Basic Mathematics-Arithmetic (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 6 - 10 of 24

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Question number: 6

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2010

MCQ▾

Question

Let I, ω and ω2 be the cube roots of unity. The lest possible degree of a polynomial, with real coefficients, having 2 ω2, 3 + 4 ω, 3 + 4 ω2 and 5 – ω – ω2 as roots is –

Choices

Choice (4) Response
a.

8

b.

5

c.

6

d.

4

Question number: 7

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2011

MCQ▾

Question

Let [x] denote the largest integer not exceeding x and {x}=x[x] . Then 02012ecos(π{x})ecos(π{x})+ecos(π{x})dx is equal to –

Choices

Choice (4) Response
a.

2012x

b.

0

c.

2012

d.

1006

Question number: 8

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2013

MCQ▾

Question

Let a, b, c, d be real numbers such that,

k=1n(ak3+bk2+ck+d)=n4

For every natural number n. Then|a|+| b|+| c|+| d|is equal to –

Choices

Choice (4) Response
a.

31

b.

16

c.

15

d.

32

Question number: 9

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2012

MCQ▾

Question

Suppose a1, a2, a3, …, a2012 are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers?

Choices

Choice (4) Response
a.

1509

b.

3018

c.

6036

d.

0

Question number: 10

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2012

MCQ▾

Question

Let (x, y) be a variable point on the curve 4x2+9y28x36y+15=0 . Then min(x22x+y24y+5)+max(x22x+y24y+5) is –

Choices

Choice (4) Response
a.

32536

b.

1325

c.

36325

d.

2513

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