# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held on 9 April 2013)

### done JEE Main Online Paper (Held on 9 April 2013) Total Questions - 30

• question_answer1)                                 If the lines $\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}$and  $\frac{x+2}{2}=\frac{y-k}{3}=\frac{z}{3}$ are coplanar, then the value of K is:      JEE Main Online Paper (Held On 09 April 2013)

A)
$\frac{11}{2}$

B)
$-\frac{11}{2}$

C)
$\frac{9}{2}$

D)
$-\frac{9}{2}$

• question_answer2)                                 Statement 1: The slope of the tangent at any point P on parabola, whose axis is the axis of $x$ and vertex is the origin, is inversely proportional to the ordinate of the point P.                 Statement 2: The system of parabolas ${{y}^{2}}=4ax$ satisfies a differential equation of degree 1 and order 1.      JEE Main Online Paper (Held On 09 April 2013)

A)
Statement -1 is true, Statement -2 is true. Statement -2 is correct explanation for statement-1.

B)
Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.

C)
Statement -1 is false. Statement-2 is true.

D)
Statement -1 is true. Statement-2 is false.

E)
Statement -1 is false. Statement-2 is true.

• question_answer3)                 If ${{Z}_{1}}\ne O$ and ${{Z}_{2}}$  be two complex numbers such that  $\frac{{{Z}_{2}}}{{{Z}_{1}}}$ is a purely imaginary number, then $\left| \frac{2{{Z}_{1}}+3{{Z}_{2}}}{2{{Z}_{1}}-3{{Z}_{2}}} \right|$ is equal to:               JEE Main Online Paper (Held On 09 April 2013)

A)
2

B)
5

C)
3

D)
1

• question_answer4)                 If $\int{\frac{dx}{x+{{x}^{7}}}=P(x)}$then,$\int{\frac{{{x}^{6}}}{x+{{x}^{7}}}=dx}$ is equal to :                   JEE Main Online Paper (Held On 09 April 2013)

A)
$ln\left| x \right|-p(x)+c$

B)
$ln\left| x \right|+p(x)+c$

C)
$x-p(x)+c$

D)
$x+p(x)+c$­­

• question_answer5)                                 If each of the lines $5x+8y=13$ and $4x-y=13$contains a diameter of the circle ${{x}^{2}}+{{y}^{2}}-2({{a}^{2}}-7+11)x-2({{a}^{2}}-6a+6)y$$+{{b}^{3}}+1=0,$ then:                   JEE Main Online Paper (Held On 09 April 2013)

A)
$a=5$ and $b\notin (-1,1)$

B)
$a=1$ and $b\notin (-1,1)$

C)
$a=2$ and $b\notin (-\infty ,1)$

D)
$a=5$ and $b\in (-\infty ,1)$

• question_answer6)                 If a, b, c, are sides of a scalene triangle, then the value of$\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|$is:      JEE Main Online Paper (Held On 09 April 2013)

A)
non negative

B)
negative

C)
positive

D)
non-positive

• question_answer7)                 If  $x=\int\limits_{0}^{y}{\frac{dt}{1+{{t}^{2}}},}$ then $\frac{{{d}^{2}}y}{d{{x}^{2}}}$ is equal to:                   JEE Main Online Paper (Held On 09 April 2013)

A)
$y$

B)
$\sqrt{1+{{y}^{2}}}$

C)
$\frac{y}{\sqrt{1+{{y}^{2}}}}$

D)
${{y}^{2}}$

• question_answer8)                 Let${{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},..$ be an A.P. such that$\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}....+{{a}_{q}}}=\frac{{{\operatorname{p}}^{3}}}{{{\operatorname{q}}^{3}}};p\ne q$.  Then$\frac{{{a}_{6}}}{{{a}_{21}}}$ is equal to:     JEE Main Online Paper (Held On 09 April 2013)

A)
$\frac{41}{11}$

B)
$\frac{121}{1681}$

C)
$\frac{11}{41}$

D)
$\frac{121}{1861}$

• question_answer9)                 Statement 1: The equation $x\log x=2-x$ is satisfied by least one value of $x$ lying between 1 and 2.                 Statement 2: The function $f(x)$= $x\log x$ is an increasing function is $[1,2]$ and $g(x)=2-x$is a decreasing function in [1,2] and the graphs represented by these functions intersect at a point in [1,2].                   JEE Main Online Paper (Held On 09 April 2013)

A)
Statement -1 is true, Statement-2 is true. Statement -2 is correct explanation for statement-1.

B)
Statement -1 is true, Statement -2 is true. Statement -2 is not correct explanation for statement-1.

C)
Statement -1 is false. Statement-2 is true.

D)
Statement -1 is true. Statement-2 is false.

• question_answer10)                 Let $\overset{\to }{\mathop{a}}\,=2\hat{i}-\hat{j}+k,\overset{\to }{\mathop{b}}\,=\hat{i}+2\hat{j}-\hat{k}$and $\overset{\to }{\mathop{c}}\,=\hat{i}+\hat{j}-2\overset{\to }{\mathop{k}}\,$be three vectors. A vector of the type $\overset{\to }{\mathop{b}}\,+\lambda \overset{\to }{\mathop{c}}\,$ for some scalar$\lambda ,$ whose projection on $\overset{\to }{\mathop{a}}\,$ is of magnitude$\sqrt{\frac{2}{3}},$ is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
$2\hat{i}+\hat{j}+5\hat{k}$

B)
$2\hat{i}+3\hat{j}-3\hat{k}$

C)
$2\hat{i}-\hat{j}+5\hat{k}$

D)
$2\hat{i}+3\hat{j}+3\hat{k}$

• question_answer11)                 The area bounded by the curve $y=\ln (x)$and the lines $y=0,$$y=\ln (3)$ and $x=0$is equal to:                  JEE Main Online Paper (Held On 09 April 2013)

A)
3

B)
$3\,\ln (3)-2$

C)
$3\,\,\ln (3)+2$

D)
2

• question_answer12)                 The Values of ?a? for which one root of the equation ${{x}^{2}}-(a+1)x+{{a}^{2}}+a-8=0$exceeds 2 and the other is lesser than 2, are given by:           JEE Main Online Paper (Held On 09 April 2013)

A)
$3<a<10$

B)
$a\ge 10$

C)
$-2<a<3$

D)
(d) $a\le -2$

• question_answer13)                 If the surface area of a sphere of radius r is increasing uniformly at the rate $8{{\operatorname{cm}}^{2}}/s,$then the rate of change of its volume is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
constant

B)
proportional to $\sqrt{r}$

C)
proportional to ${{r}^{2}}$

D)
proportional to $r$

• question_answer14)                 The probability of a man hitting a target is $\frac{2}{5}.$ He fires at the target k times (k, a given number). Then the minimum k, so that once is more than $\frac{7}{10},$ is :                   JEE Main Online Paper (Held On 09 April 2013)

A)
3

B)
5

C)
2

D)
4

• question_answer15)                 Equation of the line passing though the points of intersection of parabola ${{x}^{2}}=8y$ and the ellipse$\frac{{{x}^{2}}}{3}+{{y}^{2}}=1$ is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
$y-3=0$

B)
$y+3=0$

C)
$3y+1=0$

D)
$3y-1=0$

• question_answer16)                 The sum of the series:                 $1+\frac{1}{1+2}+\frac{1}{1+2+3}+...........$ up to 10 terms, is:          JEE Main Online Paper (Held On 09 April 2013)

A)
$\frac{18}{11}$

B)
$\frac{22}{13}$

C)
$\frac{20}{11}$

D)
$\frac{16}{9}$

• question_answer17)                 A value of $x$ for which $\sin ({{\cot }^{-1}}(1+x))=\cos ({{\tan }^{-1}}x),$ is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
$-\frac{1}{2}$

B)
1

C)
0

D)
$\frac{1}{2}$

• question_answer18)                 If a and c are positive real numbers and the ellipse$\frac{{{x}^{2}}}{4{{c}^{2}}}+\frac{{{y}^{3}}}{{{c}^{2}}}=1$has four distinct points in common with the circle ${{x}^{2}}+{{y}^{2}}=9{{a}^{2}},$ then                   JEE Main Online Paper (Held On 09 April 2013)

A)
$9a-9{{a}^{2}}-2{{c}^{2}}<0$

B)
$6ac+9{{a}^{2}}-2{{c}^{2}}<0$

C)
$9ac-9{{a}^{2}}-2{{c}^{2}}>0$

D)
$6ac+9{{a}^{2}}-2{{c}^{2}}>0$

• question_answer19)                 The vector                 $\left( \hat{i}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\hat{i}+\left( \hat{j}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\hat{j}+(\hat{k}\times \overset{\to }{\mathop{a.}}\,\overset{\to }{\mathop{b}}\,)\hat{j}$ $+(\hat{k}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\,)\hat{k}$                 is equal to                   JEE Main Online Paper (Held On 09 April 2013)

A)
$\vec{b}\times \vec{a}$

B)
$\overset{\to }{\mathop{a}}\,$

C)
$\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,$

D)
$\overset{\to }{\mathop{b}}\,$

• question_answer20)                 A light ray emerging from the point source placed at P(1, 3) is reflected at a point Q in the axis of $x$. If the reflected ray passes through the point R(6,7), then the abscissa of is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
1

B)
3

C)
$\frac{7}{2}$

D)
$\frac{5}{2}$

• question_answer21)                 The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be:               JEE Main Online Paper (Held On 09 April 2013)

A)
41

B)
49

C)
40.5

D)
42.5

• question_answer22)                 Let A = {1, 2, 3, 4} and be the relation defined by :                 R = {(1, 1), (2, 3), (3, 4), (4, 2)}. The correct statement is:             JEE Main Online Paper (Held On 09 April 2013)

A)
R does not have an inverse.

B)
R is not a one to one function.

C)
R is an onto function.

D)
R is not a function

• question_answer23) If the there lines $x-3y=p,ax+2y=q$and $ax+y=r$ form a right - angled triangle then:                     JEE Main Online Paper (Held On 09 April 2013)

A)
${{a}^{2}}-9a+18=0$

B)
${{a}^{2}}-6a-12=0$

C)
${{a}^{2}}-6a-18=0$

D)
${{a}^{2}}-9a+12=0$

• question_answer24)                 The matrix${{A}^{2}}+4A-5I,$where $I$is identity matrix and $A=\left[ \begin{matrix} 1 & 2 \\ 4 & -3 \\ \end{matrix} \right]$, equals:                 JEE Main Online Paper (Held On 09 April 2013)

A)
$4\left[ \begin{matrix} 2 & 1 \\ 2 & 0 \\ \end{matrix} \right]$

B)
$4\left[ \begin{matrix} 0 & -1 \\ 2 & 2 \\ \end{matrix} \right]$

C)
$32\left[ \begin{matrix} 2 & 1 \\ 2 & 0 \\ \end{matrix} \right]$

D)
$32\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]$

• question_answer25)                 The ratio of the coefficient of ${{x}^{15}}$ to the term in dependent of $x$ in the expansion of${{\left( {{x}^{2}}+\frac{2}{x} \right)}^{15}}$ is:            JEE Main Online Paper (Held On 09 April 2013)

A)
7 : 16

B)
7 : 64

C)
1 : 4

D)
1 : 32

• question_answer26)                 The value of $\operatorname{l}\underset{x\to 0}{\mathop{im}}\,\frac{1}{x}\left[ {{\tan }^{-1}}\left( \frac{x+1}{2x+1} \right)-\frac{\pi }{4} \right]$is :     JEE Main Online Paper (Held On 09 April 2013)

A)
1

B)
$-\frac{1}{2}$

C)
2

D)
0

• question_answer27)                 A vector$\overset{\to }{\mathop{\operatorname{n}}}\,$ is inclined to $x-$axis at${{45}^{0}}$, to$y-$axis at ${{60}^{0}}$ and at an acute angle to$z-$axis.$\operatorname{If}$$\overset{\to }{\mathop{\operatorname{n}}}\,$ is a normal to a plane passing through the point $(\sqrt{2},-1,1),$ then the equation of the plane is :                   JEE Main Online Paper (Held On 09 April 2013)

A)
$4\sqrt{2}x+7y+z=2$

B)
$\sqrt{2}x+y+z=2$

C)
$3\sqrt{2}x-4y-3z=7$

D)
$\sqrt{2}x-y-z=2$

• question_answer28)                 Statement 1: The statement $\operatorname{A}\to (\operatorname{B}\to \operatorname{A})$ is equivalent to $\operatorname{A}\to$$\left( \text{A}\wedge \text{B} \right).$                 Statement 2: The statement                 $\Rightarrow$$\tilde{\ }\left[ \left( \text{A}\wedge \text{B} \right)\to \left( \text{ }\!\!\tilde{\ }\!\!\text{ A}\vee \text{B} \right) \right]$ is a Tautology.                   JEE Main Online Paper (Held On 09 April 2013)

A)
Statement -1 is false. Statement -2 is true.

B)
Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.

C)
Statement -1 is true, Statement-2 is true. Statement -2 is correct explanation for statement-1.

D)
Statement -1 is true. Statement-2 is false.

• question_answer29)                 A committee of 4 persons is to formed from 2ladies, 2 old men and 4 young men such that it includes at least 1 lady, at lest 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:                   JEE Main Online Paper (Held On 09 April 2013)

A)
40

B)
41

C)
16

D)
32

• question_answer30)                                 Let$f(x)=\frac{{{x}^{2}}-x}{{{x}^{2}}+2x},x\ne 0,-2.$Then$\frac{d}{dx}\left[ {{f}^{-1}}(x) \right]$ (wherever it is defined) is equal to :        JEE Main Online Paper (Held On 09 April 2013)

A)
frac{-1}{{{(1-x)}^{2}}}\]

B)
$\frac{3}{{{(1-x)}^{2}}}$

C)
$\frac{1}{{{(1-x)}^{2}}}$

D)
$\frac{-3}{{{(1-x)}^{2}}}$