Level – 6

Syllabus for KACE exam

Section I – Mathematics

No. Lessons

1] Integers

2] Number Line

3] Simplification

4] Square and Square Root

5] Simple Equation

6] HCF and LCM

7] Fractions

8] Decimal Fraction

9] Recurring Decimal

10] Indices

11] Unitary Method

12] Average

13] Simple Interest

14] Compound Interest

15] Ratio and Proportion

16] Time and Work

17] Parallel Lines and Angles

18] Circle

19] Mensuration

20] Volume and Surface Area

 Section II – Logical Reasoning

No. Lessons

1) Number Series

2) Letter Series

3) Analogy

4) Odd Man Out

5) Mirror Images

6) Water Images

7) Puzzles
 Karkare Academy Competitive ExamTM
Model Question Paper - 1

Time : 1 Hr 15 Min Section I - Mathematics (Q.1 to Q.40) Marks : 100

th th st
Q.1] Find the sum of 49 , 50 and 51 odd numbers coming before 472.
1) 1118 2) 1107 3) 1119 4) 1121
Ans :    

Q.2] Solve : 356 × 936 – 356 × 836 (Write two options)

1) 35600 2) 34500 3) 356 × 102 4) 345 × 102
Ans :    

Q.3] Which of the following is a pair of co-primes?

1) (14, 35) 2) (18, 25) 3) (31, 93) 4) (32, 62)
Ans :    

Q.4] 3 × 0.3 × 0.03 × 0.003 × 30 = ?

1) 0.0000243 2) 0.000243 3) 0.00243 4) 0.0243
Ans :    

Q.5] If 2 A 6 3 ÷ 11 = 233, then find the value of A.

1) 4 2) 3 3) 6 4) 5
Ans :    
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Rough Work
Q.6] Which of the following fractions is the greatest of all?
6 4 5 7
1) 2) 3) 4)
7 5 6 8
Ans :    

Q.7] 0.8 × ? = 0.0004

1) 0.0005 2) 0.005 3) 0.5 4) 0.00005
Ans :    

a 4 3a + 2b
Q.8] If = , then =?
b 3 3a – 2b
1) 6 2) 3 3) 5 4) –1
Ans :    

Q.9] Three measuring rods are 64 cm, 80 cm and 96 cm in length. What is the
least length of cloth that can be measured exact number of times using any
one of the above rod?
1) 0.96 m 2) 19.20 m 3) 9.60 m 4) 96.00 m
Ans :    

Q.10] Find the largest four digit number exactly divisible by 88.
1) 9768 2) 8888 3) 9988 4) 9944
Ans :    

Q.11] 2.53 × 0.154 is the same as :

1) 253 × 0.00154 2) 25.3 × 1.54
3) 0.253 × 0.0154 4) 253 × 0.0154
Ans :    
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Rough Work
Q.12] When a certain number is multiplied by 13, the product consists entirely of
fives. Find such smallest number.
1) 41625 2) 42515 3) 42735 4) 42135
Ans :    

Q.13] 0.53 = ?
53 53 53 26
1) 2) 3) 4)
100 90 99 45
Ans :    

Q.14] Solve : 8 ÷ 4 (3 – 2) × 4 + 3 – 7
1) – 3 2) – 4 3) 4 4) 5
Ans :    

Q.15]  248 +  52 +  144 = ?

1) 14 2) 16 3) 15 4) 12
Ans :    

Q.16] If A : B = 5 : 7 and B : C = 6 : 11, then A : B : C = ?

1) 55 : 77 : 66 2) 30 : 42 : 77 3) 35 : 49 : 42 4) 30 : 36 : 77
Ans :    

3 2 12 7 1
Q.17] Solve : 1 – ÷ + ×
5 3 13 5 3
31 19 11
1) 1 2) 3) 4) 30
90 30 30
Ans :    
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Rough Work
Q.18] What is the cube root of 0.000027?
1) 0.3 2) 0.03 3) 0.003 4) 30
Ans :    

Q.19] The ratio of numbers is 3 : 4 and their sum is 420. Find the greater number.
1) 175 2) 200 3) 240 4) 315
Ans :    

1
Q.20] Solve : 1 +
1
2+
1
1–
2
1) 1.5 2) 1.75 3) 1.25 4) 0.2
Ans :    

Q.21] 200 = M % of 300, then M = ?

1 2
1) 33 2) 85 3) 66 4) 150
3 3
Ans :    

Q.22] The third proportional to 0.8 and 0.2 is :

1) 0.4 2) 0.8 3) 0.05 4) 0.032
Ans :    
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Rough Work
 1
Q.23] In a family, the father took of the cake and he had 3 times as much as
4
others had. Find the number of family members.
1) 3 2) 7 3) 10 4) 12
Ans :    

Q.24] The average score of a cricketer for 10 matches is 43.9 runs. If the average
for the first six matches is 53 runs. Find average for the last four matches.
1) 17.15 2) 29.75 3) 30.25 4) 31
Ans :    

Q.25] By selling an article for `100, one gains `10. Then find the gain percent.
1
1) 9% 2) 10% 3) 11 % 4) None
9
Ans :    

Q.26] A and B together can do a piece of work in 15 days. B alone can do it in

20 days. In how many days can A alone do the same work?
1) 30 days 2) 40 days 3) 45 days 4) 60 days
Ans :    

1 3 4
Q.27] 12 ×6 ÷1 =?
2 5 5
275
1) 45 2) 81 3) 405 4)
6
Ans :    
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Rough Work
Q.28] A and B can do a piece of work in 12 days; B and C in 15 days; C and A in
20 days. A alone can do the work in :
2
1) 15 days 2) 24 days 3) 30 days 4) 40 days
3
Ans :    

3 3 2
Q.29] Solve : 5.75 – × 15 +2 ÷ 1.44
7 4 35
2 3 4 2
1) 2) 3) 4)
5 7 11 9
Ans :    

Q.30] A speed of 30.6 km/hr is the same as :

1) 5.1 m/sec 2) 8.5 m/sec 3) 110.16 m/sec 4) 1.7 m/sec
Ans :    

Q.31]
1
7
+ [ 79 – ( 39 + 29 ) – 29 ] = ?
1 1 2 3
1) 2) 3) 4)
7 9 9 7
Ans :    

Q.32] A number exceeds its four seventh by 18. What is the number?
1) 36 2) 49 3) 63 4) 42
Ans :    

1 1 1
Q.33] The ratio : : is the same as :
2 3 5
1) 2 : 3 : 5 2) 5 : 3 : 2 3) 15 : 10 : 6 4) 6 : 10 : 15
Ans :    
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Rough Work
Q.34] A man crosses a 600 m long street in 5 minutes. Find his speed.
1) 7.2 kmph 2) 3.6 kmph 3) 10 kmph 4) 8.4 kmph
Ans :    

Q.35] A speed of 22.5 m/sec is the same as :

1) 40.5 km/hr 2) 81 km/hr 3) 36.8 km/hr 4) 72 km/hr
Ans :    

Q.36] A train is moving with a speed of 92.4 km/hr. How many metres will it cover
in 10 minutes?
1) 1540 m 2) 15400 m 3) 154 m 4) 15.4 m
Ans :    

Q.37] (31? ) × (279

?
)=1
1) 31 2) 93 3) 217 4) 8649
Ans :    

Q.38] A man on tour travels first 160 km at 64 km/hr and the next 160 km at
80 km/hr. Find his average speed during whole journey.
1) 35.55 km/hr 2) 71.11 km/hr 3) 36 km/hr 4) 72 km/hr
Ans :    

1 1 1 5
Q.39] Find the average of the fractions : 1 ,2 ,3 ,4
2 3 3 6
1
1) 2 2) 2 3) 3 4) 4
2
Ans :    
3
Q.40] The volume of a cube is 512 cm . What is its total surface area?
2 2 2 2
1) 64 cm 2) 256 cm 3) 384 cm 4) 512 cm
Ans :    
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Rough Work
 Section II - Logical Reasoning (Q.41 to Q.50)

ABCDE FGHIJ KLMNO PQRST UVWXY

Q.41 to Q.43 : Complete the following letter series.

Q.41] A, D, I, P, ?
1) X 2) A 3) Y 4) V
Ans :    

Q.42] T400, R324, P256, ?

1) N144 2) M169 3) O225 4) N196
Ans :    

Q.43] M26, O30, Q34, ?

1) P32 2) S38 3) T38 4) U42
Ans :    

2
Q.44] In a code language, if APPLE = 69294, then find P .
1) 16 2) 9 3) 81 4) 49
Ans :    

Q.45] Find the odd man out.

1) Parallelogram 2) Quadrilateral 3) Square 4) Trapezium
Ans :    
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Rough Work
 Q.46 to Q.48 : Complete the following number series.

Q.46] 2, 5, 11, 17, ?

1) 23 2) 21 3) 20 4) 19
Ans :    

Q.47] 99, 120, 143, ?

1) 170 2) 167 3) 168 4) 171
Ans :    

Q.48] 235, 459, 6713, 8917, ?

1) 101121 2) 11112 3) 101122 4) 91019
Ans :    

×4 ÷4 +2
Q.49] ? 7
1) 6 2) 5 3) 4 4) 2
Ans :    

Q.50] Complete the series : 22, 26, 34, 38, 46, ? (Write two options)
1) 50 2) 58 3) 62 4) 54
Ans :    
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Rough Work