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

JEE Advanced 2016 Paper 2 Offline

MCQ (Single Correct Answer)

-0

Treatment of compound O with KMnO₄/H⁺ gave P, which on heating with ammonia gave Q. The compound Q on treatment with Br₂/NaOH produced R. On strong heating, Q gave S, which on further treatment with ethyl 2-bromopropanoate in the presence of KOH following by acidification, gave a compound T.

JEE Advanced 2016 Paper 2 Offline Chemistry - Compounds Containing Nitrogen Question 17 English Comprehension

The compound T is

Glycine

Alanine

Valine

Serine

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

Let $$a,\,b \in R\,and\,{a^{2\,}} + {b^2} \ne 0$$. Suppose
$$S = \left\{ {Z \in C:Z = {1 \over {a + ibt}}, + \in R,t \ne 0} \right\}$$, where $$i = \sqrt { - 1} $$. Ifz = x + iy and z $$ \in $$ S, then (x, y) lies on

the circle with radius $${{1 \over {2a}}}$$and centre $$\left\{ {{1 \over {2a}},\,0} \right\}\,for\,a > 0\,,b \ne \,0$$

the circle with radius $$-{{1 \over {2a}}}$$and centre $$\left\{ -{{1 \over {2a}},\,0} \right\}\,for\,a < 0\,,b \ne \,0$$

the x-axis for $$a \ne \,\,0,\,b \ne \,0$$

the y-axis for $$a = \,\,0,\,b \ne \,0$$

JEE Advanced 2016 Paper 2 Offline

MCQ (Single Correct Answer)

-1

The value of

$$\sum\limits_{k = 1}^{13} {{1 \over {\sin \left( {{\pi \over 4} + {{\left( {k - 1} \right)\pi } \over 6}} \right)\sin \left( {{\pi \over 4} + {{k\pi } \over 6}} \right)}}} $$ is equal to

$$3 - \sqrt 3 $$

$$2\left( {3 - \sqrt 3 } \right)$$

$$2\left( {\sqrt 3 - 1} \right)\,\,\,$$

$$2\left( {2 - \sqrt 3 } \right)$$

JEE Advanced 2016 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

Let $$P$$ be the point on the parabola $${y^2} = 4x$$ which is at the shortest distance from the center $$S$$ of the circle $${x^2} + {y^2} - 4x - 16y + 64 = 0$$. Let $$Q$$ be the point on the circle dividing the line segment $$SP$$ internally. Then

$$SP = 2\sqrt 5 $$

$$SQ:QP = \left( {\sqrt 5 + 1} \right):2$$

the $$x$$-intercept of the normal to the parabola at $$P$$ is $$6$$

the slope of the tangent to the circle at $$Q$$ is $${1 \over 2}$$

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