1
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
For every pair of continuous function f, g : [0, 1] $$\to$$ R such that max {f(x) : x $$\in$$ [0, 1]} = max {g(x) : x $$\in$$ [0, 1]}. The correct statement(s) is (are)
A
[f(c)]2 + 3f(c) = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
B
[f(c)]2 + f(c) = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
C
[f(c)]2 + 3f(c) = [g(c)]2 + g(c) for some c $$\in$$ [0, 1]
D
[f(c)]2 = [g(c)]2 + 3g(c) for some c $$\in$$ [0, 1]
2
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let M be a 2 $$\times$$ 2 symmetric matrix with integer entries. Then, M is invertible, if
A
the first column of M is the transpose of the second row of M
B
the second row of M is the transpose of the first column of M
C
M is a diagonal matrix with non-zero entries in the main diagonal
D
the product of entries in the main diagonal of M is not the square of an integer
3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let M and N be two 3 $$\times$$ 3 matrices such that MN = NM. Further, if M $$\ne$$ N2 and M2 = N4, then
A
determinant of (M2 + MN2) is 0
B
there is a 3 $$\times$$ 3 non-zero matrix U such that (M2 + MN2) U is zero matrix
C
determinant of (M2 + MN2) $$\ge$$ 1
D
for a 3 $$\times$$ 3 matrix U, if (M2 + MN2) U equals the zero matrix, then U is the zero matrix
4
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R$$ be given by $$f(x) = {[\log (\sec x + \tan x)]^3}$$. Then,
A
f(x) is an odd function
B
f(x) is a one-one function
C
f(x) is an onto function
D
f(x) is an even function
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