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question_answer1) If A and B are any two events such that P(A) =2/5 and \[P(A\cap B)=3/20,\]then the conditional probability, \[P(A/(A'\cap B')),\]where A' denotes the complement of A, is equal to :
A)
\[\frac{8}{17}\]
done
clear
B)
\[\frac{1}{4}\]
done
clear
C)
\[\frac{5}{17}\]
done
clear
D)
\[\frac{11}{20}\]
done
clear
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question_answer2) For \[x\in R,x\ne 0,x\ne 1,\]let\[{{f}_{0}}(x)=\frac{1}{1-x}\]and\[{{f}_{n+1}}(x)={{f}_{0}}(f{{(}_{n}}(X)),\]n = 0, 1, 2, ........ Then the value of \[{{f}_{100}}(3)+{{f}_{1}}\left( \frac{2}{3} \right)+{{f}_{2}}\left( \frac{3}{2} \right)\]is equal to:
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{4}{3}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{5}{3}\]
done
clear
D)
\[\frac{8}{3}\]
done
clear
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question_answer3) The distance of the point (1, .2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes \[x-y+2z=3\] and \[2x-2y+z+12=0\], is
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{1}{\sqrt{2}}\]
done
clear
B)
2
done
clear
C)
\[\sqrt{2}\]
done
clear
D)
\[2\sqrt{2}\]
done
clear
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question_answer4) If the equations \[{{x}^{2}}+bx-1=0\]and \[{{x}^{2}}+x+b=0\]have a common root different from . 1, then | b | is equal to
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\sqrt{2}\]
done
clear
B)
2
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
3
done
clear
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question_answer5) If \[2\int\limits_{0}^{1}{{{\tan }^{-1}}xdx}=\int\limits_{0}^{1}{{{\cot }^{-1}}}(1-x+{{x}^{2}})dx\]then\[\int\limits_{0}^{1}{{{\tan }^{-1}}}(1-x+{{x}^{2}})dx\]is equal to:
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\log 2\]
done
clear
B)
\[\frac{\pi }{2}+\log 2\]
done
clear
C)
\[\log 4\]
done
clear
D)
\[\frac{\pi }{2}-\log 4\]
done
clear
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question_answer6) If \[P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\]and\[Q=PA{{P}^{T}},\]then\[{{P}^{T}}{{Q}^{2015}}P\]is
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\left[ \begin{matrix} 2015 & 1 \\ 0 & 2015 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 1 & 2015 \\ 0 & 1 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} 0 & 2015 \\ 0 & 0 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} 2015 & 0 \\ 1 & 2015 \\ \end{matrix} \right]\]
done
clear
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question_answer7) If\[\int_{{}}^{{}}{\frac{dx}{{{\cos }^{3}}x\sqrt{2\sin 2x}}={{(\tan x)}^{A}}}+C{{(\tan x)}^{B}}+k,\] where k is a constant of integration, then A + B + C equals
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{16}{5}\]
done
clear
B)
\[\frac{21}{5}\]
done
clear
C)
\[\frac{7}{10}\]
done
clear
D)
\[\frac{27}{10}\]
done
clear
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question_answer8) The point (2, 1) is translated parallel to the line \[L:x-y=4\]by \[2\sqrt{3}\]units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[2x+2y=1-\sqrt{6}\]
done
clear
B)
\[x=y=3-3\sqrt{6}\]
done
clear
C)
\[x+y=2-\sqrt{6}\]
done
clear
D)
\[x+y=3-2\sqrt{6}\]
done
clear
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question_answer9) If the function \[f(x)=\left\{ \begin{matrix} -x, & x<1 \\ a+{{\cos }^{-1}} & (x+b),1\le x\le 2 \\ \end{matrix} \right.\] is differentiable at x = 1, then\[\frac{a}{b}\]is equal to :
A)
\[\frac{-\pi -2}{2}\]
done
clear
B)
\[-1-{{\cos }^{-1}}(2)\]
done
clear
C)
\[\frac{\pi +2}{2}\]
done
clear
D)
\[\frac{\pi -2}{2}\]
done
clear
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question_answer10) The value of\[\sum\limits_{r=1}^{15}{{{r}^{2}}}\left( \frac{^{15}{{C}_{r}}}{^{15}{{C}_{r-1}}} \right)\]is equal to
JEE Main Online Paper (Held On 09 April 2016)
A)
1085
done
clear
B)
560
done
clear
C)
680
done
clear
D)
1240
done
clear
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question_answer11) In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively \[3\hat{i}+\hat{j}-\hat{k},-\hat{i}+3\hat{j}+p\hat{k}\]and\[5\hat{i}+q\hat{j}-4\hat{k},\]then the point (p, q) lies on a line
JEE Main Online Paper (Held On 09 April 2016)
A)
parallel to y-axis
done
clear
B)
making an acute angle with the positive direction of x-axis
done
clear
C)
parallel to x-axis
done
clear
D)
making an obtuse angle with the position direction of x-axis.
done
clear
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question_answer12) If\[\underset{x\to \infty }{\mathop{Lim}}\,{{\left( 1+\frac{a}{x}-\frac{4}{{{x}^{2}}} \right)}^{2x}}={{e}^{3}},\]then ?a? is equal to:
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{2}{3}\]
done
clear
B)
\[\frac{3}{2}\]
done
clear
C)
2
done
clear
D)
\[\frac{1}{2}\]
done
clear
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question_answer13) The number of \[x\in [0,2\pi ]\]for which\[\left| \sqrt{2{{\sin }^{4}}x+18{{\cos }^{2}}x}-\sqrt{2{{\cos }^{4}}x+18{{\sin }^{2}}x} \right|=1\]
JEE Main Online Paper (Held On 09 April 2016)
A)
6
done
clear
B)
4
done
clear
C)
8
done
clear
D)
2
done
clear
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question_answer14) If m and M are the minimum and the maximum values of \[4+\frac{1}{2}{{\sin }^{2}}2x-2{{\cos }^{4}}x,x\in R,\]then M-m is equal to
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{7}{4}\]
done
clear
B)
\[\frac{15}{4}\]
done
clear
C)
\[\frac{9}{4}\]
done
clear
D)
\[\frac{1}{4}\]
done
clear
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question_answer15) If a variable line drawn through the intersection of the lines\[\frac{x}{3}+\frac{y}{4}=1\]and\[\frac{x}{4}+\frac{y}{3}=1,\] meets the coordinate axes at A and B, \[(A\ne B),\] then the locus of the midpoint of AB is
JEE Main Online Paper (Held On 09 April 2016)
A)
\[7xy=6(x+y)\]
done
clear
B)
\[6xy=7(x+y)\]
done
clear
C)
\[4{{(x+y)}^{2}}-28(x+y)+49=0\]
done
clear
D)
\[14{{(x+y)}^{2}}-97(x+y)+168=0\]
done
clear
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question_answer16) If f(x) is a differentiable function in the interval \[(0,\,\,\infty )\] such that f(1) = 1 and \[\underset{t\to x}{\mathop{Lim}}\,\frac{{{t}^{2}}f(x)-{{x}^{2}}f(t)}{t-x}=1,\]for each x > 0, then \[f\left( \frac{3}{2} \right)\] is equal to :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{13}{6}\]
done
clear
B)
\[\frac{23}{18}\]
done
clear
C)
\[\frac{25}{9}\]
done
clear
D)
\[\frac{31}{18}\]
done
clear
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question_answer17) If the tangent at a point P, with parameter t, on the curve \[x=4{{t}^{2}}+3,y=8{{t}^{3}}-1,t\in R,\]meets the curve again at a point Q, then the coordinates of Q are :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[({{t}^{2}}+3,-{{t}^{3}}-1)\]
done
clear
B)
\[({{t}^{2}}+3,{{t}^{3}}-1)\]
done
clear
C)
\[(16{{t}^{2}}+3,-64{{t}^{3}}-1)\]
done
clear
D)
\[(4{{t}^{2}}+3,-4{{t}^{3}}-1)\]
done
clear
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question_answer18) If the tangent at a point on the ellipse\[\frac{{{x}^{2}}}{27}+\frac{{{y}^{2}}}{3}=1\]meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :
JEE Main Online Paper (Held On 09 April 2016)
A)
9
done
clear
B)
\[\frac{9}{2}\]
done
clear
C)
\[9\sqrt{3}\]
done
clear
D)
\[3\sqrt{3}\]
done
clear
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question_answer19) The point represented by 2+i in the Arg and plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :
JEE Main Online Paper (Held On 09 April 2016)
A)
2 + 2i
done
clear
B)
- 2 - 2i
done
clear
C)
1 + i
done
clear
D)
- 1 - i
done
clear
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question_answer20) A circle passes through (-2, 4). Which one of the following equations can represent a diameter of this circle?
JEE Main Online Paper (Held On 09 April 2016)
A)
\[4x+5y-6=0\]
done
clear
B)
\[5x+2y+4=0\]
done
clear
C)
\[2x-3y+10=0\]
done
clear
D)
\[3x+4y-3=0\]
done
clear
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question_answer21) The number of distinct real roots of the equation,\[\left| \begin{matrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \\ \end{matrix} \right|=0\]in the interval \[\left[ -\frac{\pi }{4},\frac{\pi }{4} \right]\]is:
JEE Main Online Paper (Held On 09 April 2016)
A)
4
done
clear
B)
1
done
clear
C)
2
done
clear
D)
3
done
clear
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question_answer22) The shortest distance between the lines\[\frac{x}{2}=\frac{y}{2}=\frac{z}{1}\]and\[\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}\]lies in the interval :
JEE Main Online Paper (Held On 09 April 2016)
A)
(2, 3]
done
clear
B)
[0, 1)
done
clear
C)
(3, 4]
done
clear
D)
[1, 2)
done
clear
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question_answer23) If the four letter words (need not be meaningful) are to be formed using the letters from the word MEDITERRANEAN. such that the first letter is R and the fourth letter is E, then the total number of all such words is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{11!}{{{(2!)}^{3}}}\]
done
clear
B)
59
done
clear
C)
110
done
clear
D)
56
done
clear
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question_answer24) Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation \[\text{9e}{{\text{-}}^{\text{2}}}\text{-18e}+\text{5}=0.\] If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of hyperbola, then \[{{a}^{2}}-{{b}^{2}}\]is equal to
JEE Main Online Paper (Held On 09 April 2016)
A)
- 7
done
clear
B)
- 5
done
clear
C)
5
done
clear
D)
7
done
clear
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question_answer25) Consider the following two statements : P : If 7 is an odd number, then 7 is divisible by 2. Q : If 7 is a prime number, then 7 is an odd number. If \[{{V}_{1}}\]is the truth value of contrapositive of P and \[{{V}_{2}}\] is the truth value of contrapositive of Q, then the ordered pair \[({{V}_{1}},{{V}_{2}})\] equals :
JEE Main Online Paper (Held On 09 April 2016)
A)
(F, T)
done
clear
B)
(T, F)
done
clear
C)
(F, F)
done
clear
D)
(T, T)
done
clear
View Answer play_arrow
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question_answer26) The minimum distance of a point on the curve \[y={{x}^{2}}-4\] from the origin is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{\sqrt{15}}{2}\]
done
clear
B)
\[\frac{\sqrt{19}}{2}\]
done
clear
C)
\[\sqrt{\frac{15}{2}}\]
done
clear
D)
\[\sqrt{\frac{19}{2}}\]
done
clear
View Answer play_arrow
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question_answer27) Let x, y, z be positive real numbers such that \[\text{x}+\text{y}+\text{z}=\text{12}\]and \[{{x}^{3}}{{y}^{4}}{{z}^{5}}=(0.1){{(600)}^{3}}.\]Then \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}\] is equal to
JEE Main Online Paper (Held On 09 April 2016)
A)
270
done
clear
B)
258
done
clear
C)
216
done
clear
D)
342
done
clear
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question_answer28) If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :
JEE Main Online Paper (Held On 09 April 2016)
A)
10
done
clear
B)
20.2
done
clear
C)
5.05
done
clear
D)
10.1
done
clear
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question_answer29) For\[x\in R,x=-1,\]if \[{{(1+x)}^{2016}}+x{{(1+x)}^{2015}}+{{x}^{2}}\]\[{{(1+x)}^{2014}}+...........+{{x}^{2016}}=\]\[\sum\limits_{i=0}^{2016}{{{a}_{i}}{{x}^{i}},}\]then\[{{a}_{17}}\]is equal to:
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{2016!}{16!}\]
done
clear
B)
\[\frac{2017!}{2000!}\]
done
clear
C)
\[\frac{2017!}{17!2000!}\]
done
clear
D)
\[\frac{2016!}{17!1999!}\]
done
clear
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question_answer30) The area (in sq. units) of the region described by \[A=\{(x,y)|y\ge {{x}^{2}}-5x+4,x+y\ge 1,y\le 0\}\]is :
JEE Main Online Paper (Held On 09 April 2016)
A)
\[\frac{7}{2}\]
done
clear
B)
\[\frac{13}{6}\]
done
clear
C)
\[\frac{17}{6}\]
done
clear
D)
\[\frac{19}{6}\]
done
clear
View Answer play_arrow