# NTSE 2018-19 Stage 2 Question Paper With Answer Keys

Hi Students, welcome to **Amans Maths Blogs (AMB)**. On this page, you will get NTSE 2018 Stage 2 Question Paper With Answer Keys and SAT (Maths) Solutions.

As we know that NTSE 2018-19 is a national level program which is conducted in two stages NTSE 2018 Stage 1 which was scheduled on 04 November 2018, conducted by their respective states and union territories and NTSE 2018 Stage 2 is conducted by NCERT (National Council of Educational Research and Training).

Read : NTSE 2018-19 Stage 1 Question Papers and Answer Key of All States

NTSE Stage 1 and 2 is the one of the most prestigious exams in India. To know more about NTSE like NTSE notification, syllabus, exam pattern, FAQ, previous year question papers with solution, **click here**.

On this post, you will get the **NTSE 2019 Stage 2 Question Paper & Answer Keys and Solutions**. Here, you will get NTSE 2019 Stage 2 **SAT (Maths)** Solutions. These questions are solved by me, AMAN RAJ, I am maths faculty of IIT Maths Foundation course and founder of this website **AmansMathsBlogs (AMB)**.

## NTSE 2018-19 Stage 2 MAT Question Paper

This file will be uploaded soon…

## NTSE 2018-19 Stage 2 MAT Answer Keys

NTSE 2018-9 Stage 2 Answer Keys | |||||||
---|---|---|---|---|---|---|---|

NTSE 2019 Stage 2 MAT Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

1 |
1 |
26 |
1 |
51 |
3 |
76 |
2 |

2 |
1 |
27 |
1 |
52 |
4 |
77 |
3 |

3 |
2 |
28 |
2 |
53 |
3 |
78 |
3 |

4 |
1 |
29 |
4 |
54 |
2 |
79 |
2 |

5 |
2 |
30 |
2 |
55 |
4 |
80 |
3 |

6 |
2 |
31 |
2 |
56 |
1 |
81 |
4 |

7 |
3 |
32 |
1 |
57 |
2 |
82 |
3 |

8 |
3 |
33 |
3 |
58 |
3 |
83 |
2 |

9 |
2 |
34 |
4 |
59 |
1 |
84 |
4 |

10 |
2 |
35 |
3 |
60 |
3 |
85 |
3 |

11 |
3 |
36 |
3 |
61 |
3 |
86 |
2 |

12 |
4 |
37 |
2 |
62 |
3 |
87 |
3 |

13 |
2 |
38 |
3 |
63 |
3 |
88 |
2 |

14 |
1 |
39 |
3 |
64 |
2 |
89 |
3 |

15 |
4 |
40 |
2 |
65 |
3 |
90 |
2 |

16 |
3 |
41 |
2 |
66 |
2 |
91 |
2 |

17 |
3 |
42 |
4 |
67 |
2 |
92 |
3 |

18 |
3 |
43 |
2 |
68 |
3 |
93 |
2 |

19 |
4 |
44 |
2 |
69 |
3 |
94 |
4 |

20 |
1 |
45 |
3 |
70 |
1 |
95 |
3 |

21 |
2 |
46 |
1 |
71 |
3 |
96 |
4 |

22 |
4 |
47 |
4 |
72 |
2 |
97 |
4 |

23 |
1 |
48 |
1 |
73 |
1 |
98 |
4 |

24 |
2 |
49 |
NA |
74 |
2 |
99 |
1 |

25 |
2 |
50 |
2 |
75 |
4 |
100 |
1 |

## NTSE 2018-19 Stage 2 SAT Question Paper

## NTSE 2018-19 Stage 2 SAT Answer Keys

Social Science (1 to 40) | |||||||
---|---|---|---|---|---|---|---|

Social Science NTSE 2019 Stage 2 Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

1 |
3 |
11 |
2 |
21 |
2 |
31 |
4 |

2 |
3 |
12 |
3 |
22 |
4 |
32 |
2 |

3 |
4 |
13 |
2 |
23 |
2 |
33 |
2 |

4 |
3 |
14 |
3 |
24 |
3 |
34 |
2 |

5 |
4 |
15 |
2 |
25 |
4 |
35 |
4 |

6 |
2 |
16 |
1 |
26 |
3 |
36 |
4 |

7 |
2 |
17 |
3 |
27 |
3 |
37 |
1 |

8 |
1 |
18 |
3 |
28 |
1 |
38 |
4 |

9 |
3 |
19 |
2 |
29 |
4 |
39 |
4 |

10 |
1 |
20 |
1 |
30 |
2 |
40 |
4 |

Mathematics (41 to 60) | |||||||

Maths NTSE 2018-19 Stage 2 Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

41 |
2 |
46 |
1 |
51 |
2 |
56 |
3 |

42 |
4 |
47 |
3 |
52 |
1 |
57 |
3 |

43 |
1 |
48 |
3 |
53 |
2 |
58 |
2 |

44 |
1 |
49 |
3 |
54 |
2 |
59 |
2 |

45 |
1 |
50 |
4 |
55 |
3 |
60 |
1 |

Physics (61 to 73) | |||||||

PHYSICS NTSE 2018-19 Stage 2 Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

61 |
3 |
66 |
4 |
71 |
1 |
||

62 |
3 |
67 |
2 |
72 |
3 |
||

63 |
2 |
68 |
4 |
73 |
2 |
||

64 |
NA |
69 |
1 |
||||

65 |
2 |
70 |
2 |
||||

Chemistry (74 to 87) | |||||||

CHEMISTRY NTSE 2018-19 Stage 2 Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

74 |
4 |
79 |
1 |
84 |
3 |
||

75 |
1 |
80 |
2 |
85 |
3 |
||

76 |
3 |
81 |
4 |
86 |
4 |
||

77 |
3 |
82 |
3 |
87 |
3 |
||

78 |
2 |
83 |
4 |
||||

Biology (88 to 100) | |||||||

BIOLOGY NTSE 2018-19 Stage 2 Answer Keys | |||||||

Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key | Ques No | Ans Key |

88 |
3 |
93 |
2 |
99 |
1 |
||

89 |
2 |
95 |
3 |
100 |
2 |
||

90 |
3 |
96 |
3 |
||||

91 |
1 |
97 |
3 |
||||

92 |
1 |
98 |
3 |

## NTSE Maths Combo Pack EBook

Get **900+ NTSE Maths Previous Year Question Bank** with **Solutions** and **11 Mock Test Papers EBook** for NTSE exams. For more details, Click To **NTSE Stage 1 Mock Test SAT Maths** and **NTSE Stage 2 Mock Test SAT Maths**. To get this combo ebook, click below **RED** button.

## NTSE 2018-19 Stage 2 SAT (Maths) Solutions

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 41**

If m = n^{2} – n, where n is an integer, then m^{2} – 2m is divisible by

**Options:**

1. 20

2. 24

3. 30

4. 16

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 42**

The value of √[(97 x 98 x 99 x 100) + 1] is equal to

**Options:**

1. 9901

2. 9891

3. 9801

4. 9701

**Answer Key: 4**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 43**

Let P(x) be a polynomial of degree 3 and P(n) = 1/n for n = 1, 2, 3, 4. Then, the value of P(5) is

**Options:**

1. 0

2. 1/5

3. -2/5

4. 3/5

**Answer Key: 1**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 44**

If α and β are the roots of the equation 3x^{2} – 5x + 3 = 0, then the quadratic equation whose he roots are α^{2}β and αβ^{2} is

**Options:**

1. 3x^{2} – 5x + 3 = 0

2. 3x^{2} – 8x + 3 = 0

3. 3x^{2} – 8x + 3 = 0

4. 3x^{2} – 5x – 3 = 0

**Answer Key: 1**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 45**

In village Madhubani 8 women and 12 girls can paint a large mural in 10 hours. 6 women and 8 girls can paint it in 14 hours. The number of hours taken by 7 women and 14 girls to pain the mural is

**Options:**

1. 10

2. 15

3. 20

4. 35

**Answer Key: 1**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 46**

If x = (3 + √5) / 2 and y = x^{3}, then y satisfies the quadratic equation

**Options:**

1. y^{2} – 18y + 1 = 0

2. y^{2} + 18y + 1 = 0

3. y^{2} – 18y – 1 = 0

4. y^{2} + 18y – 1 = 0

**Answer Key: 1**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 47**

If tan^{2}θ = 1 – e^{2}, then the value of secθ + tan^{3}θcosecθ is equal to

**Options:**

1. (1 – e^{2})^{1/2}

2. (2 – e^{2})^{1/2}

3. (2 – e^{2})^{3/2}

4. (1 – e^{2})^{3/2}

**Answer Key: 3**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 48**

Let the volume of a solid sphere be 288π cm^{3}. A horizontal plane cuts the sphere at a distance of 3 cm from the centre so that the ratio of the curved surface areas of the two parts of the sphere is 3 : 1. The total surface area of the bigger part of the sphere (in cm^{2}) is

**Options:**

1. 36π

2. 108π

3. 135π

4. 144π

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 49**

A solid metallic cylinder of height 10 cm and diameter 14 cm is melted to make two cones in the proportion of their volumes as 3 : 4, keeping the height 10 cm, what would be the percentage increase in the flat surface area?

**Options:**

1. 9

2. 16

3. 50

4. 200

**Answer Key: 3**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 50**

Each vertical face of square based vertical pillar of height 3 m has 7 equal, semi-cylindrical surfaces in such a way that its horizontal cross-section is as shown in the figure. If the radius of each pillar so designed (taking π = 22/7) is

**Options:**

1. 5.88

2. 6.14

3. 6.42

4. 7.2

**Answer Key: 4**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 51**

Let ABCD be a square of side 20 cm. The area of square PQRS (in cm^{2}) interior to ABCD, shown in the figure is.

**Options:**

1. 60

2. 80

3. 100

4. 400

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 52**

A circle is inscribed in a right angled triangle of perimeter 7π. Then the ratio of numerical values of circumference of the circle to the area of the right angled triangle is

**Options:**

1. 4 : 7

2. 3 : 7

3. 2 : 7

4. 1 : 7

**Answer Key: 1**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 53**

It is known that the area of cyclic quadrilateral is √(S – a)(S – b)(S – c)(S – d), where a, b, c and d are the sides and S = (a + b + c + d)/2. If a circle can also be the inscribed in the cyclic quadrilateral is

**Options:**

1. √( (ab)^{2} + (cd)^{2})

2. √(abcd)

3. √( (ac)^{2} + (bd)^{2})

4. √( (ad)^{2} + (bc)^{2})

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 54**

Two circles both of radii a touch each other and each of them touches internally a circle of radius 2a. Then the radius of the circle which touches all the three circles is

**Options:**

1. a/2

2. 2a/3

3. 3a/4

4. a

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 55**

Let D be a point on the side BC of a triangle ABC such that ∠ ADC = ∠BAC. If AC = 21 cm, then the side of an equilateral triangle whose area is equal to the area of the rectangle with sides BC and DC is

**Options:**

1. 14 x 3^{1/2}

2. 42 x 3^{-1/2}

3. 14 x 3^{3/2}

4. 42 x 3^{1/2}

**Answer Key: 3**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 56**

Let ABC be a triangle with sides a, b, c. Then, the length of medians of the triangle formed by the medians of the triangle ABC are

**Options:**

1. a/2, b/2, c/2

2. 2a/3, 2b/3, 2c/3

3. 3a/4, 3b/4, 3c/4

4. 5a/6, 5b/6, 5c/6

**Answer Key: 3**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 57**

(x + 1)^{4} is divided by (x – 1)^{3}. Then the value of the remainder at x = 1 is

**Options:**

1. -16

2. 0

3. 16

4. 32

**Answer Key: 3**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 58**

A circle passes through the vertices of triangle ABC. If the vertices are A(-2, 5), B(-2, -3), C(2, -3), then the center of the circle is

**Options:**

1. (0, 0)

2. (0, 1)

3. (-2, 1)

4. (0, -3)

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 59**

If two dice are thrown together, the probability that the difference of the numbers appearing on them is a prime number is

**Options:**

1. 2/9

2. 4/9

3. 5/12

4. 17/36

**Answer Key: 2**

**Solution:**

**NTSE 2019 Stage 2 SAT Math Solutions: Ques No 60**

Observe the following data.

If the above data has mean 50, then the missing frequencies f_{1} and f_{2} are respectively.

**Options:**

1. 28 and 24

2. 24 and 28

3. 28 and 30

4. 30 and 28

**Answer Key: 1**

**Solution:**

## NTSE Maths Combo Pack EBook

Get **900+ NTSE Maths Previous Year Question Bank** with **Solutions** and **11 Mock Test Papers EBook** for NTSE exams. For more details, Click To **NTSE Stage 1 Mock Test SAT Maths** and **NTSE Stage 2 Mock Test SAT Maths**. To get this combo ebook, click below **RED** button.