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