1
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language

Let a, b $$\in$$ R and f : R $$\to$$ R be defined by $$f(x) = a\cos (|{x^3} - x|) + b|x|\sin (|{x^3} + x|)$$. Then f is

A
differentiable at x = 0 if a = 0 and b = 1.
B
differentiable at x = 1 if a = 1 and b = 0.
C
NOT differentiable at x = 0 if a = 1 and b = 0.
D
NOT differentiable at x = 1 if a = 1 and b = 1.
2
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language

Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations

ax + 2y = $$\lambda$$

3x $$-$$ 2y = $$\mu$$

Which of the following statements is(are) correct?

A
If a = $$-$$3, then the system has infinitely many solutions for all values of $$\lambda$$ and $$\mu$$.
B
If a $$\ne$$ $$-$$3, then the system has a unique solution for all values of $$\lambda$$ and $$\mu$$.
C
If $$\lambda$$ + $$\mu$$ = 0, then the system has infinitely many solutions for a = $$-$$3.
D
If $$\lambda$$ + $$\mu$$ $$\ne$$ 0, then the system has no solution for a = -3.
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language

Let $$f:\left[ { - {1 \over 2},2} \right] \to R$$ and $$g:\left[ { - {1 \over 2},2} \right] \to R$$ be function defined by $$f(x) = [{x^2} - 3]$$ and $$g(x) = |x|f(x) + |4x - 7|f(x)$$, where [y] denotes the greatest integer less than or equal to y for $$y \in R$$. Then

A
f is discontinuous exactly at three points in $$\left[ { - {1 \over 2},2} \right]$$.
B
f is discontinuous exactly at four points in $$\left[ { - {1 \over 2},2} \right]$$.
C
g is NOT differentiable exactly at four points in $$\left( { - {1 \over 2},2} \right)$$.
D
g is NOT differentiable exactly at five points in $$\left( { - {1 \over 2},2} \right)$$.
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases:
(i) when the block is at x0; and
(ii) when the block is at x = x0 + A.
In both cases, a particle with mass m( < M) is softly placed on the block after which they stick on each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?
A
The amplitude of oscillation in the first case changes by a factor of $$\sqrt {{M \over {m + M}}} $$, whereas in the second case it remains unchanged.
B
The final time period of oscillation in both the cases is same
C
The total energy decreases in both the cases
D
The instantaneous speed at x0 of the combined masses decreases in both the cases
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