1
JEE Advanced 2017 Paper 2 Offline
+3
-0
Let O be the origin and $$\overrightarrow{OX}$$, $$\overrightarrow{OY}$$, $$\overrightarrow{OZ}$$ be three unit vectors in the directions of the sides $$\overrightarrow{QR}$$, $$\overrightarrow{RP}$$, $$\overrightarrow{PQ}$$ respectively, of a triangle PQR.
|$$\overrightarrow{OX}$$ $$\times$$ $$\overrightarrow{OY}$$| = ?
A
sin(P + Q)
B
sin(P + R)
C
sin(Q + R)
D
sin2R
2
JEE Advanced 2016 Paper 2 Offline
+3
-1
Let $$P$$ be the image of the point $$(3,1,7)$$ with respect to the plane $$x-y+z=3.$$ Then the equation of the plane passing through $$P$$ and containing the straight line $${x \over 1} = {y \over z} = {z \over 1}$$ is
A
$$x+y-3z=0$$
B
$$3x+z=0$$
C
$$x-4y+7z=0$$
D
$$2x-y=0$$
3
JEE Advanced 2015 Paper 1 Offline
+4
-0
Match the following :

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column $$I$$
(A)$$\,\,\,\,$$ In $${R^2},$$ If the magnitude of the projection vector of the vector $$\alpha \widehat i + \beta \widehat j$$ on $$\sqrt 3 \widehat i + \widehat j$$ and If $$\alpha = 2 + \sqrt 3 \beta ,$$ then possible value of $$\left| \alpha \right|$$ is/are
(B)$$\,\,\,\,$$ Let $$a$$ and $$b$$ be real numbers such that the function $$f\left( x \right) = \left\{ {\matrix{ { - 3a{x^2} - 2,} & {x < 1} \cr {bx + {a^2},} & {x \ge 1} \cr } } \right.$$ if differentiable for all $$x \in R$$. Then possible value of $$a$$ is (are)
(C)$$\,\,\,\,$$ Let $$\omega \ne 1$$ be a complex cube root of unity. If $${\left( {3 - 3\omega + 2{\omega ^2}} \right)^{4n + 3}} + {\left( {2 + 3\omega - 3{\omega ^2}} \right)^{4n + 3}} + {\left( { - 3 + 2\omega + 3{\omega ^2}} \right)^{4n + 3}} = 0,$$ then possible value (s) of $$n$$ is (are)
(D)$$\,\,\,\,$$ Let the harmonic mean of two positive real numbers $$a$$ and $$b$$ be $$4.$$ If $$q$$ is a positive real nimber such that $$a, 5, q, b$$ is an arithmetic progression, then the value(s) of $$\left| {q - a} \right|$$ is (are)

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column $$II$$
(p)$$\,\,\,\,$$ $$1$$
(q)$$\,\,\,\,$$ $$2$$
(r)$$\,\,\,\,$$ $$3$$
(s)$$\,\,\,\,$$ $$4$$
(t)$$\,\,\,\,$$ $$5$$

A
$$\left( A \right) \to p, q;\,\,\left( B \right) \to p,q;\,\,\left( C \right) \to p,q,s,t;\,\,\left( D \right) \to q,t$$
B
$$\left( A \right) \to q;\,\,\left( B \right) \to q;\,\,\left( C \right) \to p,q,s,t;\,\,\left( D \right) \to q,t$$
C
$$\left( A \right) \to q;\,\,\left( B \right) \to p,q;\,\,\left( C \right) \to p,t;\,\,\left( D \right) \to q,t$$
D
$$\left( A \right) \to q;\,\,\left( B \right) \to p,q;\,\,\left( C \right) \to p,q,s,t;\,\,\left( D \right) \to q$$
4
JEE Advanced 2015 Paper 1 Offline
+4
-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
A
$$\left( A \right) \to P,R;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P,Q;\,\,\left( D \right) \to S,T$$
B
$$\left( A \right) \to P,R,S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P,Q;\,\,\left( D \right) \to S,T$$
C
$$\left( A \right) \to P,R,S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P;\,\,\left( D \right) \to S,T$$
D
$$\left( A \right) \to S;\,\,\left( B \right) \to P;\,\,\left( C \right) \to P;\,\,\left( D \right) \to S,T$$
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