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question_answer1) The equation of the normal to the parabola, \[{{x}^{2}}=8y\]at \[x=4\]is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[x+2y=0\]
done
clear
B)
\[x+y=2\]
done
clear
C)
\[x-2y=0\]
done
clear
D)
\[x+y=6\]
done
clear
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question_answer2) The value of the integral\[\int\limits_{0}^{0.9}{\left[ x-2\left[ x \right] \right]dx,}\]where [.] denotes the greatest integer function is
JEE Main Online Paper (Held On 19 May 2012)
A)
0.9
done
clear
B)
1.8
done
clear
C)
-0.9
done
clear
D)
0
done
clear
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question_answer3) If a, b, c, are non zero complex numbers satisfying \[{{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+{{\text{c}}^{\text{2}}}=0\]and\[\left| \begin{matrix} {{b}^{2}}+{{c}^{2}} & ab & ac \\ ab & {{c}^{2}}+{{a}^{2}} & bc \\ ac & bc & {{a}^{2}}+{{b}^{2}} \\ \end{matrix} \right|=k{{a}^{2}}{{b}^{2}}{{c}^{2}},\]is equal to
JEE Main Online Paper (Held On 19 May 2012)
A)
1
done
clear
B)
3
done
clear
C)
4
done
clear
D)
2
done
clear
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question_answer4) If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{8}{15}\]
done
clear
B)
\[\frac{4}{15}\]
done
clear
C)
\[\frac{2}{15}\]
done
clear
D)
\[\frac{1}{15}\]
done
clear
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question_answer5) The sum of the series \[1+\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]upto n terms is.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{7}{6}n+\frac{1}{6}-\frac{2}{{{3.2}^{n-1}}}\]
done
clear
B)
\[\frac{5}{3}n-\frac{7}{6}+\frac{2}{{{2.3}^{n-1}}}\]
done
clear
C)
\[n+\frac{1}{2}-\frac{1}{{{2.3}^{n}}}\]
done
clear
D)
\[n-\frac{1}{3}-\frac{1}{{{3.2}^{n-1}}}\]
done
clear
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question_answer6) If\[a+b+c=0,\left| \overset{\to }{\mathop{a}}\, \right|=3,\left| \overset{\to }{\mathop{b}}\, \right|=5\]and\[\left| \overset{\to }{\mathop{c}}\, \right|=7,\]then the angle between \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\]is then f(1) equals.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{\pi }{3}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{6}\]
done
clear
D)
\[\frac{\pi }{2}\]
done
clear
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question_answer7) If\[f\left( x \right)=\int_{{}}^{{}}{\left( \frac{{{x}^{2}}+{{\sin }^{2}}x}{1+{{x}^{2}}} \right)}\sec x\,dx\]and\[f(0)=0,\]then f(1) equals.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\tan 1-\frac{\pi }{4}\]
done
clear
B)
\[\tan 1+1\]
done
clear
C)
\[\frac{\pi }{4}\]
done
clear
D)
\[1-\frac{\pi }{4}\]
done
clear
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question_answer8) Let\[p,q,r\in R\]and \[r>p>0.\]If the quadratic equation\[p{{x}^{2}}+qx+r=0\] has two complex roots \[\alpha \]and \[\beta ,\]then\[|\alpha |+|\beta |\]is.
JEE Main Online Paper (Held On 19 May 2012)
A)
equal to 1
done
clear
B)
less than 2 but not equal to 1
done
clear
C)
greater than 2
done
clear
D)
equal to 2
done
clear
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question_answer9) If three distinct points A, B, C are given in the 2- dimensional coordinate plane such that the ratio of the distance of each one of them from the point (1, 0) to the distance from (- 1,0) is equal to \[\frac{1}{2},\]then the circum centre of the triangle ABC is at, the point.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\left( \frac{5}{3},0 \right)\]
done
clear
B)
(0,0)
done
clear
C)
\[\left( \frac{1}{3},0 \right)\]
done
clear
D)
(3,0)
done
clear
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question_answer10) If the line \[y=mx+1\] meets the circle \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}+\text{3x}=0\]in two points equidistant from and on opposite sides of x-axis, then.
JEE Main Online Paper (Held On 19 May 2012)
A)
3m+2=0
done
clear
B)
3m-2=0
done
clear
C)
2m+3=0
done
clear
D)
2m-3=0
done
clear
View Answer play_arrow
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question_answer11) Let f: [1, 3]\[\to \] R be a function satisfying \[\frac{x}{[x]}\le f\left( x \right)\le \sqrt{6-x},\]for all \[x\ne 2\]and f(2) = 1, where R is the set of all real numbers and [x] denotes the largest integer less than or equal to x. Statement 1: \[\underset{x\to {{2}^{-}}}{\mathop{\lim }}\,f\left( x \right)\] exists. Statement 2: f is continuous at x = 2.
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
B)
Statement 1 is false. Statement 2 is true.
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
View Answer play_arrow
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question_answer12) The general solution of the differential equation \[\frac{dy}{dx}+\frac{2}{x}y={{x}^{2}}\]is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[y=c{{x}^{-3}}-\frac{{{x}^{2}}}{4}\]
done
clear
B)
\[y=c{{x}^{3}}-\frac{{{x}^{2}}}{4}\]
done
clear
C)
\[y=c{{x}^{2}}+\frac{{{x}^{3}}}{5}\]
done
clear
D)
\[y=c{{x}^{-2}}+\frac{{{x}^{3}}}{5}\]
done
clear
View Answer play_arrow
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question_answer13) A value of \[{{\tan }^{-1}}\left( \sin \left( {{\cos }^{-1}}\left( \sqrt{\frac{2}{3}} \right) \right) \right)\]is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{\pi }{4}\]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{6}\]
done
clear
View Answer play_arrow
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question_answer14) Let p and q be two Statements. Amongst the following, the Statement that is equivalent to \[p\to q\] is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[p\wedge \tilde{\ }q\]
done
clear
B)
\[\tilde{\ }p\vee q\]
done
clear
C)
\[\tilde{\ }p\wedge q\]
done
clear
D)
\[p\vee \tilde{\ }q\]
done
clear
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question_answer15) If the three planes \[x=5,2x-5a+3z-2=0\]and \[3bx+y-3z=0\] contain a common line, then (a, b) is equal to
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\left( \frac{8}{15},-\frac{1}{5} \right)\]
done
clear
B)
\[\left( \frac{1}{5},-\frac{8}{15} \right)\]
done
clear
C)
\[\left( -\frac{8}{15},\frac{1}{5} \right)\]
done
clear
D)
\[\left( -\frac{1}{5},\frac{8}{15} \right)\]
done
clear
View Answer play_arrow
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question_answer16) If\[f(x)=3{{x}^{10}}-7{{x}^{8}}+5{{x}^{6}}-21{{x}^{3}}+3{{x}^{2}}-7,\]then \[\underset{\alpha \to 0}{\mathop{\lim }}\,\frac{f\left( 1-\alpha \right)-f\left( 1 \right)}{{{\alpha }^{3}}+3\alpha }\]is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[-\frac{53}{3}\]
done
clear
B)
\[\frac{53}{3}\]
done
clear
C)
\[-\frac{55}{3}\]
done
clear
D)
\[\frac{55}{3}\]
done
clear
View Answer play_arrow
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question_answer17) Let Z and? F be complex numbers such that \[|Z|=|W|,\] and arg Z denotes the principal argument of Z. Statement 1. If arg Z+ arg \[W=\pi ,\]then \[Z=-\overline{W}.\] Statement1: \[|Z|=|W|,\]implies arg Z- arg \[\overline{W}=\pi .\]
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,
done
clear
B)
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 false, Statement 2 is true.
done
clear
View Answer play_arrow
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question_answer18) Consider a quadratic equation \[\text{a}{{\text{x}}^{\text{2}}}+\text{bx}+\text{c}=0,\]where \[\text{2a}+\text{3b}+\text{6c}=0\] and let\[g\left( x \right)=a\frac{{{x}^{3}}}{3}+b\frac{{{x}^{2}}}{2}+cx.\] Statement 1: The quadratic equation has at least one root in the interval (0, 1). Statement 2: The Rolle's theorem is applicable to function g(x) on the interval [0, 1].
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is false, Statement 2 is true.
done
clear
B)
Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,
done
clear
C)
Statement 2 is not a correct explanation for Statement 1.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
View Answer play_arrow
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question_answer19) Suppose \[\theta \] and \[\phi (\ne 0)\] are such that \[(\theta +\phi ),\sec \theta \]and \[\sec (\theta -\phi )\] are in A.P. If \[\cos \theta =k\cos \left( \frac{\phi }{2} \right)\] for some k, then A; is equal to
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\pm \sqrt{2}\]
done
clear
B)
\[\pm 1\]
done
clear
C)
\[\pm \frac{1}{\sqrt{2}}\]
done
clear
D)
\[\pm 2\]
done
clear
View Answer play_arrow
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question_answer20) Statement!: The shortest distance between the is lines \[\frac{x}{2}=\frac{y}{-1}=\frac{z}{2}\]and\[\frac{x-1}{4}=\frac{y-1}{-2}=\frac{z-1}{4}\]is\[\sqrt{2}.\] Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line.
JEE Main Online Paper (Held On 19 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 a correct explanation for Statement 1.
done
clear
View Answer play_arrow
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question_answer21) If \[n{{=}^{m}}{{C}_{2}},\]then the value of \[^{n}{{C}_{2}}\] is given by
JEE Main Online Paper (Held On 19 May 2012)
A)
\[3{{(}^{m+1}}{{C}_{4}})\]
done
clear
B)
\[^{m-1}{{C}_{4}}\]
done
clear
C)
\[^{m+1}{{C}_{4}}\]
done
clear
D)
\[2{{(}^{m+2}}{{C}_{4}})\]
done
clear
View Answer play_arrow
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question_answer22) If P(5) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set 5'= {1,2,3} to the set P(5) is
JEE Main Online Paper (Held On 19 May 2012)
A)
24
done
clear
B)
8
done
clear
C)
336
done
clear
D)
320
done
clear
View Answer play_arrow
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question_answer23) The number of arrangements that can be formed from the letters a, b, c, d, e, /taken 3 at a time without repetition and each arrangement containing at least one vowel, is
JEE Main Online Paper (Held On 19 May 2012)
A)
96
done
clear
B)
128
done
clear
C)
24
done
clear
D)
72
done
clear
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question_answer24) The weight W of a certain stock of fish is given by W=nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as \[n=2{{t}^{2}}+3\]and \[w={{t}^{2}}-t+2,\]then the rate of change of W with respect to t at t = 1 is
JEE Main Online Paper (Held On 19 May 2012)
A)
1
done
clear
B)
8
done
clear
C)
13
done
clear
D)
5
done
clear
View Answer play_arrow
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question_answer25) The area of the region bounded by the curve \[y={{x}^{3}},\] and the lines, y= 8, and x = 0, is
JEE Main Online Paper (Held On 19 May 2012)
A)
8
done
clear
B)
12
done
clear
C)
10
done
clear
D)
16
done
clear
View Answer play_arrow
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question_answer26) If \[\overset{\to }{\mathop{a}}\,=\hat{i}-2\hat{j}+3\hat{k},\overset{\to }{\mathop{b}}\,=2\hat{i}+3\hat{j}-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=r\hat{i}+\hat{j}+\left( 2r-1 \right)\hat{k}\]are three vectors such that \[\overset{\to }{\mathop{c}}\,\] is parallel to the plane of \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,,\] then r is equal to
JEE Main Online Paper (Held On 19 May 2012)
A)
1
done
clear
B)
-1
done
clear
C)
0
done
clear
D)
2
done
clear
View Answer play_arrow
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question_answer27) Let L be the liney = 2x, in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point \[\left( \frac{4}{5},\frac{3}{5} \right).\] Statement 2: The points (0,1) and\[\left( \frac{4}{5},\frac{3}{5} \right)\] lie on opposite sides of the line L and are at equal distance from it.
JEE Main Online Paper (Held On 19 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 true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
done
clear
D)
Statement 1 is false. Statement 2 is true.
done
clear
View Answer play_arrow
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question_answer28) The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is
JEE Main Online Paper (Held On 19 May 2012)
A)
10
done
clear
B)
20
done
clear
C)
15
done
clear
D)
12
done
clear
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question_answer29) If the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]coincide with the foci of the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25},\]then \[{{b}^{2}}\] is equal to
JEE Main Online Paper (Held On 19 May 2012)
A)
8
done
clear
B)
10
done
clear
C)
7
done
clear
D)
9
done
clear
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question_answer30) If \[{{A}^{T}}\]denotes the transpose of the matrix\[A=\left[ \begin{matrix} 0 & 0 & a \\ 0 & b & c \\ d & e & f \\ \end{matrix} \right],\]where a, b, c, d, e and f are integers such that \[abd\ne 0,\] then the number of such matrices for which \[{{A}^{-1}}={{A}^{T}}\]is
JEE Main Online Paper (Held On 19 May 2012)
A)
2(3!)
done
clear
B)
3(2!)
done
clear
C)
23
done
clear
D)
32
done
clear
View Answer play_arrow