CBSE EXAMINATION PAPER-2023

In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is Rs 20 per cm².

Based on the above, answer the following questions :

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm, and the other is hemispherical with diameter 21 cm.

Based on the above, answer the following questions :

Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.

One school is chosen at random. Then :

Which of the following quadratic equations has sum of its roots as 4?

What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90°?

If Δ ABC ~ Δ PQR, with ∠A= 32° and ∠R= 65° then the measure of ∠B is:

If ‘p’ and ‘q’ are natural numbers and ‘p’ is the multiple of ‘q’, then what is the HCF of ‘p’ and ‘q’ ?

The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and D(0, 4) are:

If the pair of equations 3x - y + 8 = 0 and 6x - ry + 16 = 0 represent coincident lines, then the value of 'r'is:

A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube?

If one zero of the polynomial 6x² + 37x + (k - 2) is reciprocal of the other, then what is the value of k?

What is the total surface area of a solid hemisphere of diameter ‘d’ ?

If three coins are tossed simultaneously, what is the probability of getting at most one tail?

In the given figure, DE || BC. If AD = 2 units, DB = AE = 3 units and EC = x units, then the value of x is:

The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is:

The zeroes of the polynomial p(x) = x² + 4x + 3 are given by:

In the given figure, the quadrilateral PQRS circumscribes a circle. Here PA + CS is equal to:

If α and β are the zeroes of the quadratic polynomial p(x) = x² - ax - b, then the value of α²+ β² is:

The area of the triangle formed by the line x/a + y/b = 1 with the coordinate axes is:

In the given figure, AB || PQ. If AB = 6 cm, PQ = 2 cm and OB = 3 cm, then the length of OP is:

Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.

Reason (R) : The lengths of tangents drawn from an external point to a circle are equal.

Assertion (A) : The polynomial p(x) = x²+ 3x + 3 has two real zeroes. Reason

(R): A quadratic polynomial can have at most two real zeroes.

If 4 cot² 45° + sec² 60° + sin² 60° + p = 3/4, then find the value of p.

Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle.

The length of the shadow of a tower on the plane ground is √3 times the height of the tower. Find the angle of elevation of the sun.

Prove that: (1/cosθ - cos θ) (1/sin θ- sinθ)= 1/ tanθ + cotθ.

If the system of linear equations 2x + 3y = 7 and 2ax + (a + b)y = 28 have infinite number of solutions, then find the values of ‘a’ and b’

If 217x + 131y = 913 and

131x + 217y = 827,

then solve the equations for the values of x and y.

In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠QAP + ∠APR = 90°.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data.