Hi students, Welcome to **Amans Maths Blogs (AMB)**. In this article, you will get **KVPY Stream SA SX SB Previous Year Question Papers with Solutions PDF**.

Since IISc (Indian Institute of Science) released **KVPY 2021 Notification** officially on its official website, You must need to solve the previous year question papers of KVPY (Kishore Vaigyanik Protsahan Yojana) for stream SA (Class 11), SX (Class 12) and SB (Class 12 passed). This is very important to solve the KVPY last year papers as it will guide you about their questions paper pattern and difficulty level etc.

All of these questions of KVPY are solved by Career Point KOTA.

Contents

## KVPY 2020 Question Paper with Solutions

### KVPY 2020 SA Question Paper with Solutions

**KVPY 2020 SA Math Questions** :

Let [x] be the greatest integer less than or equal to x, for a real number x. Then, the equation [x^{2}] = x + 1 has

(A) two solutions

(B) one solution

(C) no solution

(D) More than two solutions

For full question paper of KVPY 2020 SA with solutions, Click Below.

### KVPY 2020 SX/SB Question Paper with Solutions

**KVPY 2020 SX/SB Math Questions** :

Consider a regular decagon with the vertices on the unit circle. With one vertex fixed, draw straight lines to the other 9 vertices. Call them L1, L2, L3, … L9 and denote their lengths by *l*_{1}, *l*_{2}, *l*_{3}, …, *l*_{9} respectively. Then, the product of *l*_{1}, *l*_{2}, *l*_{3}, …, *l*_{9 }is

(A) 10

(B) 10√3

(C) 50/√3

(D) 20

For full question paper of KVPY 2020 SX/SB with solutions, Click Below.

## KVPY 2019 Question Paper with Solutions

### KVPY 2019 SA Question Paper with Solutions

**KVPY 2019 SA Math Questions** :

Let ABC be an equilateral triangle with side length a. Let R and r denote the radii of the circumcircle and the incircle of triangle ABC respectively. Then, as a function of a, the ratio of R/r.

(A) strictly increases

(B) strictly decreases

(C) remains constant

(D) strictly increases for a < 1 and strictly decreases for a > 1

For full question paper of KVPY 2019 SA with solutions, Click Below.

### KVPY 2019 SX/SB Question Paper with Solutions

**KVPY 2019 SX/SB Math Questions** :

The number of four-letter words that can be formed with letters a, b, c such that all three letters occur is

(A) 30

(B) 36

(C) 81

(D) 256

For full question paper of KVPY 2019 SX/SB with solutions, Click Below.

## KVPY 2018 Question Paper with Solutions

### KVPY 2018 SA Question Paper with Solutions

**KVPY 2018 SA Math Questions** :

The number of pairs (a, b) of positive real numbers satisfying a^{4} + b^{4} < 1 and a^{2} + b^{2} > 1 is

(A) 0

(B) 1

(C) 2

(D) More than 2

For full question paper of KVPY 2018 SA with solutions, Click Below.

### KVPY 2018 SX/SB Question Paper with Solutions

**KVPY 2018 SX/SB Math Questions** :

On any given arc of positive length on the unit circle |z| = 1 in the complex plane.

(A) there need not be any root of unity

(B) there lies exactly one root of unity

(C) there are more than one but finitely many roots of unity

(D) there are infinitely many roots of unity

For full question paper of KVPY 2018 SX/SB with solutions, Click Below.

## KVPY 2017 Question Paper with Solutions

### KVPY 2017 SA Question Paper with Solutions

**KVPY 2017 SA Math Questions** :

A quadrilateral has distinct integer side lengths. If the second-largest side has length 10, then the maximum possible length of the largest side is

(A) 25

(B) 26

(C) 27

(D) 28

For full question paper of KVPY 2017 SA with solutions, Click Below.

### KVPY 2017 SX/SB Question Paper with Solutions

**KVPY 2017 SX/SB Math Questions** :

Consider a rigid square ABCD as in the figure with A and B on the x and y axis respectively. When A and B slide along their respective axes, the locus of C forms a part of

(A) a circle

(B) a parabola

(C) a hyperbola

(D) an ellipse which is not a circle

For full question paper of KVPY 2017 SX/SB with solutions, Click Below.

## KVPY 2016 Question Paper with Solutions

### KVPY 2016 SA Question Paper with Solutions

**KVPY 2016 SA Math Questions** :

Suppose the quadratic polynomial P(x) = ax^{2} + bx + c has positive coefficients a, b, c in arithmetic

progression in that order. If P(x) = 0 has integer roots α and β then α + β + αβ equals

(A) 3

(B) 5

(C) 7

(D) 14

For full question paper of KVPY 2016 SA with solutions, Click Below.

### KVPY 2016 SX/SB Question Paper with Solutions

**KVPY 2016 SX/SB Math Questions** :

The number of triples (x, y, z) of real numbers satisfying the equation x^{4} + y^{4} + z^{4} + 1 = 4xyz is

(A) 0

(B) 4

(C) 8

(D) More than 8

For full question paper of KVPY 2016 SX/SB with solutions, Click Below.

## KVPY 2015 Question Paper with Solutions

### KVPY 2015 SA Question Paper with Solutions

**KVPY 2015 SA Math Questions** :

If n is the smallest natural number such that n + 2n + 3n + ….. + 99n is a perfect square, then the number of digits in n^{2} is –

(A) 1

(B) 2

(C) 3

(D) More than 3

For full question paper of KVPY 2015 SA with solutions, Click Below.

### KVPY 2015 SX/SB Question Paper with Solutions

**KVPY 2015 SX/SB Math Questions** :

The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations x + y^{2}

= x^{2} + y = 12 is

(A) 0

(B) 1

(C) 2

(D) 4

For full question paper of KVPY 2015 SX/SB with solutions, Click Below.

## KVPY 2014 Question Paper with Solutions

### KVPY 2014 SA Question Paper with Solutions

**KVPY 2014 SA Math Questions** :

Let r be a root of the equation x^{2} + 2x + 6 = 0. The value of (r + 2)(r + 3)(r + 4)(r + 5) is equal to-

(A) 51

(B) -51

(C) -126

(D) 126

For full question paper of KVPY 2014 SA with solutions, Click Below.

### KVPY 2014 SX/SB Question Paper with Solutions

**KVPY 2014 SX/SB Math Questions** :

For a real number r we denote by [r] the largest integer less than or equal to r. If x, y are real numbers with x, y ≥ 1 then which of the following statements is always true?

(A) [x + y] ≤ [x] + [y]

(B) [xy] ≤ [x] [y]

(C) [2^{x}] ≤ 2^{[x]}

(D) [x/y] ≤ [x]/[y]

For full question paper of KVPY 2014 SX/SB with solutions, Click Below.

## KVPY 2013 Question Paper with Solutions

### KVPY 2013 SA Question Paper with Solutions

**KVPY 2013 SA Math Questions** :

Let x, y, z be three non-negative integers such that x + y + z = 10. The maximum possible value of xyz + xy + yz + zx is

(A) 52

(B) 64

(C) 69

(D) 73

For full question paper of KVPY 2013 SA with solutions, Click Below.

### KVPY 2013 SX/SB Question Paper with Solutions

**KVPY 2013 SX/SB Math Questions** :

The sum of non-real roots of the polynomial equation x3 + 3×2 + 3x + 3 = 0

(A) equal to 0

(B) lies between 0 and 1

(C) lies between -1 and 0

(D) has absolute value bigger than 1

For full question paper of KVPY 2013 SX/SB with solutions, Click Below.

## KVPY 2012 Question Paper with Solutions

### KVPY 2012 SA Question Paper with Solutions

**KVPY 2012 SA Math Questions** :

Let f(x) be a quadratic polynomial with f(2) = 10 and f(2) = – 2. Then the coefficient of x in f(x) is

(A) 1

(B) 2

(C) 3

(D) 4

For full question paper of KVPY 2012 SA with solutions, Click Below.

### KVPY 2012 SX/SB Question Paper with Solutions

**KVPY 2012 SX/SB Math Questions** :

Three children, each accompanied by a guardian, seek admission in a school. The principal want to interview all the 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done

(A) 60

(B) 90

(C) 120

(D) 180

For full question paper of KVPY 2012 SX/SB with solutions, Click Below.

## KVPY 2011 Question Paper with Solutions

### KVPY 2011 SA Question Paper with Solutions

**KVPY 2011 SA Math Questions** :

Let a, b, x, y be real numbers such that a^{2} + b^{2} = 81, x^{2} + y^{2} = 121 and ax + by = 99. Then the set of all possible values of ay – bx is –

(A) (0, 9/11]

(B) (0, 9/11)

(C) {0}

(D) [9/11, ∞)

For full question paper of KVPY 2011 SA with solutions, Click Below.

### KVPY 2011 SX/SB Question Paper with Solutions

**KVPY 2011 SX/SB Math Questions** :

Suppose log_{a}b + log_{b}a = c. The smallest possible integer value of c for all a, b > 1 is –

(A) 4

(B) 3

(C) 2

(D) 1

For full question paper of KVPY 2011 SX/SB with solutions, Click Below.

## KVPY 2010 Question Paper with Solutions

### KVPY 2010 SA Question Paper with Solutions

**KVPY 2010 SA Math Questions** :

A student notices that the roots of the equation x2 + bx + a = 0 are each 1 less than the roots of the equation x2 + ax + b = 0. Then a + b is

(A) Possibly any real number

(B) -2

(C) -4

(D) -5

For full question paper of KVPY 2010 SA with solutions, Click Below.

### KVPY 2010 SX/SB Question Paper with Solutions

**KVPY 2010 SX/SB Math Questions** :

The number of rectangles that can be obtained by joining four of the twelve vertices of a 12-sided regular polygon is

(A) 66

(B) 30

(C) 24

(D) 15

For full question paper of KVPY 2010 SX/SB with solutions, Click Below.