UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 31

EASY

UPSC CDS

IMPORTANT

Earn 100

What is the HCF of the polynomials:

$x^{6} - 3 x^{4} + 3 x^{2} - 1$ and $x^{3} + 3 x^{2} + 3 x + 1$ ?

50% studentsanswered this correctly

Important Questions on UPSC CDS (II) Previous Year Paper 2020

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 32

The HCF and the LCM of two polynomials are

3 x + 1

and

30 x^{3} + 7 x^{2} - 10 x - 3

respectively. If one polynomial is

6 x^{2} + 5 x + 1

, then what is the other polynomial ?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 33

If

(p + 2) (2 q - 1) = 2 p q - 10

and

(p - 2) (2 q - 1) = 2 p q - 10

, then what is

p q

equal to ?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 34

What is the value of

\frac{a^{2} + a c}{a^{2} c - c^{3}} - \frac{a^{2} - c^{2}}{a^{2} c + 2 a c^{2} + c^{3}} - \frac{2 c}{a^{2} - c^{2}} + \frac{3}{a + c}

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 35

What is the square root of

4 x^{4} + 8 x^{3} - 4 x + 1

?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 36

The sum of the digits of a two-digit number is

13

and the difference between the number and that formed by reversing the digits is

27

. What is the product of the digits of the number?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 37

If

\frac{x}{b + c} = \frac{y}{c + a} = \frac{z}{b - a}

, then which one of the following is correct?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 38

X, Y and Z travel from the same place with uniform speeds

4 km / hr, 5 km / hr and 6 km / hr

respectively. Y starts

2 hours

after X. How long after Y must Z start in order that they overtake X at the same instant?

EASY

UPSC CDS

IMPORTANT

UPSC CDS Previous Year Papers>Chapter 8 - UPSC CDS (II) Previous Year Paper 2020>Elementary Mathematics>Q 39

1 - x - x^{n} + x^{n + 1}

, where

n

is a natural number, is divisible by______.