1
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
If f : R $$ \to $$ R is a twice differentiable function such that f"(x) > 0 for all x$$ \in $$R, and $$f\left( {{1 \over 2}} \right) = {1 \over 2}$$, f(1) = 1, then
A
f'(1) $$ \le $$ 0
B
f'(1) > 1
C
0 < f'(1) $$ \le $$ $${1 \over 2}$$
D
$${1 \over 2}$$ < f'(1) $$ \le $$ 1
2
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
If y = y(x) satisfies the differential equation

$${8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4 + \sqrt {9 + \sqrt x } } } \right)}^{ - 1}}}$$

dx, x > 0 and y(0) = $$\sqrt 7 $$, then y(256) =
A
16
B
3
C
9
D
80
3
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
How many 3 $$ \times $$ 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?
A
198
B
162
C
126
D
135
4
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is
A
$${1 \over {2}}$$
B
$${36 \over {55}}$$
C
$${6 \over {11}}$$
D
$${5 \over {11}}$$
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