Sequence and Series (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 6 - 9 of 9

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Question number: 6

» Sequence and Series » Sum Upto N Terms of Special Series

Appeared in Year: 2014

MCQ▾

Question

Let n3 be an integer. For a permutation σ=(a1,a2,,an) of (1, 2,n) we let fσ(x)=anXn1+an1++a2x+a1 . Let Sσ be the sum of the roots of fσ(x)=0 and let S denote the sum over all permutation σ of (1, 2,,n) of the number Sσ . Then

Choices

Choice (4) Response

a.

S<n!

b.

n!<S<0

c.

0<S<n!

d.

n!<S

Question number: 7

» Sequence and Series » Sum Upto N Terms of Special Series

Appeared in Year: 2014

MCQ▾

Question

Let C0 be a circle of radius 1. For n1 , let Cn be a circle whose area equals the area of a square inscribed in Cn1 . Then

i=0Area(Ci)

Equals to: -

Choices

Choice (4) Response

a.

π2π2

b.

π2π2

c.

1π2

d.

π2

Question number: 8

» Sequence and Series » Sum Upto N Terms of Special Series

Appeared in Year: 2013

MCQ▾

Question

For an integer n let Sn={n+1,n+2,...,n+18} . Which of the following is true for all n10 ? (Model Paper)

Choices

Choice (4) Response

a.

Sn has at least four multiples of 5

b.

Sn has a prime

c.

Sn has at most six primes

d.

Sn has a multiple of 19

Question number: 9

» Sequence and Series » Relation Between AM and GM

Appeared in Year: 2016

MCQ▾

Question

The number of triples (x,y,z) of real number satisfying the equation,

x4+y4+z4+1=4xyz is –

Choices

Choice (4) Response

a.

4

b.

More than 8

c.

8

d.

0

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