# Solved papers for JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

### done JEE Main Paper (Held on 7 May 2012) Total Questions - 30

• question_answer1) If$A=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),B=\left( \begin{matrix} \alpha +1 \\ 0 \\ 0 \\ \end{matrix} \right)$be two matrices, then $A{{B}^{T}}$is a non-zero matrix for |a| not equal to   JEE Main Online Paper (Held On 07 May 2012)

A)
2

B)
0

C)
1

D)
3

• question_answer2) If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of$6\pi c{{m}^{2}}hr,$then the rate (in mm/hr) at which the radius of the circular sheet increases is   JEE Main Online Paper (Held On 07 May 2012)

A)
1.0

B)
0.1

C)
1.1

D)
2.0

• question_answer3) The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is   JEE Main Online Paper (Held On 07 May 2012)

A)
63

B)
189

C)
728

D)
364

• question_answer4) The value of k for which the equation$(k-2){{x}^{2}}+8x+k+4=0$has both roots real, distinct and negative is   JEE Main Online Paper (Held On 07 May 2012)

A)
6

B)
3

C)
4

D)
1

• question_answer5) Let y (x) be a solution of $\frac{\left( 2+\sin x \right)}{\left( 1+y \right)}\frac{dy}{dx}=\cos x.$ If $y(0)=2,$then $y\left( \frac{\pi }{2} \right)$equals     JEE Main Online Paper (Held On 07 May 2012)

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

B)
2

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

D)
3

• question_answer6) If the eccentricity of a hyperbola $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,$which passes through (k, 2), is $\frac{\sqrt{13}}{3},$ then the value of ${{k}^{2}}$ is   JEE Main Online Paper (Held On 07 May 2012)

A)
18

B)
8

C)
1

D)
2

• question_answer7) If $\int\limits_{e}^{x}{tf(t)dt}=\sin x-x\cos x-\frac{{{x}^{2}}}{2},$for all$x\in R-\{0\},$then the value of$f\left( \frac{\pi }{6} \right)$ is   JEE Main Online Paper (Held On 07 May 2012)

A)
1/2

B)
1

C)
0

D)
-1/2

• question_answer8) If the number of 5-element subsets of the set$A=\{{{a}_{1}},{{a}_{2}},....,{{a}_{20}}\}$ of 20 distinct elements is k times the number of 5-element subsets containing${{a}_{4}},$then k is   JEE Main Online Paper (Held On 07 May 2012)

A)
5

B)
$\frac{20}{7}$

C)
4

D)
$\frac{10}{3}$

• question_answer9) If the system of equations $x+y+z=6$ $x+2y+3z=10$ $x+2y+\lambda z=0$ has a unique solution, then $\lambda$ is not equal to   JEE Main Online Paper (Held On 07 May 2012)

A)
1

B)
0

C)
2

D)
3

• question_answer10) If the straight lines $\text{x}+\text{3y}=\text{4},\text{3x}+\text{y}=\text{4}$and $\text{x}+\text{y}=0$form a triangle, then the triangle is   JEE Main Online Paper (Held On 07 May 2012)

A)
scalene

B)
equilateral triangle

C)
isosceles

D)
right angled isosceles

• question_answer11) Let fix)be an indefinite integral of ${{\cos }^{3}}x.$ Statement 1:f(x) is a periodic function of period$\pi .$ Statement 2: ${{\cos }^{3}}x$ is a periodic function.   JEE Main Online Paper (Held On 07 May 2012)

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

B)
Both the Statements are true, but Statement2 is not the correct explanation of Statement1.

C)
Both the Statements are true, and Statement2 is correct explanation of Statement 1.

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

• question_answer12) The parabola${{y}^{2}}=x$ divides the circle ${{x}^{2}}+{{y}^{2}}=2$into two parts whose areas are in the ratio   JEE Main Online Paper (Held On 07 May 2012)

A)
$9\pi +2:3\pi -2$

B)
$9\pi -2:3\pi +2$

C)
$7\pi -2:2\pi -3$

D)
$7\pi +2:3\pi +2$

• question_answer13) The equation of the circle passing through the point (1,2) and through the points of intersection of${{x}^{2}}+{{y}^{2}}-4x-6y-21=0$and $3x+4y+5=0$ is given by   JEE Main Online Paper (Held On 07 May 2012)

A)
${{x}^{2}}+{{y}^{2}}+2x=2y+11=0$

B)
${{x}^{2}}+{{y}^{2}}-2x+2y-7=0$

C)
${{x}^{2}}+{{y}^{2}}-2x-2y-3=0$

D)
${{x}^{2}}+{{y}^{2}}+2x+2y-11=0$

• question_answer14) The frequency distribution of daily working expenditure of families in a locality is as follows:  Expenditure in Rs. (x): 0-50 50-100 100-150 150-200 200-250 No. of families (f): 24 33 37 B 25
If the mode of the distribution is " 140, then the value of b is   JEE Main Online Paper (Held On 07 May 2012)

A)
34

B)
31

C)
26

D)
36

• question_answer15) The sum of the series${{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}$is   JEE Main Online Paper (Held On 07 May 2012)

A)
$m{{(2m+1)}^{2}}$

B)
${{m}^{2}}(m+2)$

C)
${{m}^{2}}(2m+1)$

D)
$m{{(m+2)}^{2}}$

• question_answer16) The point of intersection of the lines$({{a}^{3}}+3)x+ay+a-3=0$and$({{a}^{5}}+2)x+(a+2)y+2a+3=0$(a real) lies on they-axis for   JEE Main Online Paper (Held On 07 May 2012)

A)
no value of a

B)
more than two values of a

C)
exactly one value of a

D)
exactly two values of a

• question_answer17) ABCD is parallelogram. The position vectors of A and C are respectively,$3\hat{i}+3\hat{j}+5\hat{k}$ and$\hat{i}-5\hat{j}-5\hat{k}$.If M is the midpoint of the diagonal$\overset{\to }{\mathop{OM}}\,$then the magnitude of the projection of on$\overset{\to }{\mathop{OC}}\,,$ where O is the origin, is   JEE Main Online Paper (Held On 07 May 2012)

A)
$7\sqrt{51}$

B)
$\frac{7}{\sqrt{50}}$

C)
$7\sqrt{50}$

D)
$\frac{7}{\sqrt{51}}$

• question_answer18) The range of the function $f\left( x \right)=\frac{x}{1+|x|},x\in R,$is   JEE Main Online Paper (Held On 07 May 2012)

A)
R

B)
-1,1

C)
R- {0}

D)
[-1, 1]

• question_answer19) If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is   JEE Main Online Paper (Held On 07 May 2012)

A)
16

B)
18

C)
50

D)
15

• question_answer20) If $\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}$and$\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}$are coplanar vectors, then$\lambda$is equal to

A)
0

B)
-1

C)
2

D)
1

• question_answer21) Statement 1:$y=mx-\frac{1}{m}$is always a tangent to the parabola, ${{y}^{2}}=-4x$for all non-zero values of w. Statement 2: Every tangent to the parabola, ${{y}^{2}}=-4x$ will meet its axis at a point whose abscissa is non-negative.   JEE Main Online Paper (Held On 07 May 2012)

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

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 not a correct explanation of Statement 1.

• question_answer22) Let ${{Z}_{1}}$and ${{Z}_{2}}$be any two complex number. Statement1:$\left| {{Z}_{1}}-{{Z}_{2}} \right|\ge \left| {{Z}_{1}} \right|-\left| {{Z}_{2}} \right|$ Statement 2: $\left| {{Z}_{1}}+{{Z}_{2}} \right|\le \left| {{Z}_{1}} \right|+\left| {{Z}_{2}} \right|$   JEE Main Online Paper (Held On 07 May 2012)

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

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

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

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

• question_answer23) Let X and Y are two events such that$P\left( X\cup Y \right)=P(X\cap Y).$ Statement1:$P(X\cap Y')=P\left( X'\cap Y \right)=0$ Statement 2; $P(X)+P=2P\left( X\cap Y \right)$   JEE Main Online Paper (Held On 07 May 2012)

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

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

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_answer24) If$f(y)=1-(y-1)+{{(y-1)}^{2}}-{{(y-1)}^{3}}$$+...-{{(y-1)}^{17}},$then the coefficient of ${{y}^{2}}$ in it is   JEE Main Online Paper (Held On 07 May 2012)

A)
$^{17}{{C}_{2}}$

B)
$^{17}{{C}_{3}}$

C)
$^{18}{{C}_{2}}$

D)
$^{18}{{C}_{3}}$

• question_answer25) The values of a for which the two points (1, a, 1)and (-3, 0, a) lie on the opposite sides of the plane $\text{3x}+\text{4y}-\text{12z}+\text{13}=0,$ satisfy   JEE Main Online Paper (Held On 07 May 2012)

A)
$0<a<\frac{1}{3}$

B)
$-1<a<0$

C)
$a<-1$or    $a<\frac{1}{3}$

D)
$a=0$

• question_answer26) $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x-\sin x}{x} \right)\sin \left( \frac{1}{x} \right)$   JEE Main Online Paper (Held On 07 May 2012)

A)
equals 1

B)
equals 0

C)
does not exist

D)
equals? 1

• question_answer27) A line with positive direction cosines passes through the point P (2, - 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane $2x+y+z=9$ at point Q, then the length PQ equals   JEE Main Online Paper (Held On 07 May 2012)

A)
$\sqrt{2}$

B)
2

C)
$\sqrt{3}$

D)
1

• question_answer28) Let$f(x)=\sin x,g(x)=x.$ Statement1:$f(x)\le g(x)$ for x in $(0,\infty )$ Statement2:$f(x)\le 1$ for x in $(0,\infty )$ but $g(x)\to \infty$as$x\to \infty .$   JEE Main Online Paper (Held On 07 May 2012)

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

B)
Statement 1 is true. Statement 2 is true Statement 2 is a correct explanation for Statement 1.

C)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation for Statement!.

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

• question_answer29) The Statement that is TRUE among the following is   JEE Main Online Paper (Held On 07 May 2012)

A)
The contrapositive of$3x+2=8\Rightarrow x=2$is$x\ne 2$$\Rightarrow$$3x+2\ne 8.$

B)
The converse of $=0\Rightarrow x=0$ is $x\ne 0\Rightarrow \tan x=0.$

C)
$p\Rightarrow q$ is equivalent to$p\vee \tilde{\ }q.$

D)
$p\vee q$and$p\wedge q$ have the same truth table.

• question_answer30) If$x+|y|=2y,$ then y as a function of x, at x = 0 is

A)
differentiable but not continuous

B)
continuous but not differentiable

C)
continuous as well as differentiable

D)
neither continuous nor differentiable