1
JEE Advanced 2013 Paper 2 Offline
+4
-1
match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ List $$I$$
(P.)$$\,\,\,\,$$ Volume of parallelopiped determined by vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ is $$2.$$ Then the volume of the parallelepiped determined by vectors $$2\left( {\overrightarrow a \times \overrightarrow b } \right),3\left( {\overrightarrow b \times \overrightarrow c } \right)$$ and $$\left( {\overrightarrow c \times \overrightarrow a } \right)$$ is
(Q.)$$\,\,\,\,$$ Volume of parallelopiped determined by vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ is $$5.$$ Then the volume of the parallelepiped determined by vectors $$3\left( {\overrightarrow a + \overrightarrow b } \right),\left( {\overrightarrow b + \overrightarrow c } \right)$$ and $$2\left( {\overrightarrow c + \overrightarrow a } \right)$$ is
(R.)$$\,\,\,\,$$ Area of a triangle with adjacent sides determined by vectors $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$20.$$ Then the area of the triangle with adjacent sides determined by vectors $$\left( {2\overrightarrow a + 3\overrightarrow b } \right)$$ and $$\left( {\overrightarrow a - \overrightarrow b } \right)$$ is
(S.)$$\,\,\,\,$$ Area of a parallelogram with adjacent sides determined by vectors $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$30.$$ Then the area of the parallelogram with adjacent sides determined by vectors $$\left( {\overrightarrow a + \overrightarrow b } \right)$$ and $${\overrightarrow a }$$ is

$$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ List $$II$$
(1.)$$\,\,\,\,$$ $$100$$
(2.)$$\,\,\,\,$$ $$30$$
(3.)$$\,\,\,\,$$ $$24$$
(4.)$$\,\,\,\,$$ $$60$$

A
$$P = 4,Q = 2,R = 3,S = 1$$
B
$$P = 2,Q = 3,R = 1,S = 4$$
C
$$P = 3,Q = 4,R = 1,S = 2$$
D
$$P = 1,Q = 4,R = 3,S = 2$$
2
JEE Advanced 2013 Paper 2 Offline
+4
-1
Consider the lines

$${L_1}:{{x - 1} \over 2} = {y \over { - 1}} = {{z + 3} \over 1},{L_2} : {{x - 4} \over 1} = {{y + 3} \over 1} = {{z + 3} \over 2}$$

and the planes $${P_1}:7x + y + 2z = 3,{P_2} = 3x + 5y - 6z = 4.$$ Let $$ax+by+cz=d$$ be the equation of the plane passing through the point of intersection of lines $${L_1}$$ and $${L_2},$$ and perpendicular to planes $${P_1}$$ and $${P_2}.$$

Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:
List $$I$$
(P.) $$a=$$
(Q.) $$b=$$
(R.) $$c=$$
(S.) $$d=$$

List $$II$$
(1.) $$13$$
(2.) $$-3$$
(3.) $$1$$
(4.) $$-2$$

A
$$P = 3,Q = 2,R = 4,S = 1$$
B
$$P = 1,Q = 3,R = 4,S = 2$$
C
$$P = 3,Q = 2,R = 1,S = 4$$
D
$$P = 2,Q = 4,R = 1,S = 3$$
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

$$a \in R$$ (the set of all real numbers), a $$\ne$$ $$-$$1,

$$\mathop {\lim }\limits_{n \to \infty } {{({1^a} + {2^a} + ... + {n^a})} \over {{{(n + 1)}^{a - 1}}[(na + 1) + (na + 2) + ... + (na + n)]}} = {1 \over {60}}$$, Then a = ?

A
5
B
7
C
$${{ - 15} \over 2}$$
D
$${{ - 17} \over 2}$$
4
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with pij = $$\omega$$i + j. Then P2 $$\ne$$ 0, when n = ?

A
57
B
55
C
58
D
56
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