QUESTION PAPER
2022 BOARD EXAM
CBSE CLASS 10 MATHEMATICS Board Paper 2022 — Set 4
2022
MATHEMATICS
CLASS 10
CBSE EXAMINATION PAPER-2022
MATHEMATICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 19 questions. All questions are compulsory.
- This question paper is divided into 4 sections.
- Section A – questions number 1 to 3 are case based questions
- Section B – questions number 4 to 11 are very short answer
- Section C – questions number 12 to 16 are short answer
- Section D – questions number 17 to 19 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
Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea-sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as ‘The Ceramic Town’. One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. Maths teacher who was accompanying the students asked following questions :
(1) The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and radius and height of cylindrical jar in II is 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required ?
(2) If in the cylindrical jar full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar ?
(1) Find the median age of people enrolled for the camp.
[2 Marks](2) If x more people of age group 65 — 75 had enrolled for the camp, the mean age would have been 58. Find the value of x.
Section B
How many odd numbers are there between 1 and 1000 which are divisible by 5 but not by 2 ?
If the sum of the roots of the quadratic equation ky² - 11y + (k - 23) = 0 is 13/21 more than the product of the roots, then find the value of k.
If x= -2 s the common solution of quadratic equations ax²+x-3a= 0,and x²+ bx + b = 0, then find the value of a²b.
If in Fig. 1 there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ =5 cm.
The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
Find the mean of the following frequency distribution :
The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.
Section C
Find the value of 'p' for which the quadratic equation p(x-4)(x-2) + (x-1)² = 0 is shas real and equal roots.
If the last term of an AP. of 30 terms is 119 and the 8ᵗʰ term from the end (towards the first term) is 91, then find the common difference of the AP. Hence find the sum of all the terms of the AP.
An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.
Section D
In Fig. 2, if a circle touches the side QR of ΔPQR at S and extended sides PQ and PR at M and N respectively, then
prove that PM = ½(PQ + QR - PR).
From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. (Take √3= 1.732).
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