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 debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

380

320

260

JEE Advanced 2016 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let $$ - {\pi \over 6} < \theta < - {\pi \over {12}}.$$ Suppose $${\alpha _1}$$ and $${\beta_1}$$ are the roots of the equation $${x^2} - 2x\sec \theta + 1 = 0$$ and $${\alpha _2}$$ and $${\beta _2}$$ are the roots of the equation $${x^2} + 2x\,\tan \theta - 1 = 0.$$ $$If\,{\alpha _1} > {\beta _1}$$ and $${\alpha _2} > {\beta _2},$$ then $${\alpha _1} + {\beta _2}$$ equals

$$2\left( {\sec \theta - \tan \theta } \right)$$

$$2\,\sec \,\theta $$

$$ - 2\tan \theta $$

$$0$$

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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