JEE Advanced 2016 Paper 2 Offline | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

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?

If a = $$-$$3, then the system has infinitely many solutions for all values of $$\lambda$$ and $$\mu$$.

If a $$\ne$$ $$-$$3, then the system has a unique solution for all values of $$\lambda$$ and $$\mu$$.

If $$\lambda$$ + $$\mu$$ = 0, then the system has infinitely many solutions for a = $$-$$3.

If $$\lambda$$ + $$\mu$$ $$\ne$$ 0, then the system has no solution for a = -3.

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

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

f is discontinuous exactly at three points in $$\left[ { - {1 \over 2},2} \right]$$.

f is discontinuous exactly at four points in $$\left[ { - {1 \over 2},2} \right]$$.

g is NOT differentiable exactly at four points in $$\left( { - {1 \over 2},2} \right)$$.

g is NOT differentiable exactly at five points in $$\left( { - {1 \over 2},2} \right)$$.

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

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?

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.

The final time period of oscillation in both the cases is same

The total energy decreases in both the cases

The instantaneous speed at x₀ of the combined masses decreases in both the cases

JEE Advanced 2016 Paper 2 Offline

MCQ (Single Correct Answer)

-1

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10^oC. Now the end P is maintained at 10^oC, while the end S is heated and maintained at 400^oC. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 $$ \times $$ 10^-5 K^-1 , the change in length of the wire PQ is

0.78 mm

0.90 mm

1.56 mm

2.34 mm

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