NARAYANA IIT/PMT ACADEMY - Narayanaicc.com
NARAYANA IIT/PMT ACADEMY - Narayanaicc.com
NARAYANA IIT/PMT ACADEMY - Narayanaicc.com
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<strong>NARAYANA</strong> <strong>IIT</strong>/<strong>PMT</strong> <strong>ACADEMY</strong><br />
JEE ADVANCE : 2013<br />
(PAPER – II) CODE: 0<br />
PART – III : MATHEMATICS<br />
SECTION – 1 (Only or more options correct Type)<br />
This section contains 8 multiple choice questions Each question has four choices (A) (B), (C) and (D)<br />
out of the which ONE or MORE are correct<br />
41 Let be a <strong>com</strong>plex cube root of unity with 1 and P p<br />
ij<br />
be a n n matrix with<br />
Ans<br />
Sol<br />
2<br />
Then P 0, when n =<br />
(A) 57 (B) 55 (C) 58 (D) 56<br />
(B,C,D)<br />
1 1 ... ... 1 1 ... ...<br />
2 2 2 2<br />
2 2<br />
1 ... 1 ...<br />
1 ... 1 ...<br />
2 2<br />
... ... ... ... ... ...<br />
2 2<br />
1 ... 1 ...<br />
..... .....<br />
... ...<br />
p<br />
ij<br />
i<br />
j<br />
Clearly P 2 will be O if n is a multiple of 3, then only, the elements of P 2 will be reduced to<br />
2<br />
1 0<br />
2<br />
If P 0 n is not multiple of 3<br />
42 The function y 2 | x | | x 2 | | x 2 | 2 | x | has a local minimum or a local maximum at x =<br />
(A) 2<br />
(B)<br />
Ans (A, B)<br />
Sol y 2 | x | | x 2 | | x 2 | 2 | x |<br />
2<br />
3<br />
Case (i) x 2<br />
y 2x x 2 | x 2 2x |<br />
y 3x 2 | x 2|<br />
y 2x 4 … (1)<br />
Case (ii) 2 x 0<br />
y x 2 | 3x 2|<br />
So for x<br />
2<br />
3<br />
y 2x 4 … (2)<br />
(C) 2 (D) 2 3<br />
<strong>NARAYANA</strong> GROUP OF EDUCATIONAL INSTITUTIONS - INDIA<br />
25
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