1
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

$$a \in R$$ (the set of all real numbers), a $$\ne$$ $$-$$1,

$$\mathop {\lim }\limits_{n \to \infty } {{({1^a} + {2^a} + ... + {n^a})} \over {{{(n + 1)}^{a - 1}}[(na + 1) + (na + 2) + ... + (na + n)]}} = {1 \over {60}}$$, Then a = ?

A
5
B
7
C
$${{ - 15} \over 2}$$
D
$${{ - 17} \over 2}$$
2
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with pij = $$\omega$$i + j. Then P2 $$\ne$$ 0, when n = ?

A
57
B
55
C
58
D
56
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

The function $$f(x) = 2\left| x \right| + \left| {x + 2} \right| - \left| {\left| {x + 2} \right| - 2\left| x \right|} \right|$$ has a local minimum or a local maximum at x =

A
$$-$$2
B
$${{ - 2} \over 3}$$
C
2
D
$${{ 2} \over 3}$$
4
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+3
-0.75
Using the expression $$2d\sin \theta = \lambda $$, one calculates the values of d by measuring the corresponding angles $$\theta $$ in the range 0 to 90o. The wavelength $$\lambda $$ is exactly known and the error in $$\theta $$ is constant for all values of $$\theta $$. As $$\theta $$ increases from 0o
A
the absolute error in d remains constant
B
the absolute error in d increases
C
the fractional error in d remains constant
D
the fractional error in d decreases
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