i-Tutor Term Test-5

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i-Tutor Term Test-5A Mathematics-CBSE (Class IX)

Phase-I

Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005

Ph.: 011-47623456

M.M. : 80 i-Tutor Term Test-5 Time : 3 Hrs. Mathematics-CBSE (Class IX)

(i) All questions are compulsory. (ii) The question paper consists of 40 questions divided into four sections A, B, C and D. (iii) Section A comprises of 20 questions (10 MCQ, 5 FITB and 5 VSA type) of 1 mark each, Section B

comprises of 6 questions of 2 marks each, Section C comprises of 8 questions of 3 marks and Section D comprises of 6 questions of 4 marks each.

(iv) There is no overall choices in this paper. However, internal choice is provided in 2 questions of 1 mark, 2 questions of 2 marks, 3 questions of 3 marks and 3 questions of 4 Marks.

(v) Use of calculator is not permitted. (vi) It is mandatory to use Blue/Black Ballpoint Pen to write the answer.

SECTION – A

Multiple Choice Type Questions : [10×1=10] 1. With the help of a ruler and compass, it is possible to construct an angle of [1] (1) 40° (2) 48° (3) 55° (4) 75° 2. The area of an equilateral triangle with side 4 cm is [1]

(1) 4 cm2 (2) 24 3 cm

(3) 12 cm2 (4) 16 cm2 3. In a frequency distribution, the mid value of a class is 75 and the lower limit of the class is 69, then the upper

limit of the class is [1] (1) 80 (2) 81 (3) 82 (4) 63 4. The radius of a hemispherical balloon increases from 5 cm to 10 cm as air is being pumped into it. The ratio

of the surface areas of the balloon in the two cases is [1] (1) 1 : 1 (2) 1 : 2 (3) 1 : 4 (4) 2 : 1

Topics Covered :

Mathematics : Complete Syllabus of Module-II (Excluding the topics/chapters deleted by CBSE)

Code A Date : 17-01-2021

GENERAL INSTRUCTIONS :

Mathematics-CBSE (Class IX) i-Tutor Term Test-5A

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5. The lateral surface area of a cube is 1156 cm2, then the side of the cube is [1] (1) 17 2 cm (2) 28 cm

(3) 17 cm (4) 34 cm 6. The range of the data: [1] 25, 18, 22, 16, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20, is (1) 7 (2) 12 (3) 14 (4) 24

7. Which of the following cannot be the probability of any event? [1]

(1) 34

(2) 45

(3) 54

(4) 110

8. In the class intervals 10-15, 15-20, 20-25, 25-30, the number 20 is included in [1] (1) 10-15 (2) 15-20 (3) 20-25 (4) 25-30

9. In a Table-Tennis match, Manisha missed 8 services out of 20 services she played, then the probability that she did not miss service is [1]

(1) 45

(2) 35

(3) 15

(4) 25

10. Slant height of the cone, whose radius and height are 3 cm and 5 cm respectively is [1] (1) 4 cm (2) 34 cm

(3) 6 cm (4) 35 cm

Fill in the Blank Type Questions : [5×1=5] 11. The edges of a triangular board are 12 cm, 16 cm and 20 cm. The cost of painting it at the rate of 10 paise/cm2

is ______. [1] OR

An isosceles right triangle has area 18 cm2. The length of its hypotenuse is ______. [1] 12. The length of the longest rod that can be put in a room of dimensions (20 m × 20 m × 10 m) is ______. [1] 13. The total surface area of a cone whose radius is 2r and slant height is 3l is ______. [1]

14. In the given figure, O is the centre of the circle. If ∠BAC = 60°, then yx

equals ______. [1]

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15. In a survey of 400 children, 205 like apples while the rest of the children like oranges. If a child is selected at random, then the probability that he/she likes oranges is ______. [1]

Very Short Answer Type Questions : [5×1=5] 16. The diameter of a hemisphere is 5r units. Find the total surface area of the hemisphere. [1] 17. A coin is tossed twice. Find the probability of getting tails two times. [1]

OR The probability of an event lies between x and y (both are inclusive and x < y), then find the value of

x and y. [1] 18. The edge of a cube is 40 cm. How many small cubes of 8 cm edge can be formed from this cube? [1] 19. Find the area of the triangle with sides 40 cm, 41 cm and 9 cm. [1] 20. In the given figure, if ∠ABC = x°, ∠ACB = y°, then find ∠BDC in terms of x and y. [1]

SECTION – B

Short Answer Type Questions : [6×2=12] 21. The volume of a cube is 5832 cubic cm. Find the side of the cube. [2]

OR

If the area of base of the cuboid is 1600 cm2 and the volume is 40 m3, then find the height of the cuboid. [2] 22. The sides of a triangular field are in the ratio 5 : 5 : 4 and its perimeter is 84 units. Find the area of the field.[2]

OR Find the area of a triangle whose sides are 6 cm, 8 cm and 10 cm. [2] 23. 14 packets of biscuits each marked 2 kg, actually contained the following weights (in kg). 1.97, 2.02, 2.08, 2.03, 2.00, 2.05, 2.08, 1.98, 1.99, 2.06, 2.07, 1.99, 2.00, 2.04

Find the probability that any of these packets chosen at random contains

(i) More than 1.5 kg of the biscuits. [1] (ii) Less than 2 kg of the biscuits. [1] 24. A dice is rolled once. Find the probability of getting a prime number. [2]

25. If the lateral surface area of a cylinder is 251.2 cm2 and its height is 10 cm, then find the radius of its base. [Take π = 3.14] [2]

26. The class marks of a distribution are 44, 49, 54, 59, 64, 69. Determine the class limits (Class intervals). [2]

SECTION – C

Short Answer Type Questions : [8×3=24] 27. The table given below shows the percentage distribution of female teachers in the primary schools of rural

areas of various states and union territories of India.

10–20 20–30 30–40 40–50 50–60 60–70 70–80

6 11 7 4 4 2 1Percentage of female teachers

Number of States / U.T.

Draw a histogram to represent the above data. [3]

Mathematics-CBSE (Class IX) i-Tutor Term Test-5A

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OR An equilateral triangle is cut along its altitude. If the perimeter of each triangle obtained after cutting the original

triangle is ( )9 3 1+ cm, then find the area of whole triangle. [3]

28. A survey of 1200 families having 2 children, was conducted and the following data were recorded.

2 1 0

414 351 435Number of girls in a family

Number of families

Out of these families, one family is selected at random. What is the probability that the selected family has

(i) 2 boys [1]

(ii) 1 girl [1]

(iii) At least one girl [1]

OR

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes. Find the probability of getting

3 heads 2 heads No head

41 44 65OutcomesFrequency

(i) Two heads [1]

(ii) 0 head [1]

(iii) At least one head [1]

29. Two identical circles with same inside design as shown in figure are to be made at the entrance. The identical triangular leaves are to be painted orange and the remaining area purple. Find the total area to be painted orange. [3]

30. A rhombus shaped field has green grass for 15 cows. If each side of the rhombus is 200 m and its one of the

diagonals is 320 m, then find the area of the grass field that will be grazed by each cow. [3]

31. A closed wooden cuboidal box has the inner dimensions as 1.5 m, 2 m and 2.5 m and the thickness of the wood is 50 cm. Find the volume of the wood. [3]

OR

A right circular cylinder just encloses a sphere and the sphere encloses a cube of side 35 3 cm. Find the

(i) Volume of the sphere [2]

(ii) Curved surface area of the cylinder [1]

32. A right triangle PQR with sides 6 cm, 8 cm and 10 cm is revolved about the side of length 8 cm. Find the volume of the cone so generated. [Take π = 3.14] [3]


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33. The diameter of a 2.5 m long roller is 92 cm. If it takes 150 revolutions to level a playground, then find the

approximate cost of levelling the ground at the rate of 60 paise per square metre. 22use7

π =

[3]

34. Construct a triangle ABC, in which BC = 7 cm, ∠B = 45° and AC – AB = 1.5 cm. [3]

SECTION – D

Long Answer Type Questions : [6×4=24] 35. A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that it is (i) A number more than or equal to 6 [1] (ii) A black face card [1] (iii) A red ace [1] (iv) A king of heart [1]

OR On one page of a directory, there are 180 telephone numbers. The frequency distribution of the units place

digit is given as under :

0 1 2 3 4 5 6 7 8 9

10 19 27 23 18 10 17 12 24 20Units place digit

Frequency

From this page, one of the number is chosen at random. What is the probability that the unit’s place digit in the chosen number

(i) is a non-zero multiple of 3? [2] (ii) is a multiple of 4? [2] 36. From a point in the interior of an equilateral triangle, the perpendiculars are drawn on the three sides. The

lengths of the perpendiculars are 21 cm, 15 cm and 9 cm. Find the perimeter and length of median of the triangle. [4]

OR The area of a triangle is 60 cm2. If the sides of this triangle become four times, then find the area of the new

triangle. [4] 37. A well with 40 m internal diameter is dug 14 m deep. The soil taken out is spread all around to a width of

20 m to form a circular embankment, find the height of the embankment. [4] OR

A metal pipe is 154 cm long. The inner diameter of a cross-section is 8 cm, the outer diameter being 8.8 cm. Find its total surface area. [4]

38. In a circle of radius 10 cm, PQ and PR are two chords such that PQ = PR = 12 cm and centre O lies outside of ∆PQR. Find the length of the chord QR. [4]

39. Construct a ∆ABC in which ∠B = 60°, AC + AB = 7.2 cm and BC = 3.5 cm. Also write steps of construction. [4] 40. The perimeter of a triangle is 60 cm. One side of a triangle is 6 cm longer than the smaller side and the third

side is 10 cm less than twice the smaller side. Find the area of the triangle. [4]

Edition: 2020-21

i-Tutor Term Test-5

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