QUESTION PAPER
2022 BOARD EXAM
CBSE CLASS 12-PCM MATHEMATICS Board Paper 2022 — Set 2
2022
MATHEMATICS
CLASS 12-PCM
CBSE EXAMINATION PAPER-2022
MATHEMATICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 18 questions. All questions are compulsory.
- This question paper is divided into 4 sections.
- Section A – questions number 1 to 2 are case based questions
- Section B – questions number 3 to 10 are very short answer
- Section C – questions number 11 to 15 are short answer
- Section D – questions number 16 to 18 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
Kite festival
Kite festival is celebrated in many countries at different times of the year. In India, every year 14th January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites.
The picture given below, shows three kites flying together.
In Fig. 5, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be 30° and 60° respectively. Taking AD =50 m and BE = 60 m, find
(1) the lengths of strings used (take them straight) for kites A and B as shown in the figure.
(2) the distance ‘d’ between these two kites
A ‘circus’ is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents.
One such ‘Circus Tent’ is shown below.
The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find
(1) the area of the canvas used in making the tent;
(2) the cost of the canvas bought for the tent at the rate Rs 200 per sq m, if 30 sq m canvas was wasted during stitching.
Section B
Solve the quadratic equation: x² + 2√2x – 6 = 0 for x.
Which term of the AP -11/ 2, -1 / 2,..... is 49 / 2?
Find a and b so that the numbers a,7,b,23 are in A.P.
A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii 7 / 2 cm each. Find the value of n.
In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP = 60°, then find m∠C.
In Fig. 2, XAY is a tangent to the circle centered at O. If ∠ABO = 40°, then find m∠BAY and m∠AOB.
If mode of the following frequency distribution is 55, then find the value of x.
Find the sum of first 20 terms of an A.P. whose nᵗʰ term is given as aₙ=5-2n.
Section C
Draw two concentric circles of radii 2 cm and 5 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.
In Fig. 3, AB is tower of height 50 m. A man standing on its top, observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the two cars.
The mean of the following frequency distribution is 25. Find the value of f.
Find the mean of the following data using assumed mean method :
Heights of 50 students of class X of a school are recorded and following data is obtained :
Find the median height of the students.
Section D
The difference of the squares of two numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.
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