# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 12 May 2012)

### done JEE Main Paper (Held On 12 May 2012) Total Questions - 30

• question_answer1) If a, b, c, d and are distinct real numbers such that $({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2p$$(ab+bc+cd)+$$({{b}^{2}}+{{c}^{2}}+{{d}^{2}})$$\le 0,$then   JEE Main Online Paper (Held On 12 May 2012)

A)
a, b, c, d are in A.P.

B)
ab = cd

C)
ac = bd

D)
a, b, c, d are in G.P.

• question_answer2) The area of triangle formed by the lines joining the vertex of the parabola, ${{x}^{2}}=8y,$to the extremities of its latus rectum is   JEE Main Online Paper (Held On 12 May 2012)

A)
2

B)
8

C)
1

D)
4

• question_answer3) Let A and B be real matrices of the form $\left[ \begin{matrix} \alpha & 0 \\ 0 & \beta \\ \end{matrix} \right]$and $\left[ \begin{matrix} 0 & \gamma \\ \delta & 0 \\ \end{matrix} \right],$respectively. Statement 1: AB - BA is always an-invertible matrix. Statement 2: AB - BA is never an identity matrix.   JEE Main Online Paper (Held On 12 May 2012)

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

B)
Statement 1 is false, Statement 2 is true.

C)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement!.

D)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1,

• question_answer4) If in a triangle $ABC,\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13},$then cos A is equal to     JEE Main Online Paper (Held On 12 May 2012)

A)
5/7

B)
1/5

C)
35/19

D)
19/35

• question_answer5) Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is ${{d}^{p}}.$. Statement 2: The total number of selections of p different objects out of q objects is $^{q}{{C}_{p}}.$     JEE Main Online Paper (Held On 12 May 2012)

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

B)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C)
Statement 1 is false, Statement 2 is true

D)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

• question_answer6) A unit vector which is perpendicular to the vector $2\hat{i}-\hat{j}+2\hat{k}$ and is coplanar with the vectors$\hat{i}+\hat{j}-\hat{k}$and $2\hat{i}+2\hat{j}-\hat{k}$ is   JEE Main Online Paper (Held On 12 May 2012)

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

B)
$\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}$

C)
$\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}$

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

• question_answer7) The number of terms in the expansion of ${{\left( {{y}^{1/5}}+{{x}^{1/10}} \right)}^{55}},$in which powers of x and y are free from radical signs are     JEE Main Online Paper (Held On 12 May 2012)

A)
six

B)
twelve

C)
seven

D)
five

• question_answer8) If the point (1, a) lies between the straight lines  $x+y=1$ and $2(x+y)=3$then a lies in interval     JEE Main Online Paper (Held On 12 May 2012)

A)
$\left( \frac{3}{2},\infty \right)$

B)
$\left( 1,\frac{3}{2} \right)$

C)
$\left( -\infty ,0 \right)$

D)
$\left( 0,\frac{1}{2} \right)$

• question_answer9) If two vertices of a triangle are (5, -1) and (-2,3) and its orthocentre is at (0, 0), then the third vertex is                JEE Main Online Paper (Held On 12 May 2012)

A)
(4,-7)

B)
(-4,-7)

C)
(-4,7)

D)
(4,7)

• question_answer10) Statement 1: A function $f:R\to R$ is continuous at ${{x}_{0}}$if and only if $\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f(x)$ exists and $\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)=f\left( {{x}_{0}} \right)$ Statement 2: A function $f:R\to R$ is discontinuous at ${{x}_{0}}$ if and only if,$\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)$exists and $\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)\ne f\left( {{x}_{0}} \right).$     JEE Main Online Paper (Held On 12 May 2012)

A)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

B)
Statement 1 is false. Statement 2 is true.

C)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

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

• question_answer11) The sum of the series$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...$ upto 15 terms is     JEE Main Online Paper (Held On 12 May 2012)

A)
1

B)
2

C)
3

D)
4

• question_answer12) The coordinates of the foot perpendicular from the point (1,0,0) to the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}$are     JEE Main Online Paper (Held On 12 May 2012)

A)
(2.-3.8)

B)
(1,-1,-10)

C)
(5,-8,-4)

D)
(3,-4,-2)

• question_answer13) If$\vec{u}=\hat{j}+4\hat{k},\vec{v}=\hat{i}+3\hat{k}$ and $\vec{w}=\cos \theta \hat{i}+\sin \theta \hat{j}$ are vectors in 3-dimensional space, then the maximum possible value of $\left| \vec{u}\times \vec{v}.\vec{w} \right|$ is     JEE Main Online Paper (Held On 12 May 2012)

A)
$\sqrt{3}$

B)
$5$

C)
$\sqrt{14}$

D)
$7$

• question_answer14) If the mean of 4,7,2,8,6 and a is 7, then the mean deviation from the median of these observations is     JEE Main Online Paper (Held On 12 May 2012)

A)
8

B)
5

C)
1

D)
3

• question_answer15) Consider a rectangle whose length is increasing at the uniform rate of 2 m/sec, breadth is decreasing at the uniform rate of 3 m/sec and the area is decreasing at the uniform rate of it $5\,{{m}^{2}}/\sec .$ If after some time the breadth of the rectangle is 2 m then the length of the rectangle is     JEE Main Online Paper (Held On 12 May 2012)

A)
2m

B)
4m

C)
1m

D)
3m

• question_answer16) If $f'(x)=\sin (\log x)$and $y=f\left( \frac{2x+3}{3-2x} \right),$ then$\frac{dy}{dx}$ equals     JEE Main Online Paper (Held On 12 May 2012)

A)
$\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]$

B)
$\frac{12}{{{\left( 3-2x \right)}^{2}}}$

C)
$\frac{12}{{{\left( 3-2x \right)}^{2}}}\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]$

D)
$\frac{12}{{{\left( 3-2x \right)}^{2}}}\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]$

• question_answer17) The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is     JEE Main Online Paper (Held On 12 May 2012)

A)
$2|z{{|}^{2}}$

B)
$1/2|z{{|}^{2}}$

C)
$4|z{{|}^{2}}$

D)
$|z{{|}^{2}}$

• question_answer18) Statement 1: The degrees of the differential equations $\frac{dy}{dx}+{{y}^{2}}=x$ and $\frac{{{d}^{2}}y}{d{{x}^{2}}}+y\sin x$are equal. Statement 2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.     JEE Main Online Paper (Held On 12 May 2012)

A)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement!.

B)
Statement 1 is false, Statement 2 is true.

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

D)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

• question_answer19) Statement 1: If the points (1,2,2), (2,1,2) and (2,2, z) and (1,1,1) are coplanar, then z= 2. Statement 2: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is O.     JEE Main Online Paper (Held On 12 May 2012)

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

B)
Statement 1 is true. Statement 2 is false.

C)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

D)
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement!.

• question_answer20) If ${{P}_{1}}$and ${{P}_{2}}$ are two points on the ellipse $\frac{{{x}^{2}}}{4}+{{y}^{2}}=1$at which the tangents are parallel to the chord joining the points (0,1) and (2,0), then the distance between ${{P}_{1}}$ and ${{P}_{2}}$ is     JEE Main Online Paper (Held On 12 May 2012)

A)
$2\sqrt{2}$

B)
$\sqrt{5}$

C)
$2\sqrt{3}$

D)
$\sqrt{10}$

• question_answer21) The area enclosed by the curves $y={{x}^{2}},y={{x}^{3}},x=0$and $x=0$where $p>1,$is 1/6. The p equals     JEE Main Online Paper (Held On 12 May 2012)

A)
8/3

B)
16/3

C)
2

D)
4/3

• question_answer22) If $f(x)=x{{e}^{x}}^{(1-x)},x\in R,$then f(x) is     JEE Main Online Paper (Held On 12 May 2012)

A)
decreasing on [-1/2,1]

B)
decreasing on R

C)
increasing on [-1/2,1]

D)
increasing on R

• question_answer23) The integral of $\frac{{{x}^{2}}-x}{{{x}^{3}}-{{x}^{2}}+x-1}$w.r.t.x is     JEE Main Online Paper (Held On 12 May 2012)

A)
$\frac{1}{2}\log \left( {{x}^{2}}+1 \right)+C$

B)
$\frac{1}{2}\log \left| {{x}^{2}}+1 \right|+C$

C)
$\log \left( {{x}^{2}}+1 \right)+C$

D)
$\log \left| {{x}^{2}}-1 \right|+C$

• question_answer24) The logically equivalent preposition of $p\Leftrightarrow q$is     JEE Main Online Paper (Held On 12 May 2012)

A)
$\left( p\Rightarrow q \right)\wedge \left( q\Rightarrow p \right)$

B)
$p\wedge q$

C)
$\left( p\wedge q \right)\vee \left( q\Rightarrow p \right)$

D)
$\left( p\wedge q \right)\Rightarrow \left( q\vee p \right)$

• question_answer25) If$\left| \begin{matrix} -2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & b+c & -2c \\ \end{matrix} \right|$$=\alpha \left( a+b \right)\left( b+c \right)\left( c+a \right)\ne 0$then $\alpha$ is equal to     JEE Main Online Paper (Held On 12 May 2012)

A)
$a+b+c$

B)
$abc$

C)
4

D)
1

• question_answer26) If $A=\{x\in {{z}^{+}}:x<10$and x is a multiple of 3 or 4}, where ${{z}^{+}}$ is the set of positive integers, then the total number of symmetric relations on A is     JEE Main Online Paper (Held On 12 May 2012)

A)
25

B)
215

C)
210

D)
220

• question_answer27) If the sum of the square of the roots of the equation ${{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0$ is least, then $\alpha$ is equal to     JEE Main Online Paper (Held On 12 May 2012)

A)
$\frac{\pi }{6}$

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

C)
$\frac{\pi }{3}$

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

• question_answer28) If $\frac{d}{dx}G(x)=\frac{{{e}^{\tan x}}}{x},x\in (0,\pi /2),$then $\int\limits_{1/4}^{1/2}{\frac{2}{x}.{{e}^{\tan (\pi {{x}^{2}})}}}dx$ is equal to     JEE Main Online Paper (Held On 12 May 2012)

A)
$G(\pi /4)-G(\pi /16)$

B)
$2[G(\pi /4)-G(\pi /16)]$

C)
$\pi [G(1/2)-G(1/4)]$

D)
$G(1/\sqrt{2})-G(1/2)$

• question_answer29) A number w is randomly selected from the set {1,2,3,....., 1000}. The probability that$\frac{\sum\limits_{i=1}^{n}{{{i}^{2}}}}{\sum\limits_{i=1}^{n}{i}}$ is  an integer is     JEE Main Online Paper (Held On 12 May 2012)

A)
0.331

B)
0333

C)
0334

D)
0332

• question_answer30) If a straight line y - x = 2 divides the region ${{x}^{2}}+{{y}^{2}}\le 4$into two parts, then the ratio of the area of the smaller part to the area of the greater part is     JEE Main Online Paper (Held On 12 May 2012)

A)
$3\pi -8:\pi +8$

B)
$\pi -3:3\pi +3$

C)
$3\pi -4:\pi +4$

D)
$\pi -2:3\pi +2$