1
JEE Advanced 2013 Paper 1 Offline
MCQ (Single Correct Answer)
+2
-0.5
The value of $$\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)} \right)$$ is
A
$${{23} \over {25}}$$
B
$${{25} \over {23}}$$
C
$${{23} \over {24}}$$
D
$${{24} \over {23}}$$
2
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $$8:15$$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $$100$$, the resulting box has maximum volume. Then the lengths of the vsides of the rectangular sheet are
A
$$24$$
B
$$32$$
C
$$45$$
D
$$60$$
3
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-0
For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
A
NTMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric.
B
MN – NM is skew symmetric for all symmetric matrices M and N.
C
MN is symmetric for all symmetric matrices M and N.
D
(adj M)·(adj N) = adj(MN) for all invertible matrices M and N.
4
JEE Advanced 2013 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits} $$ and $$y = \left| {\cos x - \sin x} \right|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is
A
$$4\left( {\sqrt 2 - 1} \right)$$
B
$$2\sqrt 2 \left( {\sqrt 2 - 1} \right)$$
C
$$2\left( {\sqrt 2 + 1} \right)$$
D
$$2\sqrt 2 \left( {\sqrt 2 + 1} \right)$$
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