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# NMTC 2016 Junior Level Class 9 & 10

NMTC 2016 Question Papers With Solutions Junior Level Class 9 and 10 is the exam conducted by AMTI.

Read: NMTC 2019 Notification

## NMTC 2016 Junior Level Question Paper

NMTC 2016 Junior Level exam question paper as below.

To Download This Solution in PDF Format:**Click Here**

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## NMTC 2016 Junior Level Solutions

**Part A: Instruction:**

**Only One of the choices A, B, C, D is correct. For each correct response, you get 1 mark. For each incorrect response, you lose 1/2 mark.**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No 1:**

The sum of the values of x and y that satisfy the equation (x + y)2^{(y – x)} = 1 and (x + y)2^{(x – y)} = 2 simultaneously is

**Options:**

A. 2

B. 3/2

C. 5/2

D. 7/2

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 2:

If

the value of a is

**Options:**

A. 4/1007

B. 3/2016

C. 4/2017

D. None of these

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 3:

ABCD is a square inscribed in a circle of radius of 1 unit. The tangent to the circle at C meets AB produced at P. The length of PD is

**Options:**

A. 2

B. 3

C.

D.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 4:

Quadrilateral ABCD is inscribed in a circle with radius 1 unit. AC is diameter of the circle and BD = AB. The diagonals cut at P. If PC = 2/5 then the length of CD is equal to

**Options:**

A. 2/3

B. 2/7

C. 1/8

D. 3/4

**Solution: **

Read : Number Theory Syllabus for NMTC

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 5:

The number of natural numbers n for which the expression (23n2 + 18n + 4)/n is also a natural number is

**Options:**

A. 3

B. 2

C. 1

D. 0

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 6:

The cost price of 16 oranges is equal to the selling price of 12 oranges. Then there is a

**Options:**

A. 40% Profit

B. 20% Loss

C. 33 1/3% Profit

D. 23 1/3% Profit

**Solution:**

**NMTC 2016 Question Papers With Solutions Junior**** Level Ques No** 7:

The number of positive integer pairs (a, b) such that ab – 24 = 2b

**Options:**

A. 6

B. 7

C. 8

D. 9

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 8:

If A = (2 + 1)(2^{2} + 1)(2^{4} + 1)…(2^{2016} + 1), then the value of (A + 1)^{1/2016} is

**Options:**

A. 4

B. 2016

C. 2^{4032}

D. 2

**Solution:**

**NMTC 2016 Question Papers With Solutions Junior**** Level Ques No** 9:

The sum of two numbers a, b where a < b is 1215 and their HCF is 81. The number of such pairs (a, b) is

**Options:**

A. 1

B. 2

C. 3

D. 4

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 10:

The first Republic Day of India was celebrated on 26th January 1950. What was the day of the week on that date?

**Options:**

A. Tuesday

B. Wednesday

C. Thursday

D. Friday

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 11:

The 12 numbers a_{1}, a_{2}, …, a_{12} are in arithmetic progression. The sum of all these numbers is 354. Let P = a_{2} + a_{4} + … + a_{12} and Q = a_{1} + a_{3} + … + a_{11}. If the ratio of P : Q is 32 : 27, the common ratio of the progression is

**Options:**

A. 2

B. 3

C. 4

D. 5

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 12:

A shopkeepers marks the price of his goods at 20% higher than the original price. There is an increase in demand of the goods and he further increases the price by 20%. The total profit % is

**Options:**

A. 40

B. 38

C. 42

D. 44

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 13:

A circle passes through the vertices A and D and touches the side BC of a square. The side of the square 2 cm. The radius of the circle (in cm) is

**Options:**

A. 5/4

B. 4/5

C. 1

D. 5/2

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 14:

There are 4 balls – one green, one red, one blue and one yellow and there are four boxes – one green, one red, one blue and one yellow. A child playing with the balls decides to put the balls in the boxes, one ball in each box. The number of ways in which the child can put the balls in the boxes such that no ball is in a box of its own color is

**Options:**

A. 12

B. 9

C. 24

D. 6

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 15:

The 5 x 5 array of dots represents trees an orchard. If you were standing at the central spot marked C, you would not be able to see of 8 of the 24 trees (shown as x). if you were standing at the center of 9 x 9 arrays of trees, how many of the 80 trees would be hidden?

**Options:**

A. 40

B. 32

C. 36

D. 44

**Solution:**

**Part B: Instruction:**

**Write the correct answer in the space provided in the responsive sheet. For each correct response, you get 1 mark. For each incorrect response, you lose 1/4 mark.**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 16:

a and b are positive integers such that a^{2} + 2b = b^{2} + 2a + 5. The value of b is ______ .

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 17:

Fill in blank:

After full simplification, the value of the product

is ____________ .

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 18:

Fill in blank:

ABCD is rectangle with AD = 1 and AB = 2. DFEB is also a rectangle. The area of DFEB is ____ .

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 19:

Fill in blank:

The two digit number whose unit digit is exceeds the tens digit by 2 and such that the product of the number and the sum of the digits is 144 is ______ .

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 20:

Fill in blank:

If x = p/q where p, q are integers having no common divisors other than 1 satisfies

then x is ____ .

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 21:

Fill in blank:

AE and BF are medians drawn to the legs of a right angled triangle ABC. The numerical values of (AE^{2} + BF^{2}) / AB^{2} is ______.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 22:

Fill in blank:

AB is a chord of a circle with center O. AB is produced to C such that BC = OA. CO is produced to E. The value of (Angle AOE) / (Angle ACE) is _______.

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 23:

Fill in blank:

The number of two digits numbers that are less than the sum of the squares of their digits by 11 and exceed twice the product of their digits by 5 is ______.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 24:

Fill in blank:

AB is a diameter of a circle and CD is a parallel chord. P is any point in AB. The numerical value of (PC^{2} + PD^{2}) / (PA^{2} + PB^{2}) is ______.

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 25:

Fill in blank:

In the sequence of 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, …, the 2016th term is 2^{n}, then the value of n is _____.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 26:

Fill in blank:

Each root of the equation ax^{2} + bx + c = 0 is decreased by 1. The quadratic equation with these roots is x^{2} + 4x + 1 = 0. The numerical value of b + c is ______.

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 27:

Fill in blank:

The number of integers n such that (n + 2) / (n^{2} + 1) > 1/2 is _____.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 28:

Fill in blank:

P_{1} and P_{2} are two regular polygons. The number of sides of P_{1} and P_{2} respectively in the ratio 3 : 2 and the respective angles are in the ratio of 10 : 9. The number of sides of P_{1} and P_{2} is ____.

**Solution:**

**NMTC 2016 Question Papers With Solution Junior**** Level Ques No** 29:

Fill in blank:

In the triangle ABC, F and E are mid points of AB and AC respectively. P is any point on BC. The ratio of (Area of ABC) / (Area of FPE) is _______.

**Solution:**

**NMTC 2016 Junior Level Question Papers With Solutions**** Ques No** 30:

Fill in blank:

x, y, z are real and distinct numbers such that x + 1/y = y + 1/z = z + 1/x. The value of x^{2}y^{2}z^{2} is _____.

**Solution:**

**ANSWER:**

**1____ 5/2**

**2____ 4/1007**

**3____ **

**4____ 2/3**

**5____ 3**

**6____ 33 1/3%**

**7____ 8**

**8____ 4**

**9____ 4**

**10___ Thursday**

**11___ 5**

**12___ 44%**

**13___ 5/4**

**14___ 9**

**15___ 32 **

**16___ 3**

**17___ 1**

**18___ 2**

**19___ 24**

**20___ 25/16**

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