NMTC BHASKARA Junior Level 2018 Solved Question Paper PDF

NMTC BHASKARA Junior Level 2018 Solved PDF - Question 1

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The value of $$\frac{3+\sqrt{6}}{8\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}-\sqrt{27}}$$ is

A

$$\sqrt{2}$$

B

$$\sqrt{3}$$

C

$$\sqrt{6}$$

D

$$\sqrt{18}$$

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 2

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A train moving with a constant speed crosses a stationary pole in 4 seconds and a platform 75 m long in 9 seconds. The length of the train is (in meters)

A

56

B

58

C

60

D

62

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 3

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One of the factors of $$9x^2 - 4z^2 - 24xy + 16y^2 + 20y - 15x + 10$$ is

A

$$3x - 4y - 2z$$

B

$$3x + 4y - 2z$$

C

$$3x + 4y + 2z$$

D

$$3x - 4y + 2z$$

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 4

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The natural number which is subtracted from each of the four numbers $$17, 31, 25, 47$$ to give four numbers in proportion is

A

1

B

2

C

3

D

4

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 5

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The solution to the equation $$5(3^x) + 3(5^x) = 510$$ is

A

2

B

4

C

3

D

No solution

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 6

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If $$(x+1)^2 = x$$, the value of $$11x^3 + 8x^2 + 8x - 2$$ is

A

1

B

2

C

3

D

4

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 7

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There are two values of $$m$$ for which the equation $$4x^2 + mx + 8x + 9 = 0$$ has only one solution for $$x$$. The sum of these two value of $$m$$ is

A

1

B

2

C

3

D

4

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 8

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The number of zeros in the product of the first 100 natural numbers is

A

12

B

15

C

18

D

24

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 9

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The length of each side of a triangle in increased by 20% then the percentage increase of area is

A

60%

B

120%

C

80%

D

44%

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 10

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The number of pairs of relatively prime positive integers $$(a, b)$$ such that $$\frac{a}{b} + \frac{15b}{4a}$$ is an integer is

A

1

B

2

C

3

D

4

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 11

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The four digit number $$8ab9$$ is a perfect square. The value of $$a^2 + b^2$$ is

A

52

B

62

C

54

D

68

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 12

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$$a, b$$ are positive real numbers such that $$\frac{1}{a} + \frac{9}{b} = 1$$. The smallest value of $$a + b$$ is

A

15

B

16

C

17

D

18

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 13

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$$a, b$$ real numbers. The least value of $$a^2 + ab + b^2 - a - 2b$$ is

A

1

B

0

C

-1

D

2

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 14

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I is the incenter of a triangle $$ABC$$ in which $$\angle A = 80^\circ$$. $$\angle BIC =$$

A

$$120^\circ$$

B

$$110^\circ$$

C

$$125^\circ$$

D

$$130^\circ$$

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 15

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In the adjoining figure $$ABCD$$ is a square and $$DFEB$$ is a rhombus. $$\angle CDF =$$

A

$$15^\circ$$

B

$$18^\circ$$

C

$$20^\circ$$

D

$$30^\circ$$

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 16

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$$ABCD$$ is a square. $$E, F$$ are points on $$BC, CD$$ respectively and $$\angle EAF = 45^\circ$$. The value of $$\frac{EF}{BE+DF}$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 17

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The average of 5 consecutive natural numbers is 10. The sum of the second and fourth of these numbers is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 18

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The number of natural number $$n$$ for which $$n^2 + 96$$ is a perfect square is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 19

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$$n$$ is an integer and $$\sqrt{\frac{3n-5}{n+1}}$$ is also an integer. The sum of all such $$n$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 20

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$$\frac{a}{b}$$ is a fraction where $$a, b$$ have no common factors other 1. $$b$$ exceeds $$a$$ by 3. If the numerator is increased by 7, the fraction is increased by unity. The value of $$a + b$$

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 21

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If $$x = \sqrt[3]{2} + \frac{1}{\sqrt[3]{2}}$$ then the value of $$2x^3 - 6x$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 22

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The angle of a heptagon are $$160^\circ, 135^\circ, 185^\circ, 140^\circ, 125^\circ, x^\circ, x^\circ$$. The value of $$x$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 23

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$$ABC$$ is a triangle and $$AD$$ is its altitude. If $$BD = 5DC$$, then the value of $$\frac{3(AB^2-AC^2)}{BC^2}$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 24

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As sphere is inscribed in a cube that has surface area of $$24\text{cm}^2$$. A second cube is then inscribed within the sphere. The surface area of the inner cube (in $$\text{cm}^2$$) is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 25

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A positive integer $$n$$ is multiple of 7. If $$\sqrt{n}$$ lies between 15 and 16, the number of possible values (s) of n is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 26

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The value of $$x$$ which satisfies the equation $$\frac{\sqrt{x+5}+\sqrt{x-16}}{\sqrt{x+5}-\sqrt{x-16}} = \frac{7}{3}$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 27

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$$M$$ man do a work in $$m$$ days. If there had been $$N$$ men more, the work would have been finished $$n$$ days earlier, then the value of $$\frac{m}{n} - \frac{M}{N}$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 28

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The sum of the digit of a two number is 15. If the digits of the given number are reversed, the number is increased by the square of 3. The original number is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 29

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When expanded the units place of $$(3127)^{173}$$ is

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NMTC BHASKARA Junior Level 2018 Solved PDF - Question 30

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If $$a \colon (b+c) = 1 \colon 3$$ and $$c \colon (a+b) = 5 \colon 7$$, then $$b \colon (c+a)$$ is

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