KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 113 - 116 of 155

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Question number: 113

» 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

Question number: 114

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2014

MCQ▾

Question

Let S={(a,b)/a,bZ,0a,b18} . The number of elements (x,y) in S such that 3x+4y+5 is divisible by 19 is –

Choices

Choice (4) Response
a.

18

b.

1

c.

38

d.

19

Question number: 115

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2013

MCQ▾

Question

Let n be a positive integer. For a real number x , let [x] denoted the largest integer not exceeding x and {x}=x[x] . Then,

1n+1({x})[x][x]dx is equal to – (Model Paper)

Choices

Choice (4) Response
a.

loge(n)

b.

1n+1

c.

nn+1

d.

1+12++1n

Question number: 116

» Basic Mathematics » Algebra » Simplifying Expressions

Appeared in Year: 2014

MCQ▾

Question

Let f:[0, 1][0,) be a continuous function such that 01f(x)dx=10 . Which of the following statement is NOT necessarily true?

Choices

Choice (4) Response
a.

1001sin(100x)f(x)dx10

b.

01f(x)(1+x)2dx10

c.

01exf(x)dx10

d.

01f(x)2dx100

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