Sample Paper For NMTC Stage 1 Junior Level | Class 9 and 10

Hi students, welcome to Amans Maths Blogs (AMB). On this post you will get Sample Paper For NMTC Stage 1 Junior Level (Class 9 and 10). The questions of this sample paper are published on this post, it will help you to understand the level of questions asked in NMTC Stage 1 in Junior Level. So lets start with the questions as below:

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 1

For x ≥ 0, the smallest value of (4x² + 8x + 13)/(6(1 + x)) is

Options

A. 1

B. 2

C. 2/3

D. 2/9

Sample Paper For NMTC Stage 1 Junior Level Question No 2

If x satisfies  , then the value of x² lies in 

Options

A. Between 75 and 85

B. Between 65 and 75

C. Between 85 and 95

D. Between 55 and 65

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 3

Exactly five interior angles of a convex polygon are obtuse. The maximum possible number of sides for such a polygon is

Options

A. 6

B. 7

C. 8

D. 9

Sample Paper For NMTC Stage 1 Junior Level Question No 4

For xyz ≥ 0, if x + y + z = 11, then find the maximum value of (xyz + xy + yz + zx) is 

Options

A. 1562

B. 2984

C. 2420 / 27

D. 1687 / 25

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 5

The sum of all angles except one of a convex polygon is 2190 degree (where the angles are less than 180 degree). The possible number of the sides of the polygon is

Options

A. 13

B. 12

C. 17

D. 15

Sample Paper For NMTC Stage 1 Junior Level Question No 6

If the roots of the equation x² – 2ax + a² + a – 3 = 0 are real and less than 3, then 

Options

A. a > 2

B. a > 3

C. a < 2

D. a < 2 U a > 3

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 7

Let E(m) denotes the number of even digits in m, for example: E(2) = 1, E(19) = 0, E(201) = 2, E(5672) = 2 etc, Then find the value of E[E(101) x E(201) x E(301) x … x E(2001)]. 

Options

A. 1

B. 0

C. 1536

D. 1901

Sample Paper For NMTC Stage 1 Junior Level Question No 8

Evaluate  

Options

A. √2 + √3 – √5 

B. 2 + √2

C. √2 – √3 – √5

D. 3 – √5

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 9

The sides of a right angled triangle are a, a + d and a + 2d with a and d both positive. Find the ratio of a to d (means, a/d)

Options

A. 1 : 1

B. 3 : 1

C. 1 : 3

D. 2 : 3

Sample Paper For NMTC Stage 1 Junior Level Question No 10

The smallest positive integer K for which 1260K = N³, where N is an integer.

Options

A. 5324

B. 6548

C. 3256

D. 7350

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 11

a679b is a five digit number in decimal number system which is divisible by 72. Then, the value of (a + b) is

Options

A. 7

B. 5

C. 3

D. 2

Sample Paper For NMTC Stage 1 Junior Level Question No 12

The last two digits of 

is

Options

A. 43

B. 07

C. 01

D. 36

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 13

If x⁹ = 9^9^9, then the value of x is

Options

A. 9^9^8

B. 9^9^7

C. 9^9

D. 9^9^9^9

Sample Paper For NMTC Stage 1 Junior Level Question No 14

The sum of the digits of the number 1000²⁰ – 20 expressed in decimal notation is

Options

A. 510

B. 520

C. 530

D. 540

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 15

The number all integers n for which (n³ – 1) / 5 is a prime number is

Options

A. 0

B. 1

C. 2

D. More than 2

Sample Paper For NMTC Stage 1 Junior Level Question No 16

The natural numbers 1, 2, 3, . . . , up to 100 are written in that natural order to form the single number 1234…979899100. The number of times the digit 1 occurs is

Options

A. 18

B. 19

C. 20

D. 21

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 17

The length of one of the legs of a right angled triangle exceeds the length of the other leg by 10 cm but is smaller than that of the hypotenuse by 10 cm. The length of the hypotenuse is 

Options

A. 50

B. 60

C. 45

D. 62

Sample Paper For NMTC Stage 1 Junior Level Question No 18

In a triangle ABC, BE and CF are medians. BE = 9 cm, CF = 12 cm. If BE and CF are perpendicular to each other, then the area (in sq. cm) of the triangle ABC is 

Options

A. 24

B. 48

C. 72

D. 96

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 19

Nine lines drawn parallel to the base of a triangle divide the other two sides in to 10 equal parts and the area into 10 distinct parts. If the area of the largest of these parts is 2019 sq. cms, then the area of the triangle is 

Options

A. 2019

B. 2019 / 11

C. 201900

D. 201900/19

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 20

Triangle ABC is an isosceles triangle with base AC. Points P and Q are respectively in BC and AB such that AC = AP = PQ = QB. The angle B is 

Options

A. 175/7 degrees

B. 180/7 degrees

C. 72 degrees

D. 68 degrees

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 21

The ratio of the area of the equilateral triangle inscribed in a circle to that of a regular hexagon inscribed in the same circle is 

Options

A. 1 : 2

B. 2 : 3

C. 1 : 3

D. 3 : 4

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 22

P(x) is a polynomial satisfying P(x + 3/2) = P(x) for all real values of x. If P(2017) = 2019, then the value of P(2020) is

Options

A. 2017

B. 2018

C. 2019

D. 2020

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 23

If a, b, c are real numbers such that a + 1/b = 7/3, b + 1/c = 4 and c + 1/a = 1, then the value of abc is

Options

A. 1

B. 2

C. 3

D. 4

Sample Paper For NMTC Stage 1 Class 9 and 10 Question No 24

If {(3(230 + x)²)} = 492a04, then the value of a is

Options

A. 5

B. 7

C. 9

D. 8

Answer Keys

1. B

2. A

3. C

4. C

5. D

6. C

7. A

8. A

9. B

10. D

11. B

12. D

13. A

14. C

15. B

16. D

17. A

18. C

19. D

20. B

21. A

22. C

23. A

24. D