# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2011

### done AIEEE Solved Paper-2011 Total Questions - 30

• question_answer1) Consider 5 independent Bernoulli?s trials each with probability of success $\rho$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $\rho$ lies in the interval.   AIEEE  Solved  Paper-2011

A)
$\left( \frac{11}{12},1 \right]$

B)
$\left( \frac{1}{2},\frac{3}{4} \right]$

C)
$\left( \frac{3}{4},\frac{11}{12} \right]$

D)
$\left[ 0,\frac{1}{2} \right]$

• question_answer2) The coefficient of ${{x}^{7}}$in the expansion of${{(1-x-{{x}^{2}}+{{x}^{3}})}^{6}}$ is;   AIEEE  Solved  Paper-2011

A)
132

B)
144

C)
$-132$

D)
$-144$

• question_answer3) $\underset{x\to 2}{\mathop{\lim }}\,\left( \frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2} \right)$.   AIEEE  Solved  Paper-2011

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

B)
Does not exist

C)
Equals $\sqrt{2}$

D)
Equals $-\sqrt{2}$

• question_answer4) Let R be the set of real numbers. Statement-1: $A=\{(x,y)\in R\times R:y-x$ is an integer} is an equivalence relation on R. Statement-2: $B=\{(x,y)\in R\times R:x=\alpha y$ for some rational number ?} is an equivalence relation on R.   AIEEE  Solved  Paper-2011

A)
Statement-1 is false, Statement-2 is true

B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

C)
Statement-1 is true, Statement-2 is true Statement-2 is not a correct explanation for Statement-1

D)
Statement-1 is true, Statement-2 is false

• question_answer5) Let $\alpha ,\beta$ be real and z be a complex number. If ${{z}^{2}}+\alpha z+\beta =0$ has two distinct roots on the line Re $z=1$, then it is necessary that.   AIEEE  Solved  Paper-2011

A)
$\beta \in (1,\infty )$

B)
$\beta \in (0,1)$

C)
$\beta \in (-1,0)$

D)
$\left| \beta \right|=1$

• question_answer6) $\frac{{{d}^{2}}x}{d{{y}^{2}}}$ equals.   AIEEE  Solved  Paper-2011

A)
$-\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right){{\left( \frac{dy}{dx} \right)}^{-3}}$

B)
${{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}$

C)
$-{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}{{\left( \frac{dy}{dx} \right)}^{-3}}$

D)
$\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right){{\left( \frac{dy}{dx} \right)}^{-2}}$

• question_answer7) The number of values of k for which the linear equations $4x+ky+2z=0$ $kx+4y+z=0$ $\left. 2x+2y+z=0 \right|$ possess a non-zero solution is.   AIEEE  Solved  Paper-2011

A)
Zero

B)
3

C)
2

D)
1

• question_answer8) Statement-1: The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line : $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$. Statement-2: The line: $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).   AIEEE  Solved  Paper-2011

A)
Statement-1 is false, Statement-2 is true

B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

D)
Statement-1 is true, Statement-2 is false

• question_answer9) Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ?Suman is brilliant and dishonest if and only if Suman is rich? can be expressed as.   AIEEE  Solved  Paper-2011

A)
$\sim (P\wedge \sim R)\leftrightarrow Q$

B)
$\sim P\wedge (Q_{2}^{2}\sim R)$

C)
$\sim (Q_{2}^{2}(P\wedge R))$

D)
$\sim Q\leftrightarrow \sim P\wedge R$

• question_answer10) The lines ${{L}_{1}}:y-x=0$ and ${{L}_{2}}:2x+y=0$ intersect the line ${{L}_{3}}:y+2=0$ at P and Q respectively. The bisector of the acute angle between ${{L}_{1}}$ and ${{L}_{2}}$ intersects ${{L}_{3}}$ at R. Statements 1 : The ratio PR : RQ equals $2\sqrt{2}:\sqrt{5}$. Statement 2 : In any traingle, bisector of an angle divides the triangle into two similar triangles.   AIEEE  Solved  Paper-2011

A)
Statement-1 is true, Statement-2 is false

B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is the not the correct explanation of Statement-1

D)
Statement-1 is false, Statement-2 is true

• question_answer11) A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.   AIEEE  Solved  Paper-2011

A)
21 months

B)
18 months

C)
19 months

D)
20 months

• question_answer12) Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity $(-3,1)$$\sqrt{\frac{2}{5}}$ is.   AIEEE  Solved  Paper-2011

A)
$5{{x}^{2}}+3{{y}^{2}}-32=0$

B)
$3{{x}^{2}}+5{{y}^{2}}-32=0$

C)
$5{{x}^{2}}+3{{y}^{2}}-48=0$

D)
$3{{x}^{2}}+5{{y}^{2}}-15=0$

• question_answer13) If $A={{\sin }^{2}}x+{{\cos }^{4}}x$, then for all real $x$.   AIEEE  Solved  Paper-2011

A)
$\frac{3}{4}\le A\le \frac{13}{16}$

B)
$\frac{3}{4}\le A\le 1$

C)
$\frac{13}{16}\le A\le 1$

D)
$1\le A\le 2$

• question_answer14) The value of $\int\limits_{0}^{1}{\frac{8\log \left( 1+x \right)}{1+{{x}^{2}}}dx}$ is.   AIEEE  Solved  Paper-2011

A)
$\log 2$

B)
$\pi \log 2$

C)
$\frac{\pi }{8}\log 2$

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

• question_answer15) If the angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\lambda }$and the plane $x+2y+3z=4$ is ${{\cos }^{-1}}\left( \sqrt{\frac{5}{14}} \right)$, then $\lambda$ equals.   AIEEE  Solved  Paper-2011

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

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

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

D)
$\frac{2}{5}$

• question_answer16) For $x\in \left( 0,\frac{5\lambda }{2} \right)$, define $f\left( x \right)=\int\limits_{0}^{x}{\sqrt{t}\sin t\,\,dt}$ Then $f$ has.   AIEEE  Solved  Paper-2011

A)
Local maximum at $\pi$ and local $2\pi$

B)
Local maximum at $\pi$ and $2\pi$

C)
Local minimum at $\pi$ and $2\pi$

D)
Local minimum at $\pi$ and local maximum at $2\pi$

• question_answer17) The domain of the function $f(x)=\frac{1}{\sqrt{\left| x \right|-x}}$ is.   AIEEE  Solved  Paper-2011

A)
$\left( -\infty ,\infty \right)-\{0\}$

B)
$\left( -\infty ,\infty \right)$

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

D)
$\left( -\infty ,0 \right)$

• question_answer18) If the mean deviation about the median of the numbers $a,2a,\,........\,,50a$ is 50, then $\left| a \right|$ equals.   AIEEE  Solved  Paper-2011

A)
5

B)
2

C)
3

D)
4

• question_answer19) If $\vec{a}=\frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})$ and $b=\frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k})$, then the value of $(2\vec{a}-\vec{b}.[(\vec{a}\times \vec{b})\times (\vec{a}+2\vec{b})]$is.   AIEEE  Solved  Paper-2011

A)
3

B)
$-5$

C)
$-3$

D)
5

• question_answer20) The values of p and q for which the function f(x)=\left\{ \begin{align} & \frac{\sin (p+1)x+sinx}{x},\,\,\,\,\,\,x & q,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ & \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{3/2}}},\,\,\,\,\,\,\,x>0 \\ \end{align} \right.  is continuous for all $x$ in R, are.   AIEEE  Solved  Paper-2011

A)
$p=\frac{1}{2},q=\frac{3}{2}$

B)
$p=\frac{1}{2},q=-\frac{3}{2}$

C)
$p=\frac{5}{2},q=\frac{1}{2}$

D)
$p=-\frac{3}{2},q=\frac{1}{2}$

• question_answer21) The two circles ${{x}^{2}}+{{y}^{2}}=ax$ and${{x}^{2}}+{{y}^{2}}={{c}^{2}}(c>0)$ touch each other, if   AIEEE  Solved  Paper-2011

A)
$\left| a \right|=2c$

B)
$2\left| a \right|=c$

C)
$\left| a \right|=c$

D)
$a=2c$

• question_answer22) Let I be the purchase value of an equipment and                                                                                                       $V(t)$  be the value after it has been used for t years. The value                                                                                                       $V(t)$  depreciates at a rate given by differential equation                                                                            $\frac{dV(t)}{dt}=-k(T-t)$, where $k>0$ is a constant and T is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is.   AIEEE  Solved  Paper-2011

A)
${{e}^{-kT}}$

B)
${{T}^{2}}-\frac{I}{k}$

C)
$I-\frac{k{{T}^{2}}}{2}$

D)
$I-\frac{k{{\left( T-t \right)}^{\left. 2 \right|}}}{2}$

• question_answer23) If C and D are two events such that $C\subset D$ and $P(D)\ne 0$, then the correct statement among the following is.   AIEEE  Solved  Paper-2011

A)
$P(C|D)=\frac{P(D)}{P(C)}$

B)
$P(C|D)=P(C)$

C)
$P(C|D)\ge P(C)$

D)
$P(C|D)<P(C)$

• question_answer24) Let A and B be two symmetric matrices of order 3. Statement-1: A(BA) and (AB)A are symmetric matrices. Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.   AIEEE  Solved  Paper-2011

A)
Statement-1 is false, Statement-2 is true

B)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

D)
Statement-1 is true, Statement-2 is false

• question_answer25) If $\omega \,(\ne 1)$ is a cube root of unity, and${{(1+\omega )}^{7}}=A+B\omega$. Then (A, B) equals.   AIEEE  Solved  Paper-2011

A)
(?1, 1)

B)
(0, 1)

C)
(1, 1)

D)
(1, 0)

• question_answer26) Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^{9}{{C}_{3}}$. Statement-2: The number of ways of choosing any 3 places from 9 different places is $^{9}{{C}_{3}}$.   AIEEE  Solved  Paper-2011

A)
Statement-1 is false, Statement-2 is true

B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

D)
Statement-1 is true, Statement-2 is false

• question_answer27) The shortest distance between line $y-x=1$ and curve $x={{y}^{2}}$ is.   AIEEE  Solved  Paper-2011

A)
$\frac{4}{\sqrt{3}}$

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

C)
$\frac{3\sqrt{2}}{8}$

D)
$\frac{8}{3\sqrt{2}}$

• question_answer28) The area of the region enclosed by the curves $y=x$, $x=e,y=\frac{1}{x}$ and the positive x-axis is.   AIEEE  Solved  Paper-2011

A)
$\frac{5}{2}$ square units

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

C)
1 square units

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

• question_answer29) If $\frac{dy}{dx}=y+3>0$ and $y(0)=2$, then $y(In\,\,2)$ is equal to.   AIEEE  Solved  Paper-2011

A)
$-2$

B)
7

C)
5

D)
13

• question_answer30) The vectors $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying $\vec{b}\times \vec{c}=\vec{b}\times \vec{d}$and $\vec{a}.\,\vec{d}=0$. Then the vector $\vec{d}$ is equal to   AIEEE  Solved  Paper-2011

A)
$\vec{c}-\left( \frac{\vec{a}.\,\vec{c}}{a.\,\vec{b}} \right)\vec{b}$

B)
$\vec{b}-\left( \frac{\vec{b}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{c}$

C)
$\vec{b}+\left( \frac{\vec{a}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{b}$

D)
$\vec{b}+\left( \frac{\vec{b}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{c}$