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 $$\left( { - {1 \over 2},2} \right)$$.
2
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale.
The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scale
divisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main
scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by
calipers C1 and C2 respectively, are
A
2.85 and 2.82
B
2.87 and 2.83
C
2.87 and 2.86
D
2.87 and 2.87
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a
periodic motion is $$T = 2\pi \sqrt {{{7\left( {R - r} \right)} \over {5g}}} $$. The values of R and r are measured to be (60 $$ \pm $$ 1) mm and (10 $$ \pm $$ 1)
mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s,
0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of
the following statement(s) is(are) true?
A
The error in the measurement of r is 10 %
B
The error in the measurement of T is 3.57 %
C
The error in the measurement of T is 2 %
D
The error in the determined value of g is 11 %
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a
massless, rigid rod of length $$l = \sqrt {24} a$$ through their centers. This assembly is laid on a firm and flat
surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $$\omega $$. The angular momentum of the entire assembly about the point ‘O’ is $$\overrightarrow L $$ (see the figure). Which of the following statement(s) is(are) true?
A
The center of mass of the assembly rotates about the z-axis with an angular speed of $${\omega \over 5}$$
B
The magnitude of angular momentum of center of mass of the assembly about the point O is $$81\,m{a^2}\omega $$
C
The magnitude of angular momentum of the assembly about its center of mass is $${{17m{a^2}\omega } \over 2}$$
D
The magnitude of the z-component of $$\overrightarrow L $$
is $$55m{a^2}\omega $$
