Solved papers for JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

done JEE Main Paper (Held On 26 May 2012) Total Questions - 30

• question_answer1) The distance of the point $-\hat{i}+2\hat{j}+6\hat{k}$from the straight line that passes through the point $2\hat{i}+3\hat{j}-4\hat{k}$ and is parallel to the vector $6\hat{i}+3\hat{j}-4\hat{k}$ is   JEE Main Online Paper (Held On 26-May-2012)

A)
9

B)
8

C)
7

D)
10

• question_answer2) Consider the following planes $P:x+y-2z+7=0$ $Q:x+y+2z+2=0$ $R:3x+3y-6z-11=0$   JEE Main Online Paper (Held On 26-May-2012)

A)
P and R are perpendicular

B)
Q and R are perpendicular

C)
P and g are parallel

D)
P and R are parallel

• question_answer3) If$A=\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -3 & 2 & 1 \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 7 & -2 & 1 \\ \end{matrix} \right]$ then AB equals.   JEE Main Online Paper (Held On 26-May-2012)

A)
I

B)
A

C)
B

D)
0

• question_answer4) If the A.M. between ${{\text{p}}^{\text{th}}}$and ${{\text{q}}^{\text{th}}}$terms of an A.P. is equal to the A.M. between ${{\text{r}}^{\text{th}}}$and ${{\text{s}}^{\text{th}}}$ terms of the same A.P., then p + q is equal to.   JEE Main Online Paper (Held On 26-May-2012)

A)
r+s-1

B)
r+s-2

C)
r+s+1

D)
r+s

• question_answer5) The value of cos $225{}^\circ$ + sin $195{}^\circ$ is'.   JEE Main Online Paper (Held On 26-May-2012)

A)
$\frac{\sqrt{3}-1}{2\sqrt{2}}$

B)
$\frac{\sqrt{3}-1}{\sqrt{2}}$

C)
$-\frac{\sqrt{3}-1}{\sqrt{2}}$

D)
$\frac{\sqrt{3}+1}{\sqrt{2}}$

• question_answer6) The middle term in the expansion of ${{\left( 1-\frac{1}{x} \right)}^{n}}{{\left( 1-x \right)}^{n}}$ in powers of x is.   JEE Main Online Paper (Held On 26-May-2012)

A)
${{-}^{2n}}{{C}_{n-1}}$

B)
${{-}^{2n}}{{C}_{n}}$

C)
$^{2n}{{C}_{n-1}}$

D)
$^{2n}{{C}_{n}}$

• question_answer7) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left( \pi {{\cos }^{2}}x \right)}{{{x}^{2}}}$ equals.   JEE Main Online Paper (Held On 26-May-2012)

A)
$-\pi$

B)
1

C)
$-1$

D)
$\pi$

• question_answer8) The line parallel to x-axis and passing through the point of intersection of lines $ax+2by+3b=0$and $bx-2ay-3a=0,$ where $(a,b)\ne (0,0)$ is.   JEE Main Online Paper (Held On 26-May-2012)

A)
above x-oxis ata distance 2/3 from it

B)
above x-axis at a distance 3/2 from it

C)
below x-axis at a distance 3/2 from it

D)
below x-axis at a distance 2/3 from it

• question_answer9) The chord PQ of the parabola ${{y}^{2}}=x,$where one end P of the chord is at point (4, - 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$-4$

B)
$-\frac{1}{4}$

C)
4

D)
$\frac{1}{4}$

• question_answer10) Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$q\Rightarrow \tilde{\ }p$

B)
$q\wedge \tilde{\ }p$

C)
$p\wedge \tilde{\ }q$

D)
$\tilde{\ }q\Rightarrow \tilde{\ }p$

• question_answer11) If 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}}}+...$ upto n terms, when n is even, is$\frac{n{{\left( n+1 \right)}^{2}}}{2},$then the sum of the series, when n is odd, is  ,   JEE Main Online Paper (Held On 26-May-2012)

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

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

C)
$\frac{{{n}^{2}}(n+1)}{2}$

D)
${{n}^{2}}(n-1)$

• question_answer12) The area bounded by the parabola ${{y}^{2}}=4x$ and the line $\text{2x}-\text{3y}+\text{4}=0,$ in square unit, is.   JEE Main Online Paper (Held On 26-May-2012)

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

B)
$\frac{1}{3}$

C)
$1$

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

• question_answer13) Let $f;\left( -\infty ,\infty \right)\to \left( -\infty ,\infty \right)$ be defined by $f(x)={{x}^{3}}+1.$ Statement 1: The function f has a local extremumatx=0 Statement 2: The function f is continuous and differentiable on $\left( -\infty ,\infty \right)$ and f'(0)=0.   JEE Main Online Paper (Held On 26-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 the correct explanation for Statement 1.

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

• question_answer14) Let A and B be nonempty sets in R and$f:A\to B$ is a objective function. Statement 1: fis an onto function. Statement 2: There exists a function $g:B\to A$ such that $fog={{I}_{B}}.$.   JEE Main Online Paper (Held On 26-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 false. Statement 2 is true.

D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

• question_answer15) The number of common tangents of the circles given by${{x}^{2}}+{{y}^{2}}-8x-2y+1=0$and${{x}^{2}}+{{y}^{2}}+6x+8y=0$is.   JEE Main Online Paper (Held On 26-May-2012)

A)
one

B)
four

C)
two

D)
three

• question_answer16) ${{\left| {{z}_{1}}+{{z}_{2}} \right|}^{2}}+{{\left| {{z}_{1}}-{{z}_{2}} \right|}^{2}}$ is equal to.   JEE Main Online Paper (Held On 26-May-2012)

A)
$2\left( \left| {{z}_{1}}-{{z}_{2}} \right| \right)$

B)
$2\left( {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right)$

C)
$\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|$

D)
${{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}$

• question_answer17) $f\left( x \right)=\frac{dx}{{{\sin }^{6}}x}$is a polynomial of degree.   JEE Main Online Paper (Held On 26-May-2012)

A)
5 in cot x

B)
5 in tan x

C)
3 in tan x

D)
3 in cot x

• question_answer18) The equation of a plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ and the point (0,7, - 7) is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$x+y+z=0$

B)
$x+2y+z=21$

C)
$3x-2y+5z+35=0$

D)
$3x+2y+5z+21=0$

• question_answer19) Statement-1: The vectors $\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,$and $\overset{\to }{\mathop{c}}\,$ lie in the same plane if and only if $\overset{\to }{\mathop{a}}\,.\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\, \right)=0$ Statement-2: The vectors $\overset{\to }{\mathop{u}}\,$and $\overset{\to }{\mathop{v}}\,$ are perpendicular if and only if $\overset{\to }{\mathop{u}}\,.\overset{\to }{\mathop{v}}\,=0$where$\overset{\to }{\mathop{u}}\,\times \overset{\to }{\mathop{v}}\,$is a vector perpendicular to the plane of.   JEE Main Online Paper (Held On 26-May-2012)

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

B)
Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.

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 for Statement 1.

• question_answer20) Statement 1: If the system of equations$x+ky+3z=0,$$3x+ky-2z=0,$$2x+3y-4z=0$has anon- trivial solution, then the value of k is$\frac{31}{2}.$ Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.   JEE Main Online Paper (Held On 26-May-2012)

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

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 1.

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

• question_answer21) The normal at  $\left( 2,\frac{3}{2} \right)$to the ellipse,$\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{3}=1$ touches a parabola, whose equation is.   JEE Main Online Paper (Held On 26-May-2012)

A)
${{y}^{2}}=-104x$

B)
${{y}^{2}}=14x$

C)
${{y}^{2}}=26x$

D)
${{y}^{2}}=-14x$

• question_answer22) If [x] is the greatest integer $\le x,$ then the value of the integral$\int\limits_{-0.9}^{0.9}{\left( \left[ {{x}^{2}} \right]+\log \left( \frac{2-x}{2+x} \right) \right)dx}$is.   JEE Main Online Paper (Held On 26-May-2012)

A)
0.486

B)
0.243

C)
1.8

D)
0

• question_answer23) If$a,b,c\in R$ and 1 is a root of equation $a{{x}^{2}}+bx+c=0,$then the curve $y=4a{{x}^{2}}+3bx+2c,a\ne 0$intersect x-axis at.   JEE Main Online Paper (Held On 26-May-2012)

A)
two distinct points whose coordinates are always rational numbers

B)
no point

C)
exactly two distinct points

D)
exactly one point

• question_answer24) If$f(x)=a|\sin x|+b{{e}^{|x|}}+c|x{{|}^{3}},$ where $a,b,c\in R$, is differentiable at x = 0, then.   JEE Main Online Paper (Held On 26-May-2012)

A)
$a=0,b$and c are any real numbers

B)
$c=0,a=0,b$ is any real number

C)
$b=0,c=0,a$ is any real number

D)
$a=0,b=0,c$ is any real number

• question_answer25) The integrating factor of the differential equation $\left( {{x}^{2}}-1 \right)\frac{dy}{dx}+2xy=x$ is.   JEE Main Online Paper (Held On 26-May-2012)

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

B)
${{x}^{2}}-1$

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

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

• question_answer26) Consider the straight lines ${{L}_{1}}:x-y=1$ ${{L}_{2}}:x+y=1$ ${{L}_{3}}:2x+2y=5$ ${{L}_{4}}:2x-2y=7$ The correct statement is.   JEE Main Online Paper (Held On 26-May-2012)

A)
${{L}_{1}}||{{L}_{4}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}$intersect ${{L}_{4}}.$

B)
${{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{1}}$ intersect ${{L}_{2}}.$

C)
${{L}_{1}}\bot {{L}_{2}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}$ intersect ${{L}_{4}}.$

D)
${{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{2}}$ intersect ${{L}_{4}}.$

• question_answer27) Statement-1: The variance of first n odd natural numbers is$\frac{{{n}^{2}}-1}{3}$ Statement-2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is $\frac{n\left( 4{{n}^{2}}+1 \right)}{3}.$.   JEE Main Online Paper (Held On 26-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 for 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 for Statement 1.

• question_answer28) If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in $\text{c}{{\text{m}}^{\text{2}}}$/hour) is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$5\pi$

B)
$10\pi$

C)
$100\pi$

D)
$50\pi$

• question_answer29) If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$6!7!$

B)
${{(6!)}^{2}}$

C)
${{(7!)}^{2}}$

D)
$7!$

• question_answer30) There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the um and there after a ball is drawn at random from the um, then the probability that it is white is.   JEE Main Online Paper (Held On 26-May-2012)

A)
$\frac{1}{4}$

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

C)
$\frac{1}{5}$

D)
$\frac{1}{3}$