Basic Mathematics-Geometry (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 10 - 12 of 24

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Question number: 10

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2013

MCQ▾

Question

Let f(x) be a non – constant polynomial with real coefficients such that f(12)=100 and f(x)100 for all real x . Which of the following statements is NOT necessarily true? (Model Paper)

Choices

Choice (4) Response

a.

The coefficient of the highest degree term in f(x) is negative

b.

f(x) has at least two real roots

c.

If x12 then f(x)<100

d.

At least one of the coefficients of f(x) is bigger than 50 .

Question number: 11

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2014

MCQ▾

Question

Let C be the circle x2+y2=1 in the XY – plane. For each t0 , let Lt be the line passing through (0,1) and (t,0) . Note that Lt intersects C in two points, one of which is (0, 1) . Let Qt be the other point. As t varies between 1 and 1+2 , the collection of points Qt sweeps out an arc on C. The angle subtended by this are at (0, 0) is:

Choices

Choice (4) Response

a.

π3

b.

π4

c.

π8

d.

3π8

Question number: 12

» Basic Mathematics » Geometry » Triangle and Properties

Appeared in Year: 2013

MCQ▾

Question

In a triangle ABC , let G denote its centroid and let M, N be points in the interiors of the segments AB,AC , respectively, such that M,G,N are collinear. If r denotes the ratio of the area of triangle AMN to the area of ABC then, (Model Paper)

Choices

Choice (4) Response

a.

49r<12

b.

r=12

c.

49<r

d.

r>12

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