1
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language

Let $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right]$$ and I be the identity matrix of order 3. If $$Q = [{q_{ij}}]$$ is a matrix such that $${P^{50}} - Q = I$$ and $${{{q_{31}} + {q_{32}}} \over {{q_{21}}}}$$ equals

A
52
B
103
C
201
D
205
2
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language

Let bi > 1 for I = 1, 2, ......, 101. Suppose logeb1, logeb2, ......., logeb101 are in Arithmetic Progression (A.P.) with the common difference loge2. Suppose a1, a2, ......, a101 are in A.P. such that a1 = b1 and a51 = b51. If t = b1 + b2 + .... + b51 and s = a1 + a2 + ..... + a51, then

A
s > t and a101 > b101
B
s > t and a101 < b101
C
s < t and a101 > b101
D
s < t and a101 < b101
3
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.
4
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.
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