KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 110 - 112 of 172

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Question number: 110

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2013

MCQ▾

Question

Let Equation be a non – constant polynomial with real coefficients such that Equation and Equation for all real Equation . Which of the following statements is NOT necessarily true? (Model Paper)

Choices

Choice (4) Response

a.

The coefficient of the highest degree term in Equation is negative

b.

Equation has at least two real roots

c.

If Equation then Equation

d.

At least one of the coefficients of Equation is bigger than Equation .

Question number: 111

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2014

MCQ▾

Question

Let Equation be the circle Equation in the XY – plane. For each Equation , let Equation be the line passing through Equation and Equation . Note that Equation intersects C in two points, one of which is Equation . Let Equation be the other point. As Equation varies between Equation and Equation , the collection of points Equation sweeps out an arc on C. The angle subtended by this are at Equation is:

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 112

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2014

MCQ▾

Question

If Equation is a positive integer and Equation is a cube root of unity, the number of possible values of

Equation

is –

Choices

Choice (4) Response

a.

6

b.

4

c.

2

d.

3

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