JEE Advanced 2016 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2016 Paper 1 Offline

MCQ (Single Correct Answer)

-1

A computer producing factory has only two plants $${T_1}$$ and $${T_2}.$$ Plant $${T_1}$$ produces $$20$$% and plant $${T_2}$$ produces $$80$$% of the total computers produced. $$7$$% of computers produced in the factory turn out to be defective. It is known that $$P$$ (computer turns out to be defective given that it is produced in plant $${T_1}$$)
$$ = 10P$$ (computer turns out to be defective given that it is produced in plant $${T_2}$$),
where $$P(E)$$ denotes the probability of an event $$E$$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $${T_2}$$ is

$${{36} \over {73}}$$

$${{47} \over {79}}$$

$${{78} \over {93}}$$

$${{75} \over {83}}$$

JEE Advanced 2016 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Consider a pyramid $$OPQRS$$ located in the first octant $$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$ with $$O$$ as origin, and $$OP$$ and $$OR$$ along the $$x$$-axis and the $$y$$-axis, respectively. The base $$OPQR$$ of the pyramid is a square with $$OP=3.$$ The point $$S$$ is directly above the mid-point, $$T$$ of diagonal $$OQ$$ such that $$TS=3.$$ Then

the acute angle between $$OQ$$ and $$OS$$ is $${\pi \over 3}$$

the equation of the plane containing the triangle $$OQS$$ is $$x-y=0$$

the length of the perpendicular from $$P$$ to the plane containing the triangle $$OQS$$ is $${3 \over {\sqrt 2 }}$$

the perpendicular distance from $$O$$ to the straight line containing $$RS$$ is $$\sqrt {{{15} \over 2}} $$

JEE Advanced 2016 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let $$f:(0,\infty ) \to R$$ be a differentiable function such that $$f'(x) = 2 - {{f(x)} \over x}$$ for all $$x \in (0,\infty )$$ and $$f(1) \ne 1$$. Then

$$\mathop {\lim }\limits_{x \to {0^ + }} f'\left( {{1 \over x}} \right) = 1$$

$$\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {{1 \over x}} \right) = 2$$

$$\mathop {\lim }\limits_{x \to {0^ + }} {x^2}f'(x) = 0$$

$$\left| {f(x)} \right| \le 2$$ for all $$x \in (0,2)$$

JEE Advanced 2016 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let $$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where $$\alpha$$ $$\in$$ R. Suppose $$Q = [{q_{ij}}]$$ is a matrix such that PQ = kl, where k $$\in$$ R, k $$\ne$$ 0 and I is the identity matrix of order 3. If $${q_{23}} = - {k \over 8}$$ and $$\det (Q) = {{{k^2}} \over 2}$$, then

$$\alpha$$ = 0, k = 8

$$4\alpha - k + 8 = 0$$

$$\det (Padj(Q)) = {2^9}$$

$$\det (Qadj(P)) = {2^{13}}$$

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