1
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
2
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
3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let a $$\in$$ R and f : R $$\to$$ R be given by f(x) = x5 $$-$$ 5x + a. Then,
A
f(x) has three real roots , if a > 4
B
f(x) has only one real root, if a > 4
C
f(x) has three real roots, if a < $$-$$4
D
f(x) has three real roots, if $$-$$4 < a < 4
4
JEE Advanced 2014 Paper 1 Offline
Numerical
+4
-0
Let f : [0, 4$$\pi$$] $$\to$$ [0, $$\pi$$] be defined by f(x) = cos$$-$$1 (cos x). The number of points x $$\in$$ [0, 4$$\pi$$] satisfying the equation $$f(x) = {{10 - x} \over {10}}$$ is
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