CBSE EXAMINATION PAPER-2023

India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.

It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :

Based on the above information, answer the following questions :

The discus throw is an event in which an athlete attempts to throw a

discus. The athlete spins anti-clockwise around one and a half times

through a circle, then releases the throw. When released, the discus

travels along tangent to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm.

Point O is centre of the circle and ∠ABO = 30°. PQ is parallel to OA.

Based on above information :

The graph of y = p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is:

The value of k for which the pair of equations kx = y + 2 and 6x = 2y + 3 has infinitely many solutions is:

If p -1,p+1 and 2p+3 are in AP, then the value of p is:

In what ratio does the x-axis divide the line segment joining the points A(3 , 6) and B(-12, -3)?

In the given figure, PQ is tangent to the circle centred at O. If ∠AOB = 95°, then the measure of ∠APQ will be:

If 2 tan A = 3, then the value of 4 sin A + 3 cos A / 4 sin A - 3 cos A is

If α and β are the zeroes of polynomial p(x) = x² + x − 1 / α + 1 / β equals to

The least positive value of k for which the quadratic equation 2x² + kx − 4 = 0 has rational roots is:

[3/4 tan² 30°- sec² 45°+ sin² 60°] is equal to

Curved surface area of a cylinder of height 5 cm is 94.2 cm². Radius of the cylinder is (Take π = 3.14):

The distribution below gives the marks obtained by 80 students on a test :

The modal class of the distribution with marks obtained by 80 students is:

The curved surface area of a cone having height 24 cm and radius 7 cm is:

The distance between points (0, 2√5) and (-2√5, 0) is:

Which of the following is a quadratic polynomial having zeroes - 2 / 3 and 2/3 ?

If the value of each observation of a statistical data is increased by 3, then the mean of the data:

Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q. Relation between p and q is:

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 16,000 tickets are sold, how many tickets has she bought?

In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim is:

Assertion (A) : Point P(0, 2) is the point of intersection of y-axis with the line 3x + 2y = 4. Reason (R) : The distance of point P(0, 2) from x-axis is 2 units.

Assertion (A) : The perimeter of AABC is a rational number. Reason (R) : The sum of the squares of two rational numbers is always rational.

Solve the pair of equations x=3 and y= -4 graphically.

Using graphical method, find whether the following system of linear equations is consistent or not: x=0 and y =-7

In the given figure, XZ is parallel to BC. If AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm, find the length of XY.

If sin θ + cos θ= √3,then find the value of sin θ . cos θ.

A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random. Find the probability that drawn ball is

(i) red

(ii) yellow.

If sin α= 1 / √2 and cot β = √3, then find the value of cosec α + cosec β .

If (-5, 3) and (5, 3) are two vertices of an equilateral triangle, then find coordinates of the third vertex, given that origin lies inside the triangle. (Take √3 = 1.7)

In the given figure, a circle is inscribed in quadrilateral ABCD in which ∠B = 90°. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle.

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

A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find the total height of the room if it contains (1408 / 21) m³ of air. (Take π = 22/7).

An empty cone of radius 3 cm and height 12 cm .Ice cream is filled is in it so that lower part of the cone which is 1/6ᵗʰ of the volume of

the cone is unfilled but hemisphere is formed on the top. Find

volume of the ice-cream. (Take n = 3.14)

The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60°. The angle of elevation of the top of second tower from the foot of the first tower is 30°. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.

A spherical balloon of radius r subtends an angle of 60° at the eye of

an observer. If the angle of elevation of its centre is 45° from the

same point, then prove that height of the centre of the balloon is √2

times its radius.

The ratio of the 11ᵗʰ term to the 17ᵗʰ term of an A.P is 3:4. Find the ratio of the 5ᵗʰ term to the 21ˢᵗ term of the same A.P. Also, find the ratio of the sum of the first 5 terms to that of the first 21 terms.

250 logs are stacked in in the following manner :

22 logs are in the bottom row, 21 in the next, 20 in the row next to it

and so on (as shown by an example). In how many rows, are the 250

logs placed and how many logs are there in the top row ?