KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 126 - 129 of 155

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Question number: 126

» Coordinate Geometry » Distance Formula

Appeared in Year: 2013

MCQ▾

Question

Consider a triangle PQR in the XYplane with vertices P=(0, 0),Q=(2, 3) and R=(8, 3) . The line l=a intersect line QR and line PR at point M and point N, respectively, such that the area of triangle PQR is 3times of area of triangle MNR. Therefore value of a is – (Model Paper)

Choices

Choice (4) Response

a.

473

b.

4

c.

3

d.

23

Question number: 127

» Limits & Continuity » Limits

Appeared in Year: 2013

MCQ▾

Question

Let f:RR be a function such that

limx1f(x)=C>0.

Then which of the following is false? (Model Paper)

Choices

Choice (4) Response

a.

limxtanxxf(x)=0

b.

limxsin(ex)xf(x)=C

c.

limx2xf(x)sin(12x)=C

d.

limxtan(1f(x))=tanC

Question number: 128

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2013

MCQ▾

Question

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

k=1n(ak2+bk+c)=n3

For every natural number n . Then a + b + c is equal to – (Model Paper)

Choices

Choice (4) Response

a.

3

b.

15

c.

7

d.

12

Question number: 129

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2014

MCQ▾

Question

An ellipse inscribed in a semi – circle touches the circular are at two distinct points and also touches the bounding diameter. Its major axis is parallel to the bounding diameter. When the ellipse has the maximum possible area, its eccentricity is –

Choices

Choice (4) Response

a.

12

b.

13

c.

23

d.

12

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