# Solved papers for JEE Main & Advanced JEE Main Solved Paper-2015

### done JEE Main Solved Paper-2015 Total Questions - 30

• question_answer1) Let$\vec{a},\vec{b}$and$\vec{c}$be three non - zero vectors such that no two of them are collinear and$\left( \vec{a}\times \vec{b} \right)\times \vec{c}=\frac{1}{3}\left| {\vec{b}} \right|\left| {\vec{c}} \right|\vec{a}.$If $\theta$is the angle between vectors $\vec{b}$and $\vec{c},$then a value of $\sin \theta$is : [JEE Main Solved Paper-2015 ]

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

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

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

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

• question_answer2) Let O be the vertex and Q be any point on the parabola, ${{x}^{2}}=8y.$If the point P divides the line segment OQ internally in the ratio 1:3, then locus of P is : [JEE Main Solved Paper-2015 ]

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

B)
${{x}^{2}}=2y$

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

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

• question_answer3) If the angles of elevation of the top of a tower from three collinear points A,B and C, on a line leading to the foot of the tower, are 300, 450 and 600 respectively, then the ratio, AB : BC, is : [JEE Main Solved Paper-2015 ]

A)
$1:\sqrt{3}$

B)
$2:3$

C)
$\sqrt{3}:1$

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

• question_answer4) The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $\left( 0,0 \right),\left( 0,41 \right)$ and $\left( 41,0 \right),$ is [JEE Main Solved Paper-2015 ]

A)
820

B)
780

C)
901

D)
861

• question_answer5) The equation of the plane containing the line $2x-5y+z=3;x+y+4z=5,$ and parallel to the plane, $x+3y+6z=1,$ is : [JEE Main Solved Paper-2015 ]

A)
$x+3y+6z=7$

B)
$x+6y+12z=-13$

C)
$2x+6y+12z=13$

D)
$x+3y+6z=-7$

• question_answer6) Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A\times B,$ each having at least three elements is : [JEE Main Solved Paper-2015 ]

A)

B)
275

C)
510

D)
219

E)
256

• question_answer7) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\left( 1-\cos 2x \right)\left( 3+\cos x \right)}{x\tan 4x}$is equal to : [JEE Main Solved Paper-2015 ]

A)
2

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

C)
4

D)
3

• question_answer8) The distance of the point $\left( 1,0,2 \right)$from the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$and the plane $x-y+z=16,$ is : [JEE Main Solved Paper-2015 ]

A)
$3\sqrt{21}$

B)
13

C)
$2\sqrt{14}$

D)
8

• question_answer9) The sum of coefficients of integral powers of x in the binomial expansion of ${{\left( 1-2\sqrt{x} \right)}^{50}}$is [JEE Main Solved Paper-2015 ]

A)
$\frac{1}{2}\left( {{3}^{50}}-1 \right)$

B)
$\frac{1}{2}\left( {{2}^{50}}+1 \right)$

C)
$\frac{1}{2}\left( {{3}^{50}}+1 \right)$

D)
$\frac{1}{2}\left( {{3}^{50}} \right)$

• question_answer10) The sum of first 9 terms of the series$\frac{{{1}^{3}}}{1}+\frac{{{1}^{3}}+{{2}^{3}}}{1+3}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+3+5}$...............is: [JEE Main Solved Paper-2015 ]

A)
142

B)
192

C)
71

D)
96

• question_answer11) athematics The area (in sq. units ) of the region described by [JEE Main Solved Paper-2015 ]

A)
$\frac{15}{64}$

B)
$\frac{9}{32}$

C)
$\frac{7}{32}$

D)
$\frac{5}{64}$

• question_answer12) The set of all values of $\lambda$for which the system of linear equations: $2{{x}_{1}}-2{{x}_{2}}+{{x}_{3}}=\lambda {{x}_{1}}$ $2{{x}_{1}}-3{{x}_{2}}+2{{x}_{3}}=\lambda {{x}_{2}}$ $-{{x}_{1}}+2{{x}_{2}}=\lambda {{x}_{3}}$has a non- trivial solution, [JEE Main Solved Paper-2015 ]

A)
Contains two elements

B)
Contains more than two elements.

C)
Is an empty set

D)
Is a singleton.

• question_answer13) A complex number z is said to be unimodular if $\left| z \right|=1.$Suppose ${{z}_{1}}$ and ${{z}_{2}}$ are complex numbers such that $\frac{{{z}_{1}}-2{{z}_{2}}}{2-{{z}_{1}}{{\overline{z}}_{2}}}$is unimodular and ${{z}_{2}}$ is not unimodular. Then the point ${{z}_{1}}$ lies on a : [JEE Main Solved Paper-2015 ]

A)

B)

C)
Straight line parallel to x-axis

D)
Straight line parallel to y-axis Solut

• question_answer14) The number of common tangents to the circles ${{x}^{2}}+{{y}^{2}}-4x-6y-12=0$ and ${{x}^{2}}+{{y}^{2}}+6y+18y+26=0,$ is [JEE Main Solved Paper-2015 ]

A)
3

B)
4

C)
1

D)
2

• question_answer15) The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8, without repetition is : [JEE Main Solved Paper-2015 ]

A)
120

B)
72

C)
216

D)
192

• question_answer16) Let y(x) be the solution of the differential equation $\left( x\log x \right)\frac{dy}{dx}+y=2x\log x,(x\ge 1).$ The y (e)is equal to [JEE Main Solved Paper-2015 ]

A)
2

B)
2e

C)
e

D)
0

• question_answer17) If $A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \\ \end{matrix} \right]$is a matrix satisfying the equation $A{{A}^{T}}=9I,$ where I is $3\times 3$ identity matrix, then the ordered pair (a,b) is equal to : [JEE Main Solved Paper-2015 ]

A)
(2,1)

B)
-(-2,-1)

C)
(2,-1)

D)
(-2,1)

• question_answer18) ) If m is the A.M. of two distinct real numbers $l$ and $n\left( l,n>1 \right)$and ${{G}_{1}},{{G}_{2}}$and ${{G}_{3}}$ are three geometric means between $l$ and n, then $G_{1}^{4}+2G_{2}^{4}+G_{3}^{4}$equals. [JEE Main Solved Paper-2015 ]

A)
$4lm{{n}^{2}}$

B)
$4{{l}^{2}}{{m}^{2}}{{n}^{2}}$

C)
$4{{l}^{2}}mn$

D)
$4l{{m}^{2}}n$

• question_answer19) The negation of $\tilde{\ }s\vee \left( \tilde{\ }r\wedge s \right)$is equivalent to : [JEE Main Solved Paper-2015 ]

A)
$s\vee \left( r\vee \tilde{\ }s \right)$

B)
$s\wedge r$

C)
$s\wedge \tilde{\ }r$

D)
$s\wedge \left( r\wedge \tilde{\ }s \right)$

• question_answer20) The integral$\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{\left( {{x}^{4}}+1 \right)}^{{}^{3}/{}_{4}}}}}$equals: [JEE Main Solved Paper-2015 ]

A)
$-{{\left( {{x}^{4}}+1 \right)}^{\frac{1}{4}}}+c$

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

C)
${{\left( \frac{{{x}^{4}}+1}{{{x}^{4}}} \right)}^{\frac{1}{4}}}+c$

D)
${{\left( {{x}^{4}}+1 \right)}^{\frac{1}{4}}}+c$

• question_answer21) The normal to the curve ${{x}^{2}}+2xy-3{{y}^{2}}=0,$ at (1, 1) : [JEE Main Solved Paper-2015 ]

A)
meets the curve again in the third quadrant.

B)
meets the curve again in the fourth quadrant.

C)
does not meet the curve again.

D)
meets the curve again in the second quadrant.

• question_answer22) Let ${{\tan }^{-1}}y={{\tan }^{-1}}x+{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right),$where $|x|<\frac{1}{\sqrt{3}}.$Then a value of y is : [JEE Main Solved Paper-2015 ]

A)
$\frac{3x-{{x}^{3}}}{1+3{{x}^{2}}}$

B)
$\frac{3x+{{x}^{3}}}{1+3{{x}^{2}}}$

C)
$\frac{3x-{{x}^{3}}}{1-3{{x}^{2}}}$

D)
$\frac{3x+{{x}^{3}}}{1-3{{x}^{2}}}$

• question_answer23) If the function. g\left( x \right)=\left\{ \begin{align} & k\sqrt{x+1},\,\,\,\,\,\,0\le x\le 3 \\ & mx+2,\,\,\,\,\,\,\,\,3<x\le 5 \\ \end{align} \right.is differentiable, then the value of k + m is : [JEE Main Solved Paper-2015 ]

A)
$\frac{10}{3}$

B)
4

C)
2

D)
$\frac{16}{5}$

• question_answer24) The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3,4 and 5 are added to the data, then the mean of the resultant data, is: [JEE Main Solved Paper-2015 ]

A)
15.8

B)
14.0

C)
16.8

D)
16.0

• question_answer25) The integral $\int\limits_{2}^{4}{\frac{\log {{x}^{2}}}{\log {{x}^{2}}+\log \left( 36-12x+{{x}^{2}} \right)}dx}$ is equal to : [JEE Main Solved Paper-2015 ]

A)
1

B)
6

C)
2

D)
4

• question_answer26) Let $\alpha$ and $\beta$ be the roots of equation ${{x}^{2}}-6x-2=0.$ If ${{a}_{n}}={{\alpha }^{n}}-{{\beta }^{n}},$ for $n\ge 1,$ then the value $\frac{{{a}_{10}}-2{{a}_{8}}}{2{{a}_{9}}}$is equal to : [JEE Main Solved Paper-2015 ]

A)
3

B)
-3

C)
6

D)
-6

• question_answer27) Let f (x) be a polynomial of degree four having extreme values at x = 1 and x =2. If$\underset{x\to 0}{\mathop{\lim }}\,\left( 1+\frac{f\left( x \right)}{{{x}^{2}}} \right)=3,$then f(2) is equal to : [JEE Main Solved Paper-2015 ]

A)
0

B)
4

C)
-8

D)
-4

• question_answer28) The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse$\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1,$is: [JEE Main Solved Paper-2015 ]

A)
$\frac{27}{2}$

B)
27

C)
$\frac{27}{4}$

D)
18

• question_answer29) If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is : [JEE Main Solved Paper-2015 ]

A)
$220{{\left( \frac{1}{3} \right)}^{12}}$

B)
$22{{\left( \frac{1}{3} \right)}^{11}}$

C)
$\frac{55}{3}{{\left( \frac{2}{3} \right)}^{11}}$

D)
$55{{\left( \frac{2}{3} \right)}^{10}}$

• question_answer30) Locus of the image of the point $\left( 2,3 \right)$in the line$\left( 2x-3y+4 \right)+k\left( x-2y+3 \right)=0,$$k\in R,$ is a : [JEE Main Solved Paper-2015 ]

A)
circle of radius $\sqrt{2}$

B)
circle of radius $\sqrt{3}$

C)
straight line parallel to x - axis

D)
straight line parallel to y - axis