# 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.