JEE Advanced 2015 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2015 Paper 1 Offline

MCQ (Single Correct Answer)

-0

Match the following :

	Column I		Column I
(A)	$\begin{array}{l}\text { In a triangle } \Delta X Y Z \text {, let } a, b \text { and } c \text { be the lengths of the sides } \\\text { opposite to the angles } X, Y \text { and } Z \text {, respectively. If } 2\left(a^2-b^2\right)=c^2 \\\text { and } \lambda=\frac{\sin (X-Y)}{\sin Z} \text {, then possible values of } n \text { for which } \cos (n \lambda) \\=0 \text { is (are) }\end{array}$	(P)	1
(B)	$\begin{array}{l}\text { In a triangle } \triangle X Y Z \text {, let } a, b \text { and } c \text { be the lengths of the sides } \\\text { opposite to the angles } X, Y \text { and } Z \text {, respectively. If } 1+\cos 2 X-2 \\\cos 2 Y=2 \sin X \sin Y \text {, then possible value(s) of } \frac{a}{b} \text { is (are) }\end{array}$	(Q)	2
(C)	$\begin{array}{l}\text { In } \mathbb{R}^2 \text {, let } \sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j} \text { and } \beta \hat{i}+(1-\beta) \hat{j} \text { be the position } \\\text { vectors of } X, Y \text { and } Z \text { with respect of the origin } \mathrm{O} \text {, respectively. If } \\\text { the distance of } \mathrm{Z} \text { from the bisector of the acute angle of } \overrightarrow{\mathrm{OX}} \text { with } \\\overrightarrow{\mathrm{OY}} \text { is } \frac{3}{\sqrt{2}} \text {, then possible value(s) of }\|\beta\| \text { is (are) }\end{array}$	(R)	3
(D)	$\begin{array}{l}\text { Suppose that } F(\alpha) \text { denotes the area of the region bounded by } \\x=0, x=2, y^2=4 x \text { and } y=\|\alpha x-1\|+\|\alpha x-2\|+\alpha x \text {, } \\\text { where, } \alpha \in\{0,1\} \text {. Then the value(s) of } F(\alpha)+\frac{8}{2} \sqrt{2} \text {, when } \alpha=0 \\\text { and } \alpha=1 \text {, is (are) }\end{array}$	(S)	5
		(T)	6

$$\left( A \right) \to P,R;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P,Q;\,\,\left( D \right) \to S,T$$

$$\left( A \right) \to P,R,S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P,Q;\,\,\left( D \right) \to S,T$$

$$\left( A \right) \to P,R,S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P;\,\,\left( D \right) \to S,T$$

$$\left( A \right) \to S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P;\,\,\left( D \right) \to S,T$$

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let X and Y be two arbitrary, 3 $$\times$$ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 $$\times$$ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?

Y³Z⁴ $$-$$ Z⁴Y³

X⁴⁴ + Y⁴⁴

X⁴Z³ $$-$$ Z³X⁴

X²³ + Y²³

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Which of the following values of $$\alpha$$ satisfy the equation

$$\left| {\matrix{ {{{(1 - \alpha )}^2}} & {{{(1 + 2\alpha )}^2}} & {{{(1 + 3\alpha )}^2}} \cr {{{(2 + \alpha )}^2}} & {{{(2 + 2\alpha )}^2}} & {{{(2 + 3\alpha )}^2}} \cr {{{(3 + \alpha )}^2}} & {{{(3 + 2\alpha )}^2}} & {{{(3 + 3\alpha )}^2}} \cr } } \right| = - 648\alpha $$ ?

$$-$$4

$$-$$9

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let $$g:R \to R$$ be a differentiable function with $$g(0) = 0$$, $$g'(0) = 0$$ and $$g'(1) \ne 0$$. Let

$$f(x) = \left\{ {\matrix{ {{x \over {|x|}}g(x),} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$

and $$h(x) = {e^{|x|}}$$ for all $$x \in R$$. Let $$(f\, \circ \,h)(x)$$ denote $$f(h(x))$$ and $$(h\, \circ \,f)(x)$$ denote $$f(f(x))$$. Then which of the following is (are) true?

f is differentiable at x = 0.

h is differentiable at x = 0.

$$f\, \circ \,h$$ is differentiable at x = 0.

$$h\, \circ \,f$$ is differentiable at x = 0.

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