NTSE 2019-20 Stage 2 Question Paper With Answer Keys

Hi Students, welcome to Amans Maths Blogs (AMB). On this page, you will get NTSE 2019-20 Stage 2 Question Paper With Answer Keys and SAT (Maths) Solutions.

As we know that NTSE 2019-20 is a national level program  which is conducted in two stages NTSE 2018 Stage 1 which was scheduled on 17 November 2018, conducted by their respective states and union territories and due to Covid-19, the next stage exam NTSE 2019-20 Stage 2 is conducted by NCERT (National Council of Educational Research and Training) on 14 Feb 2021.

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 2019-20 Stage 2 Question Paper & Answer Keys and Solutions. Here, you will get NTSE 2019-20 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 2019-20 Stage 2 MAT Question Paper

NTSE 2019-20 Stage 2 MAT Answer Keys

NTSE 2019-20 Stage 2 SAT Question Paper

NTSE 2019-20 Stage 2 SAT Answer Keys

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 2019-20 Stage 2 SAT (Maths) Solutions

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 41

If x = (√5 – √2)/(2√(3 + √5) – √2), then the value of (x√10 + √2)/(x√10 + 2√5) is

Options:

1. (15 + √10)/41

2. (15 – √10)/41

3. (15 + √10)/43

4. (15 – √10)/47

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 42

On dividing a natural number x by 11, the remainder is 3, and on dividing x by 1, the remainder is 9. If the number x lies between 300 and 400, then the remainder on dividing x by 21 is

Options:

1. 9 but not 11

2. 11 but not 9

3. both 9 and 11

4. neither 9 nor 11

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 43

If (ax + b)(x⁵ + 1) – (5x + 1) is divisible by x² + 1, then the value of (2a + 3b) is

Options:

1. 5

2. 10

3. 12

4. 13

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 44

Suppose the graphs of 15x + 20y = -2 and x – y = -2 intersect at point P. If the graph of 2x + 3y = k² passes through P, then k is

Options:

1. an integer

2. a positive integer

3. a negative integer

4. not an integer

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 45

The sum of the squares of the third and the thirteen terms of an AP is 5, and the product of the fourth and twelfth terms if R. Then, the product of the third and thirteen terms of the AP is

Options:

1. (80 + 50R)/41

2. (80 + 50R)/82

3. (100R – 45)/82

4. (100R – 45)/41

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 46

If α and β are the roots of the quadratic equation 2x² – 5x – 6 = 0 and P_n+1 = αⁿ – βⁿ, then the value of (P₉ – 3P₇)/4P₈ is 

Options:

1. 3/8

2. 5/8

3. 7/8

4. 9/8

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 47

A number is picked up at random from the numbers from 1 to 1000. The probability that it is of the form mⁿ (where m > 1, n > 1) is

Options:

1. 1/20

2. 1/25

3. 1/30

4. 1/39

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 48

Let A(-5, 5), B(4, -5) and C(4, 5) be the vertices of the triangle ABC. If a circle passes through the vertices of ∆ABC, then the area (in sq. units) lying inside the circle but outside the ∆ABC is

Options:

1. 181π/2 – 45

2. 181π/2 – 40

3. 181π/4 – 45

4. 181π/4 – 40

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 49

The coordinates of points A, B and C are (7, 4), (3, 1) and (0, k) respectively. Then, the value of k, such that AC + BC is minimum is 

Options:

1. -5/4

2. 19/10

3. 5/4

4. 9/10

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 50

Two tangents PA and PB are drawn to a circle with centre O from an external point P. The chord AB intersects the line segments PO at Q. Then, the square of the radius of the circle is

Options:

1. OQ × QP

2. OQ × OP

3. PQ × AB

4. PA × PB

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 51

In the given figure, ABCD is rectangle. Then, the area of the shaded region is

Options:

1. 1.2 sq units

2. 1.4 sq units

3. 1.6 sq units

4. 1.8 sq units

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 52

In the given figure, the triangle ABC is an isosceles triangle with AB = AC. If AE = AF and angle BAE = 40 degree, then the measure of the angle FEC is

Options:

1. 15 degree

2. 20 degree

3. 40 degree

4. 60 degree

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 53

In an equilateral triangle ABC, side BC is produced to D and DF is perpendicular to AB such that DF is intersecting AC at E. If BC = 2CD and AF = 6 cm, then the length of BF is

Options:

1. 9

2. 12

3. 15

4. 18

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 54

Water is flowing at the rate of 10 cm/min through a pipe of diameter 10 cm into an empty bucket, which is in the form of frustum of cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Then, the time in which the level of water in bucket will rise 15 cm is

Options:

1. √17/10 minutes

2. √19/5 minutes

3. √17/5 minutes

4. √18/10 minutes

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 55

The largest possible area of the triangle ABC with AB = 5 cm and the sum of the other sides as 7 cm is 

Options:

1. 5√6 cm²

2. 5√6 / 2 cm²

3. 5√3 / 2 cm²

4. 5√3 cm²

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 56

If u = cosθ(sinθ + √(sin²θ + sin²α)), then |u| is less than or equal to 

Options:

1. √(1 + sin²α)

2. √(1 + cos²α)

3. √(2 + sin²α)

4. √(2 + cos²α)

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 57

Two straight roads OA and OB intersect at O. A tower is situated in the interior of the angle formed by them and subtends an angle of 45 degree and 30 degree at the points A and B respectively, where the roads are nearest to it. If OA = a and OB = b, then the height of the tower is

Options:

1. √[(a² – b²)/2]

2. √[(b² – a²)/2]

3. √[3(b² – a)²/2]

4. √[3(a² – b)²/2]

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 58

ABCD is square of side 8 cm, P is the mid point of AD and is joined with vertex B. A perpendicular is drawn from the vertex C on BP, which intersects BP at point E. The area of the triangle BEC is

Options:

1. 64/5 cm²

2. 64/√5 cm²

3. 32/5 cm²

4. 32/√5 cm²

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 59

The mean of three numbers is 10 more than the least number and 15 less than the greatest number, if the median of three numbers is 5, then the sum of squares of these numbers is

Options:

1. 625

2. 650

3. 675

4. 725

Answer Key: 2

Solution:

NTSE 2019-20 Stage 2 SAT Math Solutions: Ques No 60

A and B are two metallic solid spheres such that the surface area of B is 800% more than that of A. If the volume of A is x% less than that of B, then the value of x is closest to

Options:

1. 64.2

2. 72.4

3. 95.5

4. 96.3

Answer Key: 2

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.