# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 19 April 2014)

### done JEE Main Paper (Held On 19 April 2014) Total Questions - 30

• question_answer1) Let $f:R\to R$be defined by $f(x)=\frac{\left| x \right|-1}{\left| x \right|+1}$then f is:     JEE Main Online Paper (Held On 19 April 2016)

A)
both one-one and onto

B)
one-one but not onto

C)
onto but not one-one

D)
neither one-one nor onto.

• question_answer2) For all complex numbers z of the form $1+i\alpha ,\alpha \in R,$if ${{z}^{2}}=x+iy,$then     JEE Main Online Paper (Held On 19 April 2016)

A)
${{y}^{2}}-4x+2=0$

B)
${{y}^{2}}+4x-4=0$

C)
${{y}^{2}}-4x-4=0$

D)
${{y}^{2}}+4x+2=0$

• question_answer3) The equation $\sqrt{3{{x}^{2}}+x+5}x-3,$where x is real, has;     JEE Main Online Paper (Held On 19 April 2016)

A)
no solution

B)
exactly one solution

C)
exactly two solution

D)
exactly four solution

• question_answer4) Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB - BA is:     JEE Main Online Paper (Held On 19 April 2016)

A)
skewsymmetric

B)
Symmetric

C)
neither symmetric nor skewsymmetric

D)
I or - I, where I is an identity matrix.

• question_answer5) If $\Delta r=\left| \begin{matrix} r & 2r-1 & 3r-2 \\ \frac{n}{2} & n-1 & a \\ \frac{1}{2}n(n-1) & {{(n-1)}^{2}} & \frac{1}{2}(n-1)(3n-4) \\ \end{matrix} \right|$then the value of$\sum\limits_{r=1}^{n-1}{{{\Delta }_{r}}}$     JEE Main Online Paper (Held On 19 April 2016)

A)
depends only on a

B)
depends only on n

C)
depends both on a and n

D)
is independent of both a and n

• question_answer6) Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)

A)
[8, 9]

B)
[10, 12)

C)
(11, 13]

D)
(14, 17)

• question_answer7) The coefficient of ${{x}^{1012}}$in the expansion of ${{(1+{{x}^{n}}+{{x}^{253}})}^{10}},$ (where $n\le 22$is any positive integer), is     JEE Main Online Paper (Held On 19 April 2016)

A)
1

B)
$^{10}{{C}_{4}}$

C)
4n

D)
$^{253}{{C}_{4}}$

• question_answer8) The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by $10\frac{1}{2},$ then the number of terms in the A.P. is:     JEE Main Online Paper (Held On 19 April 2016)

A)
4

B)
8

C)
12

D)
16

• question_answer9) Let $f(n)=\left[ \frac{1}{3}+\frac{3n}{100} \right]n,$ where [n] denotes the greatest integer less than or equal to n. Then $\sum\limits_{n=1}^{56}{f\left( n \right)}$is equal to:     JEE Main Online Paper (Held On 19 April 2016)

A)
56

B)
689

C)
1287

D)
1399

• question_answer10) If the function$f\left( x \right)=\left\{ \begin{matrix} \frac{\sqrt{2+\cos x}-1}{{{\left( \pi -x \right)}^{2}}}, & x\ne \pi \\ k & ,x=\pi \\ \end{matrix} \right.$is continuous at $x=\pi ,$ then k equals:     JEE Main Online Paper (Held On 19 April 2016)

A)
0

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

C)
2

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

• question_answer11) Let $f:R\to R$be a function such that $\left| f\left( x \right) \right|\le {{x}^{2}},$for all $x\in R.$Then, at x = 0, f is:     JEE Main Online Paper (Held On 19 April 2016)

A)
continuous but not differentiable.

B)
continuous as well as differentiable.

C)
neither continuous nor differentiable.

D)
differentiable but not continuous.

• question_answer12) If non-zero real numbers b and c are such that min $f(x)>\max g(x)$ where $f(x)={{x}^{2}}+2bx+2{{c}^{2}}$and $g(x)=-{{x}^{2}}-2cx+{{b}^{2}}$$(x\in R);$ then$\left| \frac{c}{b} \right|$lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)

A)
$\left( 0,\frac{1}{2} \right)$

B)
$\left[ \frac{1}{2},\frac{1}{\sqrt{2}} \right)$

C)
$\left[ \frac{1}{\sqrt{2},}\sqrt{2} \right]$

D)
$\left( \sqrt{2},\infty \right)$

• question_answer13) If the volume of a spherical ball is increasing at the rate of $4\pi cc/\sec ,$then the rate of increase of its radius (in cm/sec), when the volume is $288\pi cc,$     JEE Main Online Paper (Held On 19 April 2016)

A)
$\frac{1}{6}$

B)
$\frac{1}{9}$

C)
$\frac{1}{36}$

D)
$\frac{1}{24}$

• question_answer14) If m is a non-zero number and $\int_{{}}^{{}}{\frac{{{x}^{5m-1}}+2{{x}^{4m-1}}}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{3}}}}dx=f(x)+c,$then f(x) is:     JEE Main Online Paper (Held On 19 April 2016)

A)
$\frac{{{x}^{5m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

B)
$\frac{{{x}^{4m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

C)
$\frac{2m\left( {{x}^{5m}}+{{x}^{4m}} \right)}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

D)
$\frac{\left( {{x}^{5m}}-{{x}^{4m}} \right)}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}$

• question_answer15) Let function F be defined as$F(x)=\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t}}dt,x>0$then the value of the integral$\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t+a}}dt,$where a > 0, is:     JEE Main Online Paper (Held On 19 April 2016)

A)
${{e}^{a}}\left[ F(x)-F(1+a) \right]$

B)
${{e}^{-a}}\left[ F(x+a)-F(a) \right]$

C)
${{e}^{a}}\left[ F(x+a)-F(1+a) \right]$

D)
${{e}^{-a}}\left[ F(x+a)-F(1+a) \right]$

• question_answer16) The area of the region above the x-axis bounded by the curve $y=\tan x,0\le x\le \frac{\pi }{2}$and the tangent to the curve at $x=\frac{\pi }{4}$ is:     JEE Main Online Paper (Held On 19 April 2016)

A)
$\frac{1}{2}\left( \log 2-\frac{1}{2} \right)$

B)
$\frac{1}{2}\left( \log 2+\frac{1}{2} \right)$

C)
$\frac{1}{2}\left( 1-\log 2 \right)$

D)
$\frac{1}{2}\left( 1+\log 2 \right)$

• question_answer17) If$\frac{dy}{dx}+y\tan x=\sin 2x$and$y(0)=1,$then$y(\pi )$ then y(p) is equal to:     JEE Main Online Paper (Held On 19 April 2016)

A)
1

B)
-1

C)
-5

D)
5

• question_answer18) The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $({{a}^{2}}+1,{{a}^{2}}+1)$and $(2a,-2a),a\ne 0.$Then for any a, the orthocentre of this triangle lies on the line:     JEE Main Online Paper (Held On 19 April 2016)

A)
$y-2ax=0$

B)
$y-({{a}^{2}}+1)x=0$

C)
$y+x=0$

D)
${{(a-1)}^{2}}x-{{(a+1)}^{2}}y=0$

• question_answer19) If a line L is perpendicular to the line $5x-y=1$, and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line $x+5y=0$ is:     JEE Main Online Paper (Held On 19 April 2016)

A)
$\frac{7}{\sqrt{5}}$

B)
$\frac{5}{\sqrt{13}}$

C)
$\frac{7}{\sqrt{13}}$

D)
$\frac{5}{\sqrt{7}}$

• question_answer20) The equation of circle described on the chord $3x+y+5=0$of the circle ${{x}^{2}}+{{y}^{2}}=16$as diameter is:     JEE Main Online Paper (Held On 19 April 2016)

A)
${{x}^{2}}+{{y}^{2}}+3x+y-11=0$

B)
${{x}^{2}}+{{y}^{2}}+3x+y+1=0$

C)
${{x}^{2}}+{{y}^{2}}+3x+y-2=0$

D)
${{x}^{2}}+{{y}^{2}}+3x+y-22=0$

• question_answer21) A chord is drawn through the focus of the parabola ${{y}^{2}}=6x$such that its distance from the vertex of this parabola is $\frac{\sqrt{5}}{2},$then its slope can be:     JEE Main Online Paper (Held On 19 April 2016)

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

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

C)
$\frac{2}{\sqrt{5}}$

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

• question_answer22) The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola $\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1,$ meet x-axis and y-axis at A and B respectively. Then ${{(OA)}^{2}}-{{(OB)}^{2}},$where O is the origin, equals:     JEE Main Online Paper (Held On 19 April 2016)

A)
$-\frac{20}{9}$

B)
$\frac{19}{9}$

C)
4

D)
$-\frac{4}{3}$

• question_answer23) Equation of the line of the shortest distance between the lines $\frac{x}{1}=\frac{y}{-1}=\frac{z}{1}$and $\frac{x-1}{0}=\frac{y+1}{-2}=\frac{z}{1}$is:     JEE Main Online Paper (Held On 19 April 2016)

A)
$\frac{x}{1}=\frac{y}{-1}=\frac{z}{-2}$

B)
$\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{-2}$

C)
$\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{1}$

D)
$\frac{x}{-2}=\frac{y}{1}=\frac{z}{2}$

• question_answer24) If the angle between the line  and the plane is then the value of  is:     JEE Main Online Paper (Held On 19 April 2016)

A)

B)

C)

D)

• question_answer25) If andthen the magnitude of the projection ofon is:     JEE Main Online Paper (Held On 19 April 2016)

A)
12

B)
15

C)
14

D)
13

• question_answer26) Let A and E be any two events with positive probabilities: Statement - 1: Statement ? 2:     JEE Main Online Paper (Held On 19 April 2016)

A)
Both the statements are true

B)
Both the statements are false

C)
Statement-1 is true, Statement-2 is false

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

• question_answer27) Let and be respectively the mean, mode and variance of n observations andwhere   is any number. Statement I: Variance of  is Statement II: Mean and mode of areand ? M ? a, respectively.     JEE Main Online Paper (Held On 19 April 2016)

A)
Statement I and Statement II are both false

B)
Statement I and Statement II are both true

C)
Statement I is true and Statement II is false

D)
Statement I is false and Statement II is true

• question_answer28) The function is a periodic function with period:     JEE Main Online Paper (Held On 19 April 2016)

A)

B)

C)

D)

• question_answer29) The principal value of is:     JEE Main Online Paper (Held On 19 April 2016)

A)

B)

C)

D)

• question_answer30) The contrapositive of the statement 'if I am not feeling well, then I will go to the doctor' is     JEE Main Online Paper (Held On 19 April 2016)

A)
If I am feeling well, then I will not go to the doctor

B)
If I will go to the doctor, then I am feeling well

C)
If I will not go to the doctor, then I am feeling well

D)
If I will go to the doctor, then I am not feeling well.