# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 9 April 2016)

### done JEE Main Paper (Held On 9 April 2016) Total Questions - 30

• 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)
$\frac{8}{17}$

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

C)
$\frac{5}{17}$

D)
$\frac{11}{20}$

• 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)
$\frac{4}{3}$

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

C)
$\frac{5}{3}$

D)
$\frac{8}{3}$

• 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)
$\frac{1}{\sqrt{2}}$

B)
2

C)
$\sqrt{2}$

D)
$2\sqrt{2}$

• 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)
$\sqrt{2}$

B)
2

C)
$\sqrt{3}$

D)
3

• 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)
$\log 2$

B)
$\frac{\pi }{2}+\log 2$

C)
$\log 4$

D)
$\frac{\pi }{2}-\log 4$

• 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)
$\left[ \begin{matrix} 2015 & 1 \\ 0 & 2015 \\ \end{matrix} \right]$

B)
$\left[ \begin{matrix} 1 & 2015 \\ 0 & 1 \\ \end{matrix} \right]$

C)
$\left[ \begin{matrix} 0 & 2015 \\ 0 & 0 \\ \end{matrix} \right]$

D)
$\left[ \begin{matrix} 2015 & 0 \\ 1 & 2015 \\ \end{matrix} \right]$

• 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)
$\frac{16}{5}$

B)
$\frac{21}{5}$

C)
$\frac{7}{10}$

D)
$\frac{27}{10}$

• 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)
$2x+2y=1-\sqrt{6}$

B)
$x=y=3-3\sqrt{6}$

C)
$x+y=2-\sqrt{6}$

D)
$x+y=3-2\sqrt{6}$

• 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)
$\frac{-\pi -2}{2}$

B)
$-1-{{\cos }^{-1}}(2)$

C)
$\frac{\pi +2}{2}$

D)
$\frac{\pi -2}{2}$

• 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

B)
560

C)
680

D)
1240

• 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

B)
making an acute angle with the positive direction of x-axis

C)
parallel to x-axis

D)
making an obtuse angle with the position direction of x-axis.

• 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)
$\frac{2}{3}$

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

C)
2

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

• 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

B)
4

C)
8

D)
2

• 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)
$\frac{7}{4}$

B)
$\frac{15}{4}$

C)
$\frac{9}{4}$

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

• 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)
$7xy=6(x+y)$

B)
$6xy=7(x+y)$

C)
$4{{(x+y)}^{2}}-28(x+y)+49=0$

D)
$14{{(x+y)}^{2}}-97(x+y)+168=0$

• 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)
$\frac{13}{6}$

B)
$\frac{23}{18}$

C)
$\frac{25}{9}$

D)
$\frac{31}{18}$

• 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)
$({{t}^{2}}+3,-{{t}^{3}}-1)$

B)
$({{t}^{2}}+3,{{t}^{3}}-1)$

C)
$(16{{t}^{2}}+3,-64{{t}^{3}}-1)$

D)
$(4{{t}^{2}}+3,-4{{t}^{3}}-1)$

• 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

B)
$\frac{9}{2}$

C)
$9\sqrt{3}$

D)
$3\sqrt{3}$

• 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

B)
- 2 - 2i

C)
1 + i

D)
- 1 - i

• 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)
$4x+5y-6=0$

B)
$5x+2y+4=0$

C)
$2x-3y+10=0$

D)
$3x+4y-3=0$

• 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

B)
1

C)
2

D)
3

• 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]

B)
[0, 1)

C)
(3, 4]

D)
[1, 2)

• 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)
$\frac{11!}{{{(2!)}^{3}}}$

B)
59

C)
110

D)
56

• 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

B)
- 5

C)
5

D)
7

• 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)

B)
(T, F)

C)
(F, F)

D)
(T, T)

• 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)
$\frac{\sqrt{15}}{2}$

B)
$\frac{\sqrt{19}}{2}$

C)
$\sqrt{\frac{15}{2}}$

D)
$\sqrt{\frac{19}{2}}$

• 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

B)
258

C)
216

D)
342

• 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

B)
20.2

C)
5.05

D)
10.1

• 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)
$\frac{2016!}{16!}$

B)
$\frac{2017!}{2000!}$

C)
$\frac{2017!}{17!2000!}$

D)
$\frac{2016!}{17!1999!}$

• 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)
$\frac{7}{2}$

B)
$\frac{13}{6}$

C)
$\frac{17}{6}$

D)
$\frac{19}{6}$