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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
done
clear
B)
8
done
clear
C)
7
done
clear
D)
10
done
clear
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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
done
clear
B)
Q and R are perpendicular
done
clear
C)
P and g are parallel
done
clear
D)
P and R are parallel
done
clear
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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
done
clear
B)
A
done
clear
C)
B
done
clear
D)
0
done
clear
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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
done
clear
B)
r+s-2
done
clear
C)
r+s+1
done
clear
D)
r+s
done
clear
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question_answer5) The value of cos \[225{}^\circ \] + sin \[195{}^\circ \] is'.
JEE Main Online Paper (Held On 26-May-2012)
A)
\[\frac{\sqrt{3}-1}{2\sqrt{2}}\]
done
clear
B)
\[\frac{\sqrt{3}-1}{\sqrt{2}}\]
done
clear
C)
\[-\frac{\sqrt{3}-1}{\sqrt{2}}\]
done
clear
D)
\[\frac{\sqrt{3}+1}{\sqrt{2}}\]
done
clear
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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)
\[{{-}^{2n}}{{C}_{n-1}}\]
done
clear
B)
\[{{-}^{2n}}{{C}_{n}}\]
done
clear
C)
\[^{2n}{{C}_{n-1}}\]
done
clear
D)
\[^{2n}{{C}_{n}}\]
done
clear
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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)
\[-\pi \]
done
clear
B)
1
done
clear
C)
\[-1\]
done
clear
D)
\[\pi \]
done
clear
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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
done
clear
B)
above x-axis at a distance 3/2 from it
done
clear
C)
below x-axis at a distance 3/2 from it
done
clear
D)
below x-axis at a distance 2/3 from it
done
clear
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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)
\[-4\]
done
clear
B)
\[-\frac{1}{4}\]
done
clear
C)
4
done
clear
D)
\[\frac{1}{4}\]
done
clear
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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)
\[q\Rightarrow \tilde{\ }p\]
done
clear
B)
\[q\wedge \tilde{\ }p\]
done
clear
C)
\[p\wedge \tilde{\ }q\]
done
clear
D)
\[\tilde{\ }q\Rightarrow \tilde{\ }p\]
done
clear
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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)
\[{{n}^{2}}(n+1)\]
done
clear
B)
\[\frac{{{n}^{2}}(n-1)}{2}\]
done
clear
C)
\[\frac{{{n}^{2}}(n+1)}{2}\]
done
clear
D)
\[{{n}^{2}}(n-1)\]
done
clear
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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)
\[\frac{2}{5}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[1\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
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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.
done
clear
B)
Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
C)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
done
clear
D)
Statement 1 is false, Statement 2 is true.
done
clear
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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.
done
clear
B)
Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
done
clear
C)
Statement 1 is false. Statement 2 is true.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
done
clear
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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
done
clear
B)
four
done
clear
C)
two
done
clear
D)
three
done
clear
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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)
\[2\left( \left| {{z}_{1}}-{{z}_{2}} \right| \right)\]
done
clear
B)
\[2\left( {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right)\]
done
clear
C)
\[\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|\]
done
clear
D)
\[{{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}\]
done
clear
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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
done
clear
B)
5 in tan x
done
clear
C)
3 in tan x
done
clear
D)
3 in cot x
done
clear
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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)
\[x+y+z=0\]
done
clear
B)
\[x+2y+z=21\]
done
clear
C)
\[3x-2y+5z+35=0\]
done
clear
D)
\[3x+2y+5z+21=0\]
done
clear
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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.
done
clear
B)
Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.
done
clear
C)
Statement 1 is true, Statement 2 is false.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
done
clear
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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.
done
clear
B)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
C)
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
done
clear
D)
Statement 1 is true, Statement 2 is false.
done
clear
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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)
\[{{y}^{2}}=-104x\]
done
clear
B)
\[{{y}^{2}}=14x\]
done
clear
C)
\[{{y}^{2}}=26x\]
done
clear
D)
\[{{y}^{2}}=-14x\]
done
clear
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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
done
clear
B)
0.243
done
clear
C)
1.8
done
clear
D)
0
done
clear
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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
done
clear
B)
no point
done
clear
C)
exactly two distinct points
done
clear
D)
exactly one point
done
clear
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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
done
clear
B)
\[c=0,a=0,b\] is any real number
done
clear
C)
\[b=0,c=0,a\] is any real number
done
clear
D)
\[a=0,b=0,c\] is any real number
done
clear
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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)
\[\frac{1}{{{x}^{2}}-1}\]
done
clear
B)
\[{{x}^{2}}-1\]
done
clear
C)
\[\frac{{{x}^{2}}-1}{x}\]
done
clear
D)
\[\frac{x}{{{x}^{2}}-1}\]
done
clear
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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 \[{{L}_{4}}.\]
done
clear
B)
\[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{2}}.\]
done
clear
C)
\[{{L}_{1}}\bot {{L}_{2}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{4}}.\]
done
clear
D)
\[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{2}}\] intersect \[{{L}_{4}}.\]
done
clear
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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.
done
clear
B)
Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
done
clear
C)
Statement 1 is false, Statement 2 is true.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
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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)
\[5\pi \]
done
clear
B)
\[10\pi \]
done
clear
C)
\[100\pi \]
done
clear
D)
\[50\pi \]
done
clear
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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)
\[6!7!\]
done
clear
B)
\[{{(6!)}^{2}}\]
done
clear
C)
\[{{(7!)}^{2}}\]
done
clear
D)
\[7!\]
done
clear
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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)
\[\frac{1}{4}\]
done
clear
B)
\[\frac{2}{3}\]
done
clear
C)
\[\frac{1}{5}\]
done
clear
D)
\[\frac{1}{3}\]
done
clear
View Answer play_arrow