC, DE ∥ BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is:

Given HCF(2520, 6600) = 40, LCM(2520, 6600) = 252 × k, then the value of k is:

A pair of irrational numbers whose product is a rational number is:

If a digit is chosen at random from the digits 1,2,3,4,5,6,7,8,9, then the probability that this digit is an odd prime number is:

The mean of five observations is 15. If the mean of first three observations is 14 and that of last three observations is 17, then the third observation is

Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is:

In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70° with MN. The measure of ∠MON is:

Assertion (A) : The point which divides the line segment joining the points A (1, 2) and B(-1, 1) internally in the ratio 1 : 2 is (-1/3,5/3) Reason (R) : The coordinates of the point which divides the line segment joining the points A (x₁, y₁) and B(x₂, y₂) in the ratio m₁: m₂ are [m₁x₂ +m₂x₁ / m₁ + m₂ , m₁y₂+ m₂y₁ / m₁+m₂

Assertion (A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5. Reason (R) : P(E) + P(not E) =1

One card is drawn at random from a well shuffled deck of 52 cards. Find the probability that the card drawn

(i) is queen of hearts:

(ii) is not a jack.

In the given figure, EA/EC = EB/ED, prove that ΔEAB ~ ΔECD.

Evaluate: cos 45° + sin 60° / sec 30° + cosec 30°.

If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms.

Solve the following system of linear equations graphically:

x – y + 1 = 0

x + y = 5

Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis.

Prove that sin θ – 2 sin³ θ / 2 cos³ θ – cos θ = tan θ.

The ratio of the 10ᵗʰ term to its 30th term of an A.P. is 1 : 3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P.

P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2 X 16 / 21, find the fraction.