# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2015)

### done JEE Main Paper (Held On 10 April 2015) Total Questions - 30

• question_answer1) A factory is operating in two shirts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the workers is Rs. 60, then per day mean wage of the night shift workers (in Rs.) is: JEE Main Online Paper (Held On 10 April 2015)

A)
74

B)
66

C)
75

D)
69

• question_answer2) If Rolle's theorem holds for the function $f(x)=2{{x}^{3}}+b{{x}^{2}}+cx,x\in [-1,1],$at the point $x=\frac{1}{2},$then 2b +c equals    JEE Main Online Paper (Held On 10 April 2015)

A)
2

B)
- 1

C)
-3

D)
1

• question_answer3) The area (in square units) of the region bounded by the curves $y+2{{x}^{2}}=0$and $y+3{{x}^{2}}=1,$is equal to : JEE Main Online Paper (Held On 10 April 2015)

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

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

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

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

• question_answer4) The points $\left( 0,\frac{8}{3} \right),(1,3)$and (82, 30) : JEE Main Online Paper (Held On 10 April 2015)

A)
form an acute angled triangle.

B)
form a right angled triangle.

C)
form an obtuse angled triangle.

D)
lie on a straight line.

• question_answer5) The least value of the product xyz for which the determinant $\left| \begin{matrix} x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z \\ \end{matrix} \right|$is non-negative, is : JEE Main Online Paper (Held On 10 April 2015)

A)
$- 1$

B)
$-2\sqrt{2}$

C)
$-16\sqrt{2}$

D)
$- 8$

• question_answer6) The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is: JEE Main Online Paper (Held On 10 April 2015)

A)
1120

B)
1960

C)
1880

D)
1240

• question_answer7) If the points $(1,1\lambda )$and (-3, 0, 1) are equidistant    from    the    plane, $3x+4y-12z+13=0,$then $\lambda$ satisfies the equation : JEE Main Online Paper (Held On 10 April 2015)

A)
$3{{x}^{2}}-10x+21=0$

B)
$3{{x}^{2}}-10x+7=0$

C)
$3{{x}^{2}}+10x+7=0$

D)
$3{{x}^{2}}+10x-13=0$

• question_answer8) If $f(x)=2ta{{n}^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right),x>1,$then f(5) is equal to : JEE Main Online Paper (Held On 10 April 2015)

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

B)
$\pi$

C)
${{\tan }^{-1}}\left( \frac{65}{156} \right)$

D)
$4{{\tan }^{-1}}(5)$

• question_answer9) If $2+3i$ is one of the roots of the equation $2{{x}^{3}}-9{{x}^{2}}+kx-13=0,k\in R,$ then the real root of this equation : JEE Main Online Paper (Held On 10 April 2015)

A)
exists and is equal to 1.

B)
does not exist.

C)
exists and is equal to$\frac{1}{2}$.

D)
exists and is equal to$\frac{1}{2}$

• question_answer10) An ellipse passes through the foci of the hyperbola, $9{{x}^{2}}-4{{y}^{2}}=36$and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is$\frac{1}{2},$ then which of the following points does not lie on the ellipse? JEE Main Online Paper (Held On 10 April 2015)

A)
$(\sqrt{13},0)$

B)
$\left( \sqrt{\frac{13}{2}},\sqrt{6} \right)$

C)
$\left( \frac{1}{2}\sqrt{13},\frac{\sqrt{3}}{2} \right)$

D)
$\left( \frac{\sqrt{39}}{2},\sqrt{3} \right)$

• question_answer11) Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : JEE Main Online Paper (Held On 10 April 2015)

A)
28

B)
31

C)
29.5

D)
26.5

• question_answer12) In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :  5% families own both a car and a phone.   35% families own either a car or a phone.    40,000 families live in the town. Then, JEE Main Online Paper (Held On 10 April 2015)

A)
only  and  are correct.

B)
Only  and  are correct.

C)
All ,  and  are correct.

D)
Only  and  are correct.

• question_answer13) For $x>0,$let $f(x)=\int\limits_{1}^{x}{\frac{\log t}{1+t}}dt.$ Then  $f(x)+f\left( \frac{1}{x} \right)$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{1}{4}\log {{x}^{2}}$

B)
$\frac{1}{4}{{(\log x)}^{2}}$

C)
$\frac{1}{2}{{(\log x)}^{2}}$

D)
$\log x$

• question_answer14) If the coefficients of the three successive terms in the binomial expansion of ${{(1+x)}^{n}}$are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is : JEE Main Online Paper (Held On 10 April 2015)

A)
8th

B)
6th

C)
9th

D)
7th

• question_answer15) Let $\overset{\to }{\mathop{a}}\,$ arid $\overset{\to }{\mathop{b}}\,$ be two unit vectors such that|$\left| \overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\, \right|=\sqrt{3}.$If$\overset{\to }{\mathop{c}}\,=\overset{\to }{\mathop{a}}\,+2\overset{\to }{\mathop{b}}\,+3\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right),$then $2|\overset{\to }{\mathop{c}}\,|$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$\sqrt{51}$

B)
$\sqrt{37}$

C)
$\sqrt{43}$

D)
$\sqrt{55}$

• question_answer16) Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If ${{L}_{1}}$ is the line perpendicular to L and passing through the point (-2, 1),then the point of intersection of I and L JEE Main Online Paper (Held On 10 April 2015)

A)
$\left( \frac{3}{5},\frac{23}{10} \right)$

B)
$\left( \frac{11}{20},\frac{29}{10} \right)$

C)
$\left( \frac{4}{5},\frac{12}{5} \right)$

D)
$\left( \frac{3}{10},\frac{17}{5} \right)$

• question_answer17) In a $\Delta ABC,\frac{a}{b}=2+\sqrt{3}$and $\angle C={{60}^{o}}.$ Then the ordered pair $(\angle A,\angle B)$is equal to: JEE Main Online Paper (Held On 10 April 2015)

A)
$({{105}^{o}},{{15}^{o}})$

B)
$({{45}^{o}},{{75}^{o}})$

C)
$({{15}^{o}},{{105}^{o}})$

D)
$({{75}^{o}},{{45}^{o}})$

• question_answer18) Let the tangents drawn to the circle, ${{x}^{2}}+{{y}^{2}}=16$from the point P(0/ h) meet me r-axis at points A and B. If the area of $\Delta APB$is minimum, men h is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
$4\sqrt{2}$

B)
$4\sqrt{3}$

C)
$3\sqrt{2}$

D)
$3\sqrt{3}$

• question_answer19) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{\sin }^{2}}x}$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
3

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

C)
2

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

• question_answer20) The value of $\sum\limits_{r=16}^{30}{(r+2)(r-3)}$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
7785

B)
7775

C)
7780

D)
7770

• question_answer21) If $y+3x=0$ is the equation of a chord of the circle, ${{x}^{2}}+{{y}^{2}}-30x=0,$then the equation of the circle with this chord as diameter is: JEE Main Online Paper (Held On 10 April 2015)

A)
${{x}^{2}}+{{y}^{2}}+3x+9y=0$

B)
${{x}^{2}}+{{y}^{2}}-3x+9y=0$

C)
${{x}^{2}}+{{y}^{2}}-3x-9y=0$

D)
${{x}^{2}}+{{y}^{2}}+3x-9y=0$

• question_answer22) The integral $\int_{{}}^{{}}{\frac{dx}{{{(x+1)}^{\frac{3}{4}}}{{(x-2)}^{\frac{5}{4}}}}}$is equal to: JEE Main Online Paper (Held On 10 April 2015)

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

B)
$-\frac{4}{3}{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C$

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

D)
$-\frac{4}{3}{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C$

• question_answer23) The distance, from the origin, of the normal to the curve, $x=2\cos t+2t\sin t,$$y=2\sin t-2t\cos t$at$t=\frac{\pi }{4},$is: JEE Main Online Paper (Held On 10 April 2015)

A)
2

B)
$\sqrt{2}$

C)
$2\sqrt{2}$

D)
4

• question_answer24) If the shortest distance between the lines $\frac{x-1}{\alpha }=\frac{y+1}{-1}=\frac{z}{1},(\alpha \ne -1)$and$x+y+z+1=0=2x-y+z+3$is$\frac{1}{\sqrt{3}},$ a value of $\alpha$ is : JEE Main Online Paper (Held On 10 April 2015)

A)
$-\frac{16}{19}$

B)
$-\frac{19}{16}$

C)
$\frac{19}{32}$

D)
$\frac{32}{19}$

• question_answer25) If$A=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right],$ then which one of the following statements is not correct ? JEE Main Online Paper (Held On 10 April 2015)

A)
${{A}^{4}}-I={{A}^{2}}+I$

B)
${{A}^{3}}+I=A({{A}^{3}}-I)$

C)
${{A}^{3}}-I=A(A-I)$

D)
${{A}^{2}}+I=A({{A}^{2}}-I)$

• question_answer26) Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is : JEE Main Online Paper (Held On 10 April 2015)

A)
$\frac{({{2}^{10}}-1)}{{{2}^{20}}}$

B)
$\frac{({{2}^{10}}-1)}{{{2}^{10}}}$

C)
$\frac{^{20}{{C}_{10}}}{{{2}^{10}}}$

D)
$\frac{^{20}{{C}_{10}}}{{{2}^{20}}}$

• question_answer27) If the tangent to the conic,$y-6={{x}^{2}}$at (2, 10) touches the circle, ${{x}^{2}}+{{y}^{2}}+8x-2y=k$(for some fixed k) at a point $(\alpha ,\beta );$ then $(\alpha ,\beta )$is : JEE Main Online Paper (Held On 10 April 2015)

A)
$\left( -\frac{7}{17},\frac{6}{17} \right)$

B)
$\left( -\frac{8}{17},\frac{2}{17} \right)$

C)
$\left( -\frac{4}{17},\frac{1}{17} \right)$

D)
$\left( -\frac{6}{17},\frac{10}{17} \right)$

• question_answer28) The contrapositive of the statement "If it is raining, then I will not come", is : JEE Main Online Paper (Held On 10 April 2015)

A)
If I will come, then it is raining.

B)
If I will not come, then it is raining.

C)
I will come, then it is not raining.

D)
If I will not come, then it is not raining.

• question_answer29) The largest value of r for which the region represented by the set$\{\omega \in C/|\omega -4-i|\le r\}$is contained in the region represented by the set $\{z\in C/|z-1|\le |z+i|\},$is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
$2\sqrt{2}$

B)
$\sqrt{17}$

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

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

• question_answer30) If y(x) is the solution of the differential equation $(x+2)\frac{dy}{dx}={{x}^{2}}+4x-9,x\ne -2$and $y(0)=0,$then $y(-4)$ is equal to : JEE Main Online Paper (Held On 10 April 2015)

A)
-1

B)
2

C)
1

D)
0