CBSE EXAMINATION PAPER-2023

A golf ball is spherical with about 300 - 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but are available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm.

Based on the above, answer the following questions :

A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.

Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you ‘win’. One such outcome is written as ‘RB’.

Based on the above, answer the following questions :

In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by h = 20t - 16t².

Based on the above, answer the following questions :

The number of polynomials having zeroes -3 and 5 is:

The pair of equations ax + 2y = 9 and 3x + by = 18 represent parallel lines, where a, b are integers, if:

The common difference of the A.P. whose nᵗʰ term is given by an = 3n + 7, is:

In the given figure, DE ∥ BC. The value of x is:

A quadratic equation whose roots are (2 + √3) and (2 - √3) is:

If tan θ = 5/12, then the value of sinθ + cos θ / sin θ - cos θ is :

The distance between the points P(-11 / 3,5) and Q( -2/3 , 5) is:

In the given figure, AB = BC = 10 cm. If AC = 7 cm, then the length of BP is:

Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes?

If the mean and the median of a data are 12 and 15 respectively, then its mode is:

In the given figure, AB is a tangent to the circle centered at O. If OA = 6 cm and ∠OAB = 30°, then the radius of the circle is:

(2 tan 30° / 1 + tan² 30° )is equal to:

In Δ ABC and Δ DEF , AB / DE= BC/FD Which of the following makes the two triangles similar?

The 11th term from the end of the A.P.: 10, 7, 4, ..., -62 is:

In the given figure, AC and AB are tangents to a circle centered at O. If ∠COD = 120°, then ∠BAO is equal to:

Which of the following numbers cannot be the probability of happening of an event?

Assertion (A) : If the points A(4, 3) and B(x, 5) lie on a circle with centre 0(2, 3), then the value of x is 2.

Reason (R): Centre of a circle is the mid-point of each chord of the circle.

Assertion (A) : The number 5ᵗʰ cannot end with the digit 0, where n is a natural number.

Reason (R): Prime factorisation of 5 has only two factors, 1 and 5.

In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA. PB = PC² - AC².

Find the ratio in which y-axis divides the line segment joining the points (5, -6) and (-1, -4).

Prove that: √sec A-1/ √sec A +1 + √sec A + 1 / √ sec A - 1 = 2 cosec A

If pᵗʰ term of an A.P. is q and qᵗʰ term is p, then prove that its nᵗʰ term is (p + q – n).

In the given figure, CD is the perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that CF / CD = FG / DG .

Prove that: tan θ / 1 - cot θ + cot θ / 1- tan θ = 1 + sec θ cosec θ

Find the mean of the following frequency distribution:

One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away estimates the angle of elevation to be 30°. Find:

(a) The height of the basket from the ground.

(b) The distance of the basket from the first observer’s eye..

(c) The horizontal distance of the second observer from the basket.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area Δ ABC = 90 cm².

Two pipes together can fill a tank in 15/8 hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.