# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 25 April 2013)

### done JEE Main Paper (Held On 25 April 2013) Total Questions - 30

• question_answer1)                 Given a sequence of 4 numbers, first  three of with are in G.P. and the last there are in A.P. with common difference six If first and last terms of this sequence are equal then the last term is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
16

B)
8

C)
4

D)
2

• question_answer2)                 Statement I: The only circle having radius$\sqrt{10}$ and a diameter along line is ${{x}^{2}}+{{y}^{2}}-6x+2y=0.$                 Statement II:$2x+y=5$ is a normal to the circle ${{x}^{2}}+{{y}^{2}}-6x-2y=0.$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement I is false; statement II is true.

B)
Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I.

C)
Statement I is true; Statement II is false.

D)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.

• question_answer3)                 If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle ${{60}^{o}}$on the circumference of the first circle, then the of the first circle, then the radius of the are is:            JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\sqrt{3}$

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

C)
$1$

D)
$\sqrt{2}$

• question_answer4)                 If the image of point P(2,3) in a line L is Q(4,5), the image of point R(0,0) in the same line is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
(2, 2)

B)
(4, 5)

C)
(3, 4)

D)
(7, 7)

• question_answer5)                 Consider the system of equations:                 $x+ay=0,$$y+az=0$and$z+ax=0$. Then the set of all real values of ?a? for with the system has a unique solution is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$R-\{1\}$

B)
$R-\{-1\}$

C)
$\{1,-1\}$

D)
$\{1,0,-1\}$

• question_answer6)                 A common tangent to the conics and $2{{x}^{2}}-4{{y}^{2}}=9$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$x-y=\frac{3}{2}$

B)
$x+y=1$

C)
$x+y=\frac{9}{2}$

D)
$x-y=1$

• question_answer7)                 Let                 $\operatorname{S}=\left\{ \left( \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right):{{a}_{\operatorname{i}\operatorname{j}}}\in \{0,1,2\},{{a}_{11}}={{a}_{22}} \right\}$                 Then the number of non ? singular matrices in the set S is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
27

B)
24

C)
10

D)
20

• question_answer8)                 Let $x$$\in$(0, 1). The set of all $x$ such that$\text{si}{{\text{n}}^{-\text{1}}}x>{{\cos }^{-1}}x,$ is the interval :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( \frac{1}{2},\frac{1}{\sqrt{2}} \right)$

B)
$\left( \frac{1}{\sqrt{2}},1 \right)$

C)
$\left( 0,1 \right)$

D)
$\left( 0,\frac{\sqrt{3}}{2} \right)$

• question_answer9)                 Let A (-3,2) and B(-2,1) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line $3x+4y+2=0,$ the vertex C lies on the line:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$4x+3y+5=0$

B)
$3x+4y+3=0$

C)
$4x+3y+3=0$

D)
$3x+4y+5=0$

• question_answer10)                 Let ABC be a triangle with vertices at points A (2,3,5), B (-1,3,2) and C ($\lambda ,5,\mu$) in three dimensional space. If the median through A is equally inclined with the axes, the is$\left( \lambda ,\mu \right)$equal to:                    JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( 10,7 \right)$

B)
$\left( 7,5 \right)$

C)
$\left( 7,10 \right)$

D)
$\left( 5,7 \right)$

• question_answer11)                 If the integral $\int{\frac{\cos 8x+1}{\cot 2x-\tan 2x}dx=A\cos }$$8x+k,$where K is an arbitrary constant, then A is equal to :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$-\frac{1}{16}$

B)
$\frac{1}{16}$

C)
$\frac{1}{8}$

D)
$-\frac{1}{8}$

• question_answer12)                 The equation of the curve passing through the origin and satisfying the differential equation                 $(1+{{x}^{2}})\frac{\operatorname{dy}}{\operatorname{dx}}+2xy=4{{x}^{2}}$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$(1+{{x}^{2}})y={{x}^{3}}$

B)
$3(1+{{x}^{2}})y=2{{x}^{3}}$

C)
$1(1+{{x}^{2}})y=3{{x}^{3}}$

D)
$3(1+{{x}^{2}})y=4{{x}^{3}}$

• question_answer13)                 For$0\le x\le \frac{\pi }{2},$ the value of$\int\limits_{0}^{{{\sin }^{2}}x}{{{\sin }^{-1}}(\sqrt{t})\operatorname{dt}+}\int\limits_{0}^{{{\cos }^{2}}x}{{{\cos }^{-1}}(\sqrt{t})\operatorname{dt}}$equals:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\frac{\pi }{4}$

B)
0

C)
1

D)
$-\frac{\pi }{4}$

• question_answer14)                 Let f: $\left[ -2,3 \right]\to \left[ 8,\infty \right]$be a continuous function such that $f(1-x)=f(x)$ for all $x\in [-1,3].$                 If ${{\operatorname{R}}_{1}}$is the numerical value of the area of the region bounded by $y=f(x),x=-2$, $x=3$and          the axis of $x$ and${{R}_{2}}=\int\limits_{-2}^{3}{xf(x)\operatorname{d}x,\operatorname{then}:}$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$3{{R}_{1}}=2{{R}_{2}}$

B)
$2{{R}_{1}}=3{{R}_{2}}$

C)
${{R}_{1}}={{R}_{2}}$

D)
${{R}_{1}}=2{{R}_{2}}$

• question_answer15)                 Let$\vec{a}=2\hat{i}+\hat{j}-2\hat{k},\,\vec{b}=\hat{i}+\hat{j}$. If$\vec{c}$ is a vector such that $\vec{a}\cdot \vec{c}=|\vec{c}|,\,|\vec{c}-\vec{a}|=2\sqrt{2}$and the angle between $\vec{a}\times \vec{b}$ and $\vec{c}$is ${{30}^{o}}$, then $|(\vec{a}\times \vec{b})\times \vec{c}|$ equals:     JEE Main Online Paper ( Held On 25  April 2013 )

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

B)
$\frac{3\sqrt{3}}{2}$

C)
3

D)
$\frac{3}{2}$

• question_answer16)                 Let p and q be any two logical statements and $\operatorname{r}:p\to (\sim \operatorname{p}\vee \operatorname{q}).$If r has truth values of p and q are respectively:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
F, F

B)
T, T

C)
T, F

D)
F, T

• question_answer17)                 If the events A and B are mutually exclusive events such that $\operatorname{P}(\operatorname{A})=\frac{3x+1}{3}$$\operatorname{P}(\operatorname{B})=\frac{1+x}{4},$ then the set of possible values of $x$ lies in the interval:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left[ 0,1 \right]$

B)
$\left[ \frac{1}{3},\frac{1}{3} \right]$

C)
$\left[ -\frac{1}{3},\frac{5}{9} \right]$

D)
$\left[ -\frac{7}{9},\frac{4}{9} \right]$

• question_answer18)                 The equation of a plane though the of intersection of the planes $x+2y=3,$of the planes $x+2y=3,$$y-2z+1=0$ and perpendicular to the first plane is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$2x-y-10z=9$

B)
$2x-y+7z=11$

C)
$2x-y+10z=11$

D)
$2x-y-9z=10$

• question_answer19)                 If for positive integers$\operatorname{r}>1,\operatorname{n},>2,$the coefficients of the ${{(3r)}^{\operatorname{th}}}$and ${{(\operatorname{r}+2)}^{\operatorname{th}}}$  powers of $x$in the expansion of ${{(1+x)}^{2n}}$ are equal, then n is equal to     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$2r+1$

B)
$2r-1$

C)
3r

D)
$r+1$

• question_answer20)                                 If p and q are non-zero real numbers and${{\alpha }^{3}}+{{\beta }^{3}}=-p,\,\,\alpha \beta =q,$then a quadratic equation whose roots are$\frac{{{\alpha }^{2}}}{\beta },\frac{{{\beta }^{2}}}{\alpha }$is:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$p{{x}^{2}}-qx+{{p}^{2}}=0$

B)
$q{{x}^{2}}+px+{{q}^{2}}=0$

C)
$p{{x}^{2}}+qx+{{p}^{2}}=0$

D)
$q{{x}^{2}}-px+{{q}^{2}}=0$

• question_answer21)                 A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in${{\operatorname{cm}}^{2}}/\min .$) of the balloon when its diameter is 14 cm, is     JEE Main Online Paper ( Held On 25  April 2013 )

A)
10

B)
$\sqrt{10}$

C)
$100$

D)
$10\sqrt{10}$

• question_answer22)                 Let $\operatorname{A}=\{\theta :\sin (\theta )=\tan (\theta )\}$ and $B=\{\theta :\cos (\theta )=1\}$ be two sets. Then:     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\operatorname{A}=B$

B)
$\operatorname{A}\not\subset B$

C)
$\operatorname{B}\not\subset \operatorname{A}$

D)
$A\subset B$and$B-A\ne \phi$

• question_answer23)                 Let z satisfy $\left| z \right|=1$ and $\left| z \right|=1-\overset{-}{\mathop{z}}\,$                     Statement I : z is a real number                 Statement II : Principal argument of$z$ is $\frac{\pi }{3}$     JEE Main Online Paper ( Held On 25  April 2013 )

A)
Statement I true: Statement II is true; Statement II is a correct explanation for statement I

B)
Statement I is false; Statement II is true.

C)
Statement I is true; statement II is false.

D)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I.

• question_answer24)                 Consider the function                 $f(x)=[x]+\left| 1-x \right|,-1\le x\le 3$where$\left[ x \right]$is the greatest integer function.                 Statement I: $f$in not continuous at $x=0,$1,2 and 3.                 Statement II: $f(x)\left( \begin{matrix} -x, & -1\le x<0 \\ 1-x, & 0\le x<1 \\ 1+x, & 1\le x<2 \\ 2+x, & 2\le x\le 3 \\ \end{matrix} \right.$

A)
Statement I is true; Statement II is false.

B)

C)
Statement I is true: Statement II is true; Statement II is a correct explanation for Statement I.

D)
Statement I is false; Statement ii is true.

• question_answer25)                 Let $f(1)=-2$ and $f'(x)\ge 4.2$ for 1 $\le x\le 6.$The possible value of $f(6)$ lies in the interval     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( 15,19 \right)$

B)
$\left( -\infty ,12 \right)$

C)
$[12,\,15)$

D)
$[19,\,\infty )$

• question_answer26)                                  In a set of 2n observations, half of them ear equal to $'a'$ and the remaining half are equal to $'-a'$ If the standard deviation of all the observations is 2; then the value of $\left| a \right|$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2

B)
$\sqrt{2}$

C)
4

D)
$2\sqrt{2}$

• question_answer27)                 The value of${{1}^{2}}+{{3}^{2}}+{{5}^{2}}+..........+{{25}^{2}}$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
2925

B)
1469

C)
1728

D)
1456

• question_answer28)                 If an equation of a tangent to the curve,$y=\cos (x+y),-1\le x\le 1+\pi$, is $x+2y=k$then $k$is equal to     JEE Main Online Paper ( Held On 25  April 2013 )

A)
1

B)
2

C)
$\frac{\pi }{4}$

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

• question_answer29)                 5-digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed  20000 and $q$ be the number of those that lie between 30000 and 90000 , then p:q is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
6:5

B)
3:2

C)
4:3

D)
5:3

• question_answer30) A point on the ellipse,$4{{x}^{2}}+9{{y}^{2}}=36,$where the normal is parallel to the line, $4x-2y-5=0,$is :     JEE Main Online Paper ( Held On 25  April 2013 )

A)
$\left( \frac{9}{5},\frac{8}{5}, \right)$

B)
$\left( \frac{8}{5},-\frac{9}{5}, \right)$

C)
$\left( -\frac{9}{5},\frac{8}{5}, \right)$

D)
$\left( -\frac{8}{5},\frac{9}{5} \right)$