EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 6

HARD

IOQM - PRMO and RMO

IMPORTANT

Earn 100

Find the number of positive integers less than $101$ that cannot be written as the difference of two squares of integers.

50% studentsanswered this correctly

Important Questions on Polynomials

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 7

Find the largest value of

a^{b}

such that the positive integers

a, b > 1

satisfy

a^{b} b^{a} + a^{b} + b^{a} = 5329

.

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 8

What is the smallest prime number

p

such that

p^{3} + 4 p^{2} + 4 p

has exactly

30

positive divisors?

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2018>Q 9

The equation

166 \times 56 = 8590

is valid in some base

b \geq 10

(that is,

1, 6, 5, 8, 9, 0

are digits in base

b

in the above equation). Find the sum of all possible values of

b \geq 10

satisfying the equation.

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2018>Q 10

Integers

a, b, c

satisfy

a + b - c = 1

and

a^{2} + b^{2} - c^{2} = - 1 .

What is the sum of all possible values of

a^{2} + b^{2}

+ c^{2} ?

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2018>Q 11

If

a, b, c \geq 4

are integers, not all equal and

4 a b c = (a + 3) (b + 3) (c + 3)

, then what is the value of

a + b + c ?

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Polynomials>IOQM - PRMO and RMO 2018>Q 12

Let

P (x) = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n}

be a polynomial in which

a_{i}

is a non-negative integer for each

i \in \{0, 1, 2, 3, \dots, n\}

. If

P (1) = 4

and

P (5) = 136

, what is the value of

P (3)

?