NMTC KAPREKAR Sub-Junior 2018 Solved Question Paper PDF

NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 1

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The fraction greater than $$8\frac{4}{9}$$ is

A

$$8\frac{1}{3}$$

B

$$\frac{150}{18}$$

C

$$8\frac{2}{3}$$

D

$$\frac{216}{27}$$

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 2

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A car is slowly driven in a road full of fog. The car passes a man who was walking at the rate of 3 km an hour in the same direction. He could see the car for 4 minutes and was visible for up to a distance of 100 meters. The speed of the car is (in km per hours)

A

$$4\frac{1}{2}$$

B

4

C

$$3\frac{1}{2}$$

D

3

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 3

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Kiran sells pens at a profit of 20% for Rs. 60. But due to lack of demand he reduced its price to Rs. 55. Then

A

He gets a profit of 10%

B

He gets a profit of 12%

C

He incurs a loss of 10%

D

He incurs a loss of 8%

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 4

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If 40% of a number is added to another number then it becomes 125% of itself. The ratio of the second to the first number is

A

$$5 \colon 8$$

B

$$7 \colon 5$$

C

$$8 \colon 5$$

D

None of these

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 5

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The length of a rectangular sheet of paper is 33 cm. It is rolled along its length into a cylinder so that width becomes height of the cylinder. The volume is 1386 cubic cms. The width of the rectangular sheet (in cm) is

A

14

B

15

C

16

D

18

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 6

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If $$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \ldots + \frac{1}{n \times (n+1)} = \frac{19}{20}$$ then $$n =$$

A

18

B

19

C

20

D

25

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 7

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$$a, b$$ are natural numbers. If $$9a^2 = 12a + 96$$ and $$b^2 = 2b + 3$$, the value of $$2018(a+b)$$ is

A

14226

B

14128

C

14126

D

14246

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 8

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Shanti has three daughters. The average age of them is 15 years. Their ages are in the ratio $$3 \colon 5 \colon 7$$. The age of the youngest daughter is (in years)

A

8

B

9

C

10

D

12

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 9

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In the adjoining figure, $$ABCD$$ is a quadrilateral. The bisectors of $$\angle B$$ and the exterior angle at $$D$$ meet at $$P$$. Given $$\angle C = 80^\circ$$, $$\angle ADC = \frac{1}{2}\angle A$$ and $$\angle A = \angle C + 40^\circ$$. Then $$\angle DPB$$ is

A

$$50^\circ$$

B

$$60^\circ$$

C

$$70^\circ$$

D

$$80^\circ$$

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 10

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The number of 3-digit number which contain 6 and 7 is

A

52

B

60

C

62

D

64

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 11

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The difference between the biggest and the smallest three digit number each of which has different digits is

A

864

B

875

C

885

D

895

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 12

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If $$3x+1=2y-1=5z+3=7w+1=15$$, the value of $$6x-3y+5z-8w$$ is

A

1

B

2

C

3

D

None of these

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 13

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Five years ago the average age of Aruna, Roy, David and salman is 45 years. Sita joins them now. The average age of all the five now is 49 years. The present age of sita is (in years)

A

45

B

43

C

51

D

48

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 14

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The fraction $$\frac{B}{3x-1}$$ is subtracted from the fraction $$\frac{A}{2x+3}$$. The resulting fraction is $$\frac{-11}{(2x+3)(3x-1)}$$. Then $$A+B=$$

A

11

B

-11

C

5

D

-5

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 15

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There are some cows and ducks. The total number of legs is equal to 14 more than twice the number of heads. The number of cows is

A

5

B

6

C

7

D

8

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 16

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The sum of 5% of a number and 9% another number is equal to sum of the 8% first number and 7% of the second number. The ratio between the numbers is

A

$$3 \colon 2$$

B

$$5 \colon 7$$

C

$$7 \colon 9$$

D

$$2 \colon 3$$

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 17

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The length of two sides of an isosceles triangle are 8 cm and 14 cm. The perimeter of the triangle (in cm) is

A

30

B

36

C

19

D

30 or 36

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 18

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There are three cell phones A, B, C. A is 50% costlier than C and B is 25% costlier than C. A is a % costlier than B. Then $$a=$$

A

25

B

20

C

15

D

10

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 19

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Sushant wrote a two digit number. He added 5 to the tens digit and subtracted 3 from the unit digit of the number and got a number equal to twice the original number. The original number is

A

47

B

74

C

37

D

73

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 20

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The units digit of $$5^{2018} - 3^{2018}$$ is

A

5

B

6

C

7

D

4

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 21

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The smallest natural number that has to be added to 803642 to get a number which is divisible by 9 is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 22

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The greatest two digit number that will divided 398, 436, and 542 leaving respectively 7, 11 and 15 as remainders is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 23

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$$\frac{2}{3}$$ is ___ of $$\frac{1}{3}$$.

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 24

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The sum of 5 positive integers is 280. The average of the first 2 number is 40. The average of the third and fourth number is 60. The fifth number is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 25

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If $$a \colon b = 3 \colon 4$$ and $$\frac{p}{q}=\frac{a^2+b^2+ab}{a^2+b^2-ab}$$, where $$p, q$$ have no common divisors other than 1, $$p+q$$ is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 26

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$$a$$ is a natural number such that a has exactly two divisors and $$(a+1)$$ has exactly three divisors. The number of divisors of $$a+2$$ is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 27

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The first term of a series is $$\frac{2}{5}$$. If $$x$$ is a term of this series, the next term is $$\frac{1-x}{1+x}$$. If $$t_n$$ denotes the $$n$$ th term and $$t_{2018}-t_{2017}=\frac{p}{q}$$, where $$p, q$$ are integers having no common factors other than 1, $$p+q$$ is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 28

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In the adjoining figure, the side of the square is $$\sqrt{\frac{2018}{\pi}}\text{cm}$$. The area of the unshaded region is $$\left(\frac{\pi-2}{\pi}\right)A$$ sq. cms. The value of $$A$$ is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 29

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$$n$$ is a natural number. The square root of the sum of the square of $$n$$ and 19 is equal to the next natural number to $$n$$. The value of $$n$$ is

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NMTC KAPREKAR Sub-Junior 2018 Solved PDF - Question 30

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Using only the digits 1, 2, 4, 5, two-digit numbers are formed. The digits of the two digit number may be the same or different. The number of such two-digit number is

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