# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2016)

### done JEE Main Paper (Held On 10 April 2016) Total Questions - 30

• question_answer1)           Let C be a curve given by$y(x)=1+\sqrt{4x-3},x>\frac{3}{4}$. If P is a point on C, such that the tangent at P has slope$\frac{2}{3}$, then a point through which the normal at P passes, is   JEE Main Online Paper (Held On 10 April 2016)

A)
(3, - 4)

B)
(1, 7)

C)
(4, - 3)

D)
(2, 3)

• question_answer2) Let $a{{ }_{1}},{{a}_{2}},{{a}_{3}}........\,\,{{a}_{n}}..........$be in A.P. If ${{a}_{3}}+{{a}_{7}}+{{a}_{11}}+{{a}_{15}}=72$ then the sum of its first 17 terms is equal to   JEE Main Online Paper (Held On 10 April 2016)

A)
153

B)
306

C)
612

D)
204

• question_answer3) If $A>0,\,B>0$and $B=\frac{\pi }{6}$, then the minimum value of tanA + tanB is   JEE Main Online Paper (Held On 10 April 2016)

A)
$2-\sqrt{3}$

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

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

D)
$4-2\sqrt{3}$

• question_answer4) The contrapositive of the following statement, ?If the side of a square doubles, then its area increases four times", is                   JEE Main Online Paper (Held On 10 April 2016)

A)
If the area of a square does not increase four times, then its side is not doubled.

B)
If the area of a square increases four times, then its side is not doubled.

C)
If the area of a square increases four times, then its side is doubled.

D)
If the side of a square is not doubled, then its area does not increase four times.

• question_answer5) Let A be a $3\times 3$ matrix such that ${{A}^{2}}-5A+7I=0$. Statement. - I : ${{A}^{-1}}=\frac{1}{7}(5I-A)$. Statement -II : The polynomial ${{A}^{3}}-2{{A}^{2}}-3A+I$ can be reduced to $5(A-41)$. Then   JEE Main Online Paper (Held On 10 April 2016)

A)
Statement- I is false, but Statement-II is true.

B)
Both the statements are false.

C)
Both the statements are true.

D)
Statement-I is true, but Statement-II is false.

• question_answer6) Equation of the tangent to the circle, at the point (1, - 1), whose centre is the point of intersection of the straight lines $x-y=1$ and $2x+y=3$ is   JEE Main Online Paper (Held On 10 April 2016)

A)
$3x-y-4=0$

B)
$x+4y+3=0$

C)
$x-3y-4=0$

D)
$4x+y-3=0$

• question_answer7) The sum$\sum\limits_{r=1\grave{\ }}^{10}{({{r}^{2}}+1)\times (r!)}$is equal to   JEE Main Online Paper (Held On 10 April 2016)

A)
$10\times (11!)$

B)
$101\times (10!)$

C)
$(11!)$

D)
$11\times (11!)$

• question_answer8) Let ABC be a triangle whose circumventer is at P. If the position vectors of A,B,C and P are $\overrightarrow{a}\,,\,\overrightarrow{b},\,\,\overrightarrow{c}$and$\frac{\overrightarrow{a}\,,\,+\overrightarrow{b},\,+\,\overrightarrow{c}}{4}$respectively, then the position vector of the orthocenter of this triangle, is   JEE Main Online Paper (Held On 10 April 2016)

A)
$\overrightarrow{0}$

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

C)
$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$

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

• question_answer9) Let $f(x)={{\sin }^{4}}x+{{\cos }^{4}}x$. Then f is an increasing function in the interval   JEE Main Online Paper (Held On 10 April 2016)

A)
$\left] \frac{\pi }{4},\frac{\pi }{2} \right[$

B)
$\left] \frac{5\pi }{8},\frac{3\pi }{4} \right[$

C)
$\left] 0,\frac{\pi }{4} \right[$

D)
$\left] \frac{\pi }{2},\frac{5\pi }{8} \right[$

• question_answer10) Let $z=1+ai$be a complex number, a > 0 such that ${{z}^{3}}$ is a real number. Then the sum $1+z+{{z}^{2}}+.....+{{z}^{11}}$is equal to   JEE Main Online Paper (Held On 10 April 2016)

A)
$-1250\sqrt{3}\,i$

B)
$1250\sqrt{3}\,i$

C)
$-1350\sqrt{3}\,i$

D)
$1365\sqrt{3}\,i$

• question_answer11) Let $P=\{\theta \,:\,\sin \theta -\cos \theta =\sqrt{2}\cos \theta =\sqrt{2}\cos \theta \}$and $Q=\{\theta :\sin +\cos \theta =\sqrt{2}\,\sin \theta \}$ be two sets. Then   JEE Main Online Paper (Held On 10 April 2016)

A)
$Q\,\not\subset P$

B)
$P\,\not\subset Q$

C)
$P\subset Q\,$and $Q-P\ne \phi$

D)
P = Q

• question_answer12) The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1,2 and 6, then the mean deviation from the mean of the data is   JEE Main Online Paper (Held On 10 April 2016)

A)
2.5

B)
2.8

C)
2.6

D)
2.4

• question_answer13) The number of distinct real values of $\lambda$ for which the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{2}=\frac{z+3}{{{}^{2}}}$and$\frac{x-3}{1}=\frac{y-2}{{{}^{2}}}=\frac{z-1}{2}$are coplanar is   JEE Main Online Paper (Held On 10 April 2016)

A)
3

B)
2

C)
1

D)
4

• question_answer14) The angle of elevation of the top of a vertical tower from a point A, due east of it is ${{45}^{o}}$. The angle of elevation of the top of the same tower from a point B, due south of A is ${{30}^{o}}$. If the distance between A and B is $54\sqrt{2}$m, then the height of the tower (in metres), is   JEE Main Online Paper (Held On 10 April 2016)

A)
54

B)
108

C)
$54\sqrt{3}$

D)
36 3

• question_answer15) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1-\cos 2x)}^{2}}}{2x\ \tan x-x{{\tan }^{2}}x}$is   JEE Main Online Paper (Held On 10 April 2016)

A)
$2$

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

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

D)
$-2$

• question_answer16) The solution of the differential equation$\frac{dy}{dx}+y\frac{y}{2}\sec \,x=\frac{\tan x}{2y}$, where$\le \,x<\frac{\pi }{2}$ and y(0) = 1, is given by   JEE Main Online Paper (Held On 10 April 2016)

A)
${{y}^{2}}=1-\frac{x}{\sec x\,+\tan x}$

B)
${{y}^{2}}=1+\frac{x}{\sec x\,+\tan x}$

C)
$y=1+\frac{x}{\sec x\,+\tan x}$

D)
$y=1-\frac{x}{\sec x\,+\tan x}$

• question_answer17) P and Q are two distinct points on the parabola, ${{y}^{2}}=4x$, with parameters t and ${{t}_{1}}$ respectively. If the normal at p passes through Q, then the minimum value of $t_{1}^{2}$ is   JEE Main Online Paper (Held On 10 April 2016)

A)
4

B)
6

C)
8

D)
2

• question_answer18) A hyperbola whose transverse axis is along the major axis of the conic,$\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is$\frac{3}{2}$, then which of the following points does NOT lie on it?   JEE Main Online Paper (Held On 10 April 2016)

A)
$\left( \sqrt{5},2\sqrt{2} \right)$

B)
$\left( 5,2\sqrt{3} \right)$

C)
$\left( 0,\,\,2 \right)$

D)
$\left( \sqrt{10},\,\,2\sqrt{3} \right)$

• question_answer19) For $x\,\in \,R,\,x\,\ne 0$, if y(x) is a differentiable function such that$x\int\limits_{1}^{x}{y(t)dt=(x+1)\int\limits_{1}^{x}{ty(t)dt}}$, then y(x) equals(where C is a constant)   JEE Main Online Paper (Held On 10 April 2016)

A)
$C{{x}^{3}}{{e}^{\frac{1}{x}}}$

B)
$\frac{C}{x}{{e}^{\frac{-1}{x}}}$

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

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

• question_answer20) ABC is a triangle in a plane with vertices A(2,3,5), B(-1,3,2) and C$(\lambda ,\,\,5,\,\,\mu )$. If the median through A is equally inclined to the coordinate axes, then the value of ($({{\lambda }^{3}}+{{\mu }^{3}}+5)$is   JEE Main Online Paper (Held On 10 April 2016)

A)
676

B)
1130

C)
1348

D)
1077

• question_answer21) A ray of light is incident along a line which meets another line, $7x-y+1=0$, at the point (0, 1). The ray is then reflected from this point along the line, $y+2x=1$. Then the equation of the line of incidence of the ray of light is   JEE Main Online Paper (Held On 10 April 2016)

A)
$41x+38y-38=0$

B)
$41x-38y+38=0$

C)
$41x+25y-25=0$0

D)
$41x-25y+25=0$

• question_answer22) A straight line through origin O meets the line $3y=10-4x$ and $8x+6y+5=0$ at points A and Respectively. Then O divides the segment AB in the ratio   JEE Main Online Paper (Held On 10 April 2016)

A)
3 : 4

B)
1 : 2

C)
2 : 3

D)
4 : 1

• question_answer23) The value of the integral$\int\limits_{4}^{10}{\frac{[{{x}^{2}}]dx}{[{{x}^{2}}-28x+196]+[{{x}^{2}}]}}$ , where [x] denotes the greatest integer less than or equal to x, is   JEE Main Online Paper (Held On 10 April 2016)

A)
3

B)
7

C)
6

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

• question_answer24) If $\frac{^{n+2}{{C}_{6}}}{^{n-2}{{P}_{2}}}=11$, then n satisfies the equation   JEE Main Online Paper (Held On 10 April 2016)

A)
${{n}^{2}}+n-110=0$

B)
${{n}^{2}}+5n-84=0$

C)
${{n}^{2}}+3n-180=0$

D)
${{n}^{2}}+2n-80=0$

• question_answer25) If the coefficients of ${{x}^{-2}}$ and ${{x}^{-4}}$ in the expansion of, ${{\left( {{x}^{\frac{1}{3}}}\frac{1}{2{{x}^{\frac{1}{3}}}} \right)}^{18}}$ , (x > 0) )are m and n respectively, then $\frac{m}{n}$ is equal to   JEE Main Online Paper (Held On 10 April 2016)

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

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

C)
$27$

D)
$182$

• question_answer26) If $A=\left[ \begin{matrix} -4 & -1 \\ 3 & 1 \\ \end{matrix} \right]$, then the determinant of the matrix $({{A}^{2016}}-2{{A}^{2015}}-{{A}^{2014}})$ is   JEE Main Online Paper (Held On 10 April 2016)

A)
$2014$

B)
$2016$

C)
$-175$

D)
$- 25$

• question_answer27) If x is a solution of the equation, $\sqrt{2x+1}-\sqrt{2x-1}=1\,,\,\,\left( x\le \frac{1}{2} \right)$ , then $\sqrt{4{{x}^{2}}-1}$ is equal to   JEE Main Online Paper (Held On 10 April 2016)

A)
$2$

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

C)
$2\sqrt{2}$

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

• question_answer28) An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is   JEE Main Online Paper (Held On 10 April 2016)

A)
$\frac{192}{729}$

B)
$\frac{256}{729}$

C)
$\frac{240}{729}$

D)
$\frac{496}{729}$

• question_answer29) The integral $\int{\frac{dx}{\left( 1+\sqrt{x} \right)\sqrt{x-{{x}^{2}}}}}$ is equal to (where C is a constant of integration)   JEE Main Online Paper (Held On 10 April 2016)

A)
$-2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C$

B)
$-2\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C$

C)
$-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C$

D)
$2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C$

• question_answer30) Let a,b $\in$ R, $(a\ne 0)$ If the function f defined as $f(x)=\left\{ \begin{matrix} 2{{x}^{2}}, & 0\le x<1 \\ a, & {} \\ a, & 1\le x<\sqrt{2} \\ \frac{2{{b}^{2}}-4b}{{{x}^{3}}} & \sqrt{2}\le x<\infty \\ \end{matrix} \right.$

A)
$\left( \sqrt{2},1-\sqrt{3} \right)$

B)
$\left( \sqrt{2},1-\sqrt{3} \right)$

C)
$\left( \sqrt{2},-1+\sqrt{3} \right)$

D)
$\left( -\sqrt{2},1+\sqrt{3} \right)$