# Sainik School 2009 Solved paper- Mathematics

Sainik Academy, Coimbatore- SSE-2009 –Solutions- Class VI 2009

All India Sainik School Entrance Examination Solved Paper-of 2009 Mathematics and Language

(Time: 2 hours Max Marks: 200)

Directions: 1. This question paper contains two parts and you have to answer all the questions in both parts.

2. Part” A” Mathematical knowledge test has 30 questions

Q. No. 1 to 10 carry 2 marks each, 11 to 20 carry 3 marks each

and 21 to 30 carry 5 marks each. 3. Part “B” Language Ability test contains 9 questions.

Q. No. 1 and 2 carry 15 marks each and remaining questions carry 10 marks each. P

ART ‘A’ Mathematics-

Section –I (Each question carries 2 marks)

Q. 1. Write the smallest and greatest 5-digit number using 8, 7, 0, 5, and 1

Q. 2. Arrange the following number in descending order- 39217, 36905, 36915, 37505, 38207

Q.3. Write the following Hindu-Arabic numerals in Roman numerals:- a) 19 b) 85

Q.4. Find the quotient of the following:- a) 6.25 ÷ 0.25 b) 169 ÷ 1.3

Q.5. Find first three common multiples of 3, 4 and 5

Q. 6. Find the value of 8 3/7 Divide by 59 / 49

Q.7. Which of the following can be the angels of a Triangle? a) 45º, 75º, 60º b) 75º, 45º, 65º

Q.8.A bus starts from Agra to Delhi at 8.30 a.m. and reaches Delhi at 11:20 a.m. How much time was taken by the bus to reach Delhi?

Q.9.The cost of 17 umbrellas is Rs.1020. Find out the cost of 7 such umbrellas.

Q. 10. An arm of a square is of 30 m. The area of that square is equal to a rectangle field, whose one arm is of 20 m. Find another arm of that rectangular filed?

SECTION- II (EACH QUESTION CARRIES 3 MARKS)

Q. 11. Simplify:- 7 3/6 x 1 1/2 divided by 3 7/15 + 1/2 of 20

Q.12.What will be the volume of a rectangle box whose internal measures are 17.6 cm, 12.5 cm and 8 cm?

Q.13. A shopkeeper buys a bag of sugar for Rs.1000 and earns a profit of 20%. Find the total profit of shopkeeper on a bag of sugar?

Q.14. Classify each of the following as Acute, Obtuse or Right Angle a) 127º, b) 87 º, c) 102º, d) 90 º, e) 27 º, f) 93º

Q. 15. A filed whose length is 60 m and 25 cm and breadth is 30 m and 25 cm is to be surrounded by a wire. Find the length of wire required.

Q.16.The circumference of a circle is 44 cm. Find the diameter of that circle.

Q.17. In the adjoining figure PQR is a Triangle and PQ = PR and Angle Q = 90º Find the values of other two angles of the triangle.

Q.18. Write True or False a) b) c) 22: 7 = 88 : 28

Q. 19. Mahendra was born in the same year on 26 April. Today he is of 62 days. Find the date of today.

Q.20. Add 7 hours 48 minutes 12seconds and 2 hours 52 minutes 48 seconds. S

ECTION- III

Q.21. Hari gets Rs.55 out of 240, while Mohan gets Rs.70 out of Rs.360. Who gets Better percentage?

Q.22. ( i ) Convert the following into decimal numbers

a) 12% b) 32% c) 4/5 d) 5% e) 5/8

(ii) Convert the following decimals into a simple fraction.

a) 5.05 b) 0.08 c) 6.6 d) 0.200

Q.23.Write the following fractions in ascending order:-

Q.24. Find the least five digit number which is exactly divisible by 75

Q.25 Mohan spends 1/5 of his income as hose expenditure as house expenditure and he spends 2/7 of his income on transport and he saves Rs.2034. Find income of Mohan. Q

.26. Draw an angle of 90 Degrees with the help of a pencil and a compass

Q.27.Length of a park is 25 m and breadth is 20 m. The park is surrounded by a wire. If the wire is folded into a circle, find the diameter of that circle .

Q. 28. Three men A, B and C working earn Rs.2740, between the amount of A and B the ratio is 4:9 while C gets Rs.790. Find the difference in the amount of A and B.

Q.29. Fill in the blanks:-

a) (8.9 + 1.1) ÷ …… = 1

b) C.P is Rs.420, profit is Rs.80, then S.P = Rs.____

c) The sum of all four angles of a Rhombus = _________

d) Area of Circle = ∏x ……

e) In a parallelogram the opposite angles = …..

Q.30. Match the following:-

A) Complementary of 75º ( i ) 85º

B) An obtuse angle is ( ii ) Five

C) If the sum of two angles is 90 º then they are called (iii) 15 º

D) Supplementary of 95 º (iv) Complementary

E) No of arms in a pentagon is (v) Greater than 90 º .

(For the ease of calculations we have given the formulae which students should write and memorize them)

a) Roman Numerals Roman Numerals

Chart M=1000 D = 500

31 XXXII 32 LXIII

63 XCIV 94 II 2 XXXIII 33 LXIV

64 XCV 95 III 3 XXXIV 34 LXV

65 XCVI 96 IV 4 XXXV 35 LXVI

66 XCVII 97 V 5 XXXVI 36 LXVII 67 XCVIII

98 VI 6 XXXVII 37 LXVIII 68 XCIX 99 VII 7 XXXVIII

38 LXIX 69 C 100 VIII 8 XXXIX 39 LXX 70 IX 9 XL 40 LXXI

71 EX. X 10 XLI 41 LXXII 72 DI 501 XI 11 XLII 42 LXXIII

73 DL 550 XII 12 XLIII 43 LXXIV 74 DXXX 530 XIII 13 XLIV

44 LXXV 75 DCCVII 707 XIV 14 XLV 45 LXXVI 76 DCCCXC 890 XV 15

XLVI 46 LXXVII 77 MD 1500 XVI 16 XLVII 47 LXXVIII 78 MDCCC

1800 XVII 17 XLVIII 48 LXXIX 79 CM 900 XVIII 18 XLIX

49 LXXX 80 XIX 19 L 50 LXXXI 81 XX 20 LI 51 LXXXII 82 XXI 21 LII

52 LXXXIII 83 XXII 22 LIII 53 LXXXIV 84 XXIII 23 LIV 54 LXXXV

85 XXIV 24 LV 55 LXXXVI 86 XXV 25 LVI 56 LXXXVII 87 XXVI 26 LVII 57 LXXXVIII

88 XXVII 27 LVIII 58 LXXXIX 89 XXVIII 28 LIX 59 XC 90 XXIX 29 LX 60 XCI

91 XXX 30 LXI 61 XCII 92 XXXI 31 LXII 62 XCIII 93 S

ainik Academy, Coimbatore- SSE-2009 –Solutions- Class VI

Q. No: Your answer Correct answer Formula to be used Marks

1 10578 Smallest 87510

Greatest 2 2 39217, 38207, 37503,36915, 36905

3 19 = XIX 85 = LXXXV 50 = L 2

4 a) 6.25 ÷ 0.25 b) 169 ÷ 1.3

Convert the numbers into full by removing decimals

6.25/0.25= 625/25 = 25 169/1.3 = 1690/13 = 130 2 5 60, 120, 180 2 6 = 7

Convert the fraction into improper fraction = 2 7

a) 45º, 75º, 60º = 45º + 75º + 60º = 180 ( are the angles of a Triangle) Because a full triangle has 180 degrees. b) 75º, 45º, 65º by adding all the angles we get 75º+ 45º+ 65º = 185 º

( Since the sum of all the three angles of a triangle is 180 º, this cannot be a triangle) 2

8 2 hr 50 mins

Step -1 Given Start time 8.30 a.m Finish time 11.20 a.m

Step 2: To find Total time taken for the journey S

tep 3:- Formula Reaching time – Starting time = Total time taken for the journey

Step 4:- Solution ( subtract start time from finish time)

i.e. 11.20 - 8. 30 2. 50h ( 1 hour has 60 mins hence 60 borrowed and it becomes 10.80

8.30 = 2.50 h Answer 2 9 Rs.420 Step -1 Given Cost of 17 Umbrellas is Rs.1020

Step-2 – To find Cost of 7 such Umbrellas

Step 3: Formulae to be used Unitary method ( i.e. find the cost of one and then multiply the cost on one with number of umbrellas required.)

Step 4. Solution: (working) Cost price of 17 = Rs. 1020

Divide the total price by number of umbrellas to get the price of one i.e. = 1020÷17 = Rs.60

Therefore cost of 7 umbrellas We have to multiply 60 x 7 =Rs.420 ( ANSWER)

2 10 45m Step 1 : Given One side (arm) of square is 30 m Also One side of a rectangle is 20m

Step 2: To find the Area of a square filed = 30 x30 =900 Sq.m To find the other of a rectangle whose area is same as the square and whose one side is 20 m

Step 3: Formulae: Area of a Square = side x side Area of a rectangle = L x B

Step 4: working Since area of Sq = area of Rectangle 900 sq.m = 900 sq.m one side of the rectangle is 20 m since area of a rectangle is L x B consider 20 m as B then to find the L

we use the formulae Area ÷ Breadth = 900 ÷ 20 = 45 m Therefore the another arm of the rectangle is 45 m ( answer) 2

Section- II

11 working:- ( Convert all the fractions into improper fraction use DMAS to solve) 12 1760 cubic cm 13 Rs.200 14 A) 127º = Obtuse angle

B) 87º = Acute angle

C) 102º = obtuse angle

D) 90 º= Right angle

E) 27 º = acute angle

F) 93 º = obtuse angle 3 15 181m 16 14 cm 17 45º - and the given angle is Right Angle

18 A) False B) False C) True 19 26 days 20 10 hours 41 mins and 0 seconds

Section –III

21 Hari get better marks Hari = 22.92% Mohan = 19.44%

22 A) 12% = 0.12 B) 32%= 0.32 C) 4/5 = 0.8 D) 5% = 0.05 E) 5/8 = 0.625 (

II) A) 5 1/20 B)2/25 C) 6 2/3 D) 1/5

23 1/3 =0.33 3/5 = 0.6 9/11 = 0.818 5/7 =0.714 7/9 = 0.777 24 10050

25 Rs.3955 26 Angle BCD = 90 degrees 27 28.64 cm

28 Rs. 750 29

A) 10

B) Rs.500

C) 360 degrees

D) r x r

E) Equal 30 A= iii b= v c = iv d = i e = ii

3 Working method of the above sums Q.11.

Q.12.What will be the volume of a rectangle box whose internal measures are 17.6 cm, 12.5 cm and 8 cm?

Step 1: what is given? Internal measurements of a box = 17.6 cm x 12.5 cm x 8 S

tep 2: to find the volume of the box

Step 3 : use the formulae Volume of a cuboid = l x b x h

Step 4: working substitute the value of l , b and h and multiply to get cubic units 17.6 x 12.5 x 8 cubic cm = 220 x 8 = 1760 cubic cm Answer Therefore the internal volume of the box is 1760 cubic cm Answer

Q.13. A shopkeeper buys a bag of sugar for Rs.1000 and earns a profit of 20%.

Find the total profit of shopkeeper on a bag of sugar?