CBSE EXAMINATION PAPER-2024

BINGO is a game of chance. The box has 75 balls numbered 1 through 75. Each card has some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whoever cancels all the numbers on his/her card says BINGO and wins the game. The table below shows data of one such game where 48 balls were used before Tara said ‘BINGO’.

Based on the above information, answer the following :

A backyard is in the shape of a right angled triangle ABC with right angle at B. AB = 7 m and BC = 15 m. A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP =x m.

Based on the above information, answer the following questions :

If the sum of zeroes of the polynomial p(x) = 2x² - k√2 x + 1 is √2, then value of k is:

If the probability of a player winning a game is 0.79, then the probability of his losing the same game is

If the roots of the equation ax² + bx + c = 0, a ≠ 0 are real and equal, then which of the following relation is true?

In an AP, if the first term a = 7, nth term aₙ = 84 and the sum of first n terms Sₙ = 2093/2, then n is equal to

If two positive integers p and q can be expressed as p = 18 a²b⁴ and q = 20 a³ b², where a and b are prime numbers, then LCM (p, q) is

AD is a median of Δ ABC with vertices A(5,-6) B (6,4) C (0,0) Length AD is equal to:

If secθ × tanθ = m, then the value of secθ + tanθ is

From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining data is

For some data x₁, x₂, ......xₙ , with respective frequencies f₁, f₂, ...fₙ , the value of ⁿ∑₁ fᵢ (xᵢ - x̅ )equal to:

The zeroes of a polynomial x² + p x + q are twice the zeroes of the polynomial 4x² - 5x + 6. The value of p is:

If the distance between the points (3, -5) and (x,- 5) is 15 units, then the values of x are:

if cos (α+β)=0,then pf cos (α+β / 2) is equal to :

A solid sphere is cut into two hemispheres. The ratio of the surface areas of the sphere to that of two hemispheres taken together, is:

The middle most observation of every data arranged in order is called:

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is:

Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5 is:

The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at:

In the given figure, graphs of two linear equations are shown. The pair of these linear equations is

Assertion (A) : The tangents drawn at the end points of a diameter of a circle, are parallel.

Reason(R) : Diameter of a circle is the longest chord.

Assertion (A) : If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial.

Reason (R): A polynomial of degree n(n >1) can have at most n Zeroes.

If A = 60° and B = 30°, verify that:

sin(A+B) = sin A cos B + cos A sin B.

In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠B and ∠D both. Prove that:

(i) ΔABD ~ ΔCBD

(ii) AB = BC.

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

Find the ratio in which the point (8/5,y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

ABCD is a rectangle formed by the points A (-1, -1), B (-1, 6), C (3, 6) and D (3, -1). P, Q, R and S are midpoints of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other.

Prove that: tanθ/1-cotθ + cot θ/ 1-tanθ= 1+sec θ cosecθ

A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points of contact as shown. If AD is perpendicular to DC, BC = 30 cm and BS = 24 cm, then find the length DC.

An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find

(i) the length of the arc

(ii) the area of the minor segment of the circle made by the corresponding chord.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

In the given figure PA, QB and RC are each perpendicular to AC. If Ap= x, BQ = y and CR = z, then prove that 1/x+1/z=1/y