Solved papers for JEE Main & Advanced JEE Main Solved Paper-2014

done JEE Main Solved Paper-2014 Total Questions - 30

• question_answer1) The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$in the plane $2x-y+z+3=0$is the line:   JEE Main  Solved  Paper-2014

A)
$\frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}$

B)
$\frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}$

C)
$\frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}$

D)
$\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}$

• question_answer2) If the coefficients of ${{x}^{3}}$and ${{x}^{4}}$ in the expansion of $(1+ax+b{{x}^{2}}){{(1-2x)}^{18}}$in powers of x are both zero, then (a, b) is equal to:   JEE Main  Solved  Paper-2014

A)
$\left( 16,\frac{251}{3} \right)$

B)
$\left( 14,\frac{251}{3} \right)$

C)
$\left( 14,\frac{272}{3} \right)$

D)
$\left( 16,\frac{272}{3} \right)$

• question_answer3) If $a\in R$and the equation $-3{{(x-[x])}^{2}}+2(x-[x])+{{a}^{2}}=0$(where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of alie in the interval:   JEE Main  Solved  Paper-2014

A)
$(-1,0)\cup (0,1)$

B)
$(-2,-1)$

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

• question_answer4) If $\left[ \vec{a}\times \vec{b}\,\vec{b}\times \vec{c}\,\vec{c}\times \vec{a} \right]=\lambda {{\left[ \vec{a}\,\vec{b}\,\,\vec{c} \right]}^{2}}$then$\lambda$is equal to:   JEE Main  Solved  Paper-2014

A)
2

B)
3

C)
0

D)
1

• question_answer5) The variance of first 50 even natural numbers is:   JEE Main  Solved  Paper-2014

A)
$\frac{833}{4}$

B)
$833$

C)
$437$

D)
$\frac{437}{4}$

• question_answer6) A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is $45{}^\circ$. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is:   JEE Main  Solved  Paper-2014

A)
$40\left( \sqrt{2}-1 \right)$

B)
$40\left( \sqrt{3}-\sqrt{2} \right)$

C)
$20\sqrt{2}$

D)
$20\left( \sqrt{3}-1 \right)$

• question_answer7) The integral$\int\limits_{0}^{\pi }{\sqrt{1+4{{\sin }^{2}}\frac{x}{2}-4\sin \frac{x}{2}}dx}$equals:   JEE Main  Solved  Paper-2014

A)
$\pi -4$

B)
$\frac{2\pi }{3}-4-4\sqrt{3}$

C)
$4\sqrt{3}-4$

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

• question_answer8) The statement $\tilde{\ }(p\leftrightarrow \tilde{\ }q)$ is:   JEE Main  Solved  Paper-2014

A)
equivalent to $p\leftrightarrow q$

B)
equivalent to $\tilde{\ }p\leftrightarrow q$

C)
a tautology

D)
a fallacy

• question_answer9) If A is an $3\times 3$ non ? singular matrix such that AA′ = A′A and B = A−1 A′, then BB′ equals:   JEE Main  Solved  Paper-2014

A)
$I+B$

B)
$I$

C)
${{B}^{-1}}$

D)
$({{B}^{-1}})'$

• question_answer10) The integral$\int_{{}}^{{}}{\left( 1+x-\frac{1}{x} \right)}{{e}^{x+\frac{1}{x}}}dx$is equal to   JEE Main  Solved  Paper-2014

A)
$(x-1){{e}^{x+\frac{1}{x}}}+c$

B)
$x{{e}^{x+\frac{1}{x}}}+c$

C)
$(x+1){{e}^{x+\frac{1}{x}}}+c$

D)
$-x{{e}^{x+\frac{1}{x}}}+c$

• question_answer11) If z is a complex number such that$|z|\ge 2,$then the minimum value of $\left| z+\frac{1}{2} \right|:$   JEE Main  Solved  Paper-2014

A)
is equal to $\frac{5}{2}$

B)
lies in the interval (1, 2)

C)
is strictly greater than $\frac{5}{2}$

D)
is strictly greater than $\frac{3}{2}$but less than $\frac{5}{2}$

• question_answer12) If g is the inverse of a function f and $(x)=\frac{1}{1+{{x}^{5}}},$then g′ (x) is equal to :   JEE Main  Solved  Paper-2014

A)
$1+{{x}^{5}}$

B)
$5{{x}^{4}}$

C)
$\frac{1}{1+{{\left\{ g(x) \right\}}^{5}}}$

D)
$1+{{\{g(x)\}}^{5}}$

• question_answer13) If$\alpha ,\beta \ne 0,$and$f(n)={{\alpha }^{n}}+{{\beta }^{n}}$and$\left| \begin{matrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \\ \end{matrix} \right|=K$${{(1-\alpha )}^{2}}{{(1-\beta )}^{2}}{{(\alpha -\beta )}^{2}},$then K is equal to:   JEE Main  Solved  Paper-2014

A)
$\alpha \beta$

B)
$\frac{1}{\alpha \beta }$

C)
$1$

D)
$-1$

• question_answer14) Let ${{f}_{k}}(x)=\frac{1}{k}(si{{n}^{k}}x+co{{s}^{k}}x),$where$x\in R$and$k\ge 1.$Then${{f}_{4}}(x)-{{f}_{6}}(x)$equals:   JEE Main  Solved  Paper-2014

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

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

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

D)
$\frac{1}{12}$

• question_answer15) Let $\alpha$ and $\beta$ be the roots of equation $p{{x}^{2}}+qx+r=0,p\ne 0.$If p, q, r are in A.P. and $\frac{1}{\alpha }+\frac{1}{\beta }=4,$then the value of $|\alpha -\beta |$is :   JEE Main  Solved  Paper-2014

A)
$\frac{\sqrt{61}}{9}$

B)
$\frac{2\sqrt{17}}{9}$

C)
$\frac{\sqrt{34}}{9}$

D)
$\frac{2\sqrt{13}}{9}$

• question_answer16) Let A and B be two events such that $P(\overline{A\cup B})=\frac{1}{16}.P(A\cap B)=\frac{1}{4}$and$P(\overline{A})=\frac{1}{4},$where$\overline{A}$stands for the complement of the event A. Then the events A and B are :   JEE Main  Solved  Paper-2014

A)
mutually exclusive and independent.

B)
equally likely but not independent.

C)
independent but not equally likely.

D)
independent and equally likely.

• question_answer17) If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6,then for some $c\in \}0,1[:$   JEE Main  Solved  Paper-2014

A)
$2f'(c)=g'(c)$

B)
$2f'(c)=3g'(c)$

C)
$f'(c)=g'(c)$

D)
$f'(c)=2g'(c)$

• question_answer18) Let the population of rabbits surviving at a time t be governed by the differential equation$\frac{dp(t)}{dt}=\frac{1}{2}p(t)-200.$ If $p(0)=100,$then p(t) equals :   JEE Main  Solved  Paper-2014

A)
$400-300\,{{\text{e}}^{\text{t/2}}}$

B)
$300-200\,{{\text{e}}^{\text{-t/2}}}$

C)
$600-500\,{{\text{e}}^{\text{t/2}}}$

D)
$400-300\,{{\text{e}}^{\text{-t/2}}}$

• question_answer19) Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to :   JEE Main  Solved  Paper-2014

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

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

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

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

• question_answer20) The area of the region described by $A=\{(x,\text{ }y):{{x}^{2}}+{{y}^{2}}\le 1$and ${{y}^{2}}\le 1-x\}$is   JEE Main  Solved  Paper-2014

A)
$\frac{\pi }{2}+\frac{4}{3}$

B)
$\frac{\pi }{2}-\frac{4}{3}$

C)
$\frac{\pi }{2}-\frac{2}{3}$

D)
$\frac{\pi }{2}+\frac{2}{3}$

• question_answer21) Let a, b, c and d be non−zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$and $5bx+2by+d=$ lies in the fourth quadrant and is equidistant from the two axes then : JEE Main  Solved  Paper-2014

A)

B)

C)

D)

• question_answer22) Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R (7, 3). The equation ofthe line passing through (1, −1) and parallel to PS is :   JEE Main  Solved  Paper-2014cc

A)
$4x-7y-11=0$

B)
$2x+9y+7=0$

C)
$4x+7y+3=0$

D)
$2x-9y-11=0$

• question_answer23) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi co{{s}^{2}}x)}{{{x}^{2}}}$is equal to:   JEE Main  Solved  Paper-2014

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

B)
1

C)
$-\pi$

D)
$\pi$

• question_answer24) If $X=\{{{4}^{n}}-1:n\varepsilon N\}$ and$Y=\{9(n-1):n\varepsilon N\},$ where N is the set of natural numbers, then $X\cup Y$ is equal to :   JEE Main  Solved  Paper-2014

A)
N

B)
Y − X

C)
X

D)
Y

• question_answer25) The locus of the foot of perpendicular drawn from the centre of the ellipse ${{x}^{2}}+3{{y}^{2}}=6$ on any tangent to it is :   JEE Main  Solved  Paper-2014

A)
${{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}$

B)
${{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}$

C)
${{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}$

D)
${{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}$

• question_answer26) Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :   JEE Main  Solved  Paper-2014

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

B)
$3+\sqrt{2}$

C)
$2-\sqrt{3}$

D)
$2+\sqrt{3}$

• question_answer27) If ${{(10)}^{9}}+2{{(11)}^{1}}{{(10)}^{8}}+3{{(11)}^{2}}{{(10)}^{7}}+...+10$${{(11)}^{9}}=k{{(10)}^{9}},$then k is equal to :   JEE Main  Solved  Paper-2014

A)
$\frac{121}{10}$

B)
$\frac{441}{100}$

C)
$100$

D)
$110$

• question_answer28) The angle between the lines whose direction cosines satisfy the equations $\ell +m+n=0$and${{\ell }^{2}}={{m}^{2}}+{{n}^{2}}$is :   JEE Main  Solved  Paper-2014

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

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

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

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

• question_answer29) The slope of the line touching both the parabolas ${{y}^{2}}=4x$and ${{x}^{2}}=-32y$is :   JEE Main  Solved  Paper-2014

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

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

C)
$\frac{1}{8}$

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

• question_answer30) If x = −1 and x = 2 are extreme points of $f(x)=\alpha log|x|+\beta {{x}^{2}}+x$then :   JEE Main  Solved  Paper-2014

A)
$\alpha =-6,\beta =\frac{1}{2}$

B)
$\alpha =-6,\beta =-\frac{1}{2}$

C)
$\alpha =2,\beta =-\frac{1}{2}$

D)
$\alpha =2,\beta =\frac{1}{2}$