# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

### done JEE Main Paper (Held On 11 April 2015) Total Questions - 30

• question_answer1) Let $A=\{{{x}_{1}},{{x}_{2}},...,{{x}_{7}}\}$and $B=\{{{y}_{1}},{{y}_{2}},{{y}_{3}}\}$be two sets containing seven and three distinct elements respectively. Then the total number of functions$f:A\to B$ that are onto, if there exist exactly three elements x in A such that$f(x)={{y}_{2}},$ is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$14.{{\,}^{7}}{{C}_{2}}$

B)
$16.{{\,}^{7}}{{C}_{3}}$

C)
$12.{{\,}^{7}}{{C}_{2}}$

D)
$14.{{\,}^{7}}{{C}_{3}}$

• question_answer2) If z is a non-real complex number, then the minimum value of $\frac{\operatorname{Im}\,{{z}^{5}}}{{{(Im\,z)}^{5}}}$is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
-1

B)
-2

C)
-4

D)
-5

• question_answer3) If the two roots of the equation, $(a-1)({{x}^{4}}+{{x}^{2}}+1)+(a+1){{({{x}^{2}}+x+1)}^{2}}=0$are real and distinct, then the set of all values of 'a' is: [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$(-\infty ,-2)\cup (2,\infty )$

C)
$\left( -\frac{1}{2},0 \right)\cup \left( 0,\frac{1}{2} \right)$

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

• question_answer4) If A is a $3\times 3$ matrix such that |5. adjA| = 5, then A| is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\pm \frac{1}{5}$

B)
$\pm \,5$

C)
$\pm \,1$

D)
$\pm \,\frac{1}{25}$

• question_answer5) $\left| \begin{matrix} {{x}^{2}}+x & x+1 & x-2 \\ 2{{x}^{2}}+3x-1 & 3x & 3x-3 \\ {{x}^{2}}+2x+3 & 2x-1 & 2x-1 \\ \end{matrix} \right|=ax-12,$then 'a' is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
12

B)
24

C)
-12

D)
-24

• question_answer6) If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
10

B)
12

C)
9

D)
6

• question_answer7) The term independent of x in the binomial expansion of$\left( 1-\frac{1}{x}+3{{x}^{5}} \right){{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{8}}$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
400

B)
406

C)
-400

D)
-496

• question_answer8) The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
7290

B)
320

C)
640

D)
2430

• question_answer9) If $\sum\limits_{n=1}^{5}{\frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3},}$then k is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{55}{336}$

B)
$\frac{17}{105}$

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

D)
$\frac{19}{112}$

• question_answer10) Let k be a non-zero real number. If\begin{align} & f(x)=\left\{ \frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{k} \right)\log \left( 1+\frac{x}{4} \right)},x\ne 0 \right. \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,12\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,x=0 \\ \end{align} is a continuous function, then the value of k is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
1

B)
2

C)
3

D)
4

• question_answer11) The equation of a normal to the curve,$\sin y=x\sin \left( \frac{\pi }{3}+y \right)$ at $x=0,$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$2x+\sqrt{3}y=0$

B)
$2x-\sqrt{3}x=0$

C)
$2y+\sqrt{3}x=0$

D)
$2x-\sqrt{3}y=0$ $x=0\Rightarrow y=0$

• question_answer12) Let k and K be the minimum and the maximum values of the function$f(x)=\frac{{{(1+x)}^{0.6}}}{1+{{x}^{0.6}}}$in $[0,1]$respectively, then the ordered pair (k, K) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$(1,{{2}^{0.6}})$

B)
$({{2}^{-0.4}}1,{{2}^{0.6}})$

C)
$({{2}^{-0.6}},1)$

D)
$({{2}^{-0.4}},1)$

• question_answer13) From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g=32\text{ }m/{{s}^{2}},$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
100

B)
88

C)
128

D)
112

• question_answer14) 2015 / If $\int_{{}}^{{}}{\frac{\log \left( t+\sqrt{1+{{t}^{2}}} \right)}{\sqrt{1+{{t}^{2}}}}}dt=\frac{1}{2}{{\left( g(t) \right)}^{2}}+C,$where C is a constant, then g(2) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$2\log (2+\sqrt{5})$

B)
$\log (2+\sqrt{5})$

C)
$\frac{1}{\sqrt{5}}\log (2+\sqrt{5})$

D)
$\frac{1}{2}\log (2+\sqrt{5})$

• question_answer15) Let $f:R\to R$be a function such that$f(2-x)=f\,(2+x)$ and$f(4-x)=f\,(4+x),$for all $x\in R$and $\int\limits_{0}^{2}{f(x)}dx=5.$Then the value of $\int\limits_{10}^{50}{f(x)}\,dx$is:

A)
80

B)
100

C)
125

D)
200

• question_answer16) Let $f:(-1,1)\to R$ be a continuous function. If $\int\limits_{0}^{\sin x}{f(t)dt}=\frac{\sqrt{3}}{2}x,$ then$f\left( \frac{\sqrt{3}}{2} \right)$is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$\sqrt{3}$

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

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

• question_answer17) The solution of the differential equation $ydx-(x+2{{y}^{2}})dy=0$is$x=f(y).$ If $f(-1)=1,$ then$f(1)$is equal to: [JEE Main Online Paper (Held On 11 April 2015)]

A)
4

B)
3

C)
2

D)
1

• question_answer18) A straight line L through the point (3, - 2) is inclined at an angle of 60° to the line $\sqrt{3}x+y=1.$If L also intersects the x-axis, then the equation of L is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$y+\sqrt{3}x+2-3\sqrt{3}=0$

B)
$y-\sqrt{3}x+2+3\sqrt{3}=0$

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

D)
$\sqrt{3}y+x-3+2\sqrt{3}=0$

• question_answer19) If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is $3x+4y+3=0,$ then the equation of the circumcircle of this triangle is : [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
${{x}^{2}}+{{y}^{2}}-2x-2y-14=0$

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

D)
${{x}^{2}}+{{y}^{2}}-2x-2y-7=0$

• question_answer20) If a circle passing through the point (-1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is : [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$\frac{5}{2}$

C)
3

D)
5

• question_answer21) If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is : [JEE Main Online Paper (Held On 11 April 2015)]

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

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

C)
$\sqrt{2}-1$

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

• question_answer22) Let PQ be a double ordinate of the parabola, ${{y}^{2}}=-4x,$where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$9{{y}^{2}}=4x$

B)
$9{{y}^{2}}=-4x$

C)
$3{{y}^{2}}=2x$

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

• question_answer23) The shortest distance between the z-axis and the line $x+y+2z-3=0=2x+3y+4z-4,$ is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
1

B)
2

C)
3

D)
4

• question_answer24) A plane containing the point (3, 2, 0) and the line $\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}$also contains the point : [JEE Main Online Paper (Held On 11 April 2015)]

A)
(0, -3, 1)

B)
(0, 7, 10)

C)
(0, 7, -10)

D)
(0, 3, 1)

• question_answer25) In a parallelogram $ABCD,\left| \overrightarrow{AB} \right|=a,\left| \overrightarrow{AD} \right|=b$and $\left| \overrightarrow{AC} \right|=c,$ then $\overrightarrow{AB}.\overrightarrow{AB}$ has the value : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{2}\left( {{a}^{2}}-{{b}^{2}}+{{c}^{2}} \right)$

B)
$\frac{1}{4}\left( {{a}^{2}}+{{b}^{2}}-{{c}^{2}} \right)$

C)
$\frac{1}{3}\left( {{b}^{2}}+{{c}^{2}}-{{a}^{2}} \right)$

D)
$\frac{1}{2}\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}} \right)$

E)
None of these

• question_answer26) If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{26}$

B)
$\frac{1}{27}$

C)
$\frac{1}{21}$

D)
$\frac{1}{15}$

• question_answer27) If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{16}$

B)
$\frac{9}{16}$

C)
$\frac{3}{4}$

D)
$\frac{15}{16}$

• question_answer28) If $\cos \alpha +\cos \beta =\frac{3}{2}$and $\sin \alpha +\sin \beta =\frac{1}{2}$and $\theta$is the arithmetic mean of $\alpha$ and $\beta ,$ then $\sin 2\theta +\cos 2\theta$is equal to: [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$\frac{4}{5}$

C)
$\frac{7}{5}$

D)
$\frac{8}{5}$

• question_answer29) Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $\alpha$at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from 0 is 'a' ; then the distance between two consecutive poles, is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{h\sin \alpha +a\cos \alpha }{9\sin \alpha }$

B)
$\frac{h\cos \alpha -a\sin \alpha }{9\cos \alpha }$

C)
$\frac{h\cos \alpha -a\sin \alpha }{9\sin \alpha }$

D)
$\frac{h\sin \alpha +a\cos \alpha }{9\cos \alpha }$

• question_answer30) Consider the following statements : P : Suman is brilliant. Q : Suman is rich. R : Suman is honest. The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\wedge R$

B)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee R$

C)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee \tilde{\ }R$

D)
$\tilde{\ }Q\leftrightarrow P\wedge \tilde{\ }R$