Basic Mathematics-Algebra (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 1 - 5 of 7

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Question number: 1

» Basic Mathematics » Algebra » Simplifying Expressions

Appeared in Year: 2010

MCQ▾

Question

Let f:RR be a differentiable function such that f(a)=f(b)=0 and f(a)f(b)>0 for some a < b. Then the minimum numbers of roots of f(x)=0 in the interval (a, b) is –

Choices

Choice (4) Response

a.

0

b.

1

c.

3

d.

2

Question number: 2

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2012

MCQ▾

Question

In the real number system, the equation x+34x1+x+86x1=1 has –

Choices

Choice (4) Response

a.

No solution

b.

Exactly two distinct solutions

c.

Infinitely many solutions

d.

Exactly four distinct solutions

Question number: 3

» Basic Mathematics » Algebra » Simplifying Expressions

Appeared in Year: 2013

MCQ▾

Question

Let ω be a cube root of unity not equal to 1. Then the maximum possible value of a+bω+cω2 where a, b, c ∈ {+1, -1} is –

Choices

Choice (4) Response

a.

1+3

b.

2

c.

3

d.

0

Question number: 4

» Basic Mathematics » Algebra » Simplifying Expressions

Appeared in Year: 2012

MCQ▾

Question

The maximum value M of 3x+5x9x+15x25x , as x varies over real, satisfies –

Choices

Choice (4) Response

a.

3<M<5

b.

9 < M < 25

c.

0<M<2

d.

5<M<9

Question number: 5

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2014

MCQ▾

Question

Suppose a parabola y=ax2+bx+c has two x intercepts one positive and one negative, and its vertex is (2,2) . Then which of the following is true –

Choices

Choice (4) Response

a.

ab>0

b.

bc>0

c.

ca>0

d.

a+b+c>0

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