KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 18 - 22 of 155

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Question number: 18

» Sequence and Series » Geometric Progressions

Appeared in Year: 2011

MCQ▾

Question

Suppose n is a natural number such that i+2i2+3i3++nin =182, where i is the square root of – 1. Then n is –

Choices

Choice (4) Response

a.

18

b.

9

c.

36

d.

72

Question number: 19

» Sequence and Series » Arithmetico - Geometric Progression

Appeared in Year: 2011

MCQ▾

Question

The minimum value of n for which 22+42+62++(2n)212+32+52++(2n1)2<1.01

Choices

Choice (4) Response

a.

Is 101

b.

Is 121

c.

Is 151

d.

All of the above

Question number: 20

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2010

MCQ▾

Question

Suppose m, n are positive integers such that 6m+2m+n3w+2n=332 . The value of the expression m2+mn+n2 is –

Choices

Choice (4) Response

a.

19

b.

21

c.

7

d.

13

Question number: 21

» Matrices and Determinants » Solution of Simultaneous Linear Equations in Two or Three Variables

Appeared in Year: 2011

MCQ▾

Question

Let P be an m × m matrix such that P2 = P. Then (1 + P) n equals –

Choices

Choice (4) Response

a.

I+(2n1)P

b.

I+nP

c.

I+P

d.

I+2nP

Question number: 22

» Matrices and Determinants » Evaluation of Determinants

Appeared in Year: 2011

MCQ▾

Question

Let A and B be any two n × n matrices such that the following conditions hold: AB = BA and there exist positive integers k and l such that Ak=I (the identity matrix) and Bl=0 (the zero matrix). Then –

Choices

Choice (4) Response

a.

Det(A+B)0

b.

Det(AB)=0

c.

A+B=I

d.

(A+B)m=0 for some integer m

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