# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2010

### done AIEEE Solved Paper-2010 Total Questions - 30

• question_answer1) Consider the following relations $R=\{(x,y)|x,y$are real numbers and$x=wy$for some rational number w}; $S=\left\{ \left( \frac{m}{n},\frac{p}{q} \right) \right\}=|m,n,p$and q are integers such that$n,q\ne 0$and$qm=pn\}$. Then -

A)
R is an equivalence relation but S is not an equivalence relation

B)
Neither R nor S is an equivalence relation

C)
S is an equivalence relation but R is not an equivalence relation

D)
R and S both are equivalence relations

• question_answer2)   The number of complex numbers z such that $|z-1|=|z+1|=|z-i|$equals -       AIEEE  Solved  Paper-2010

A)
0

B)
1

C)
2

D)
$\infty$

• question_answer3)   If$\alpha$and$\beta$are the roots of the equation ${{x}^{2}}x$$+1=0,$ then${{\alpha }^{2009}}+{{\beta }^{2009}}=$       AIEEE  Solved  Paper-2010

A)
-2

B)
-1

C)
1

D)
2

• question_answer4) Consider the system of linear equations : ${{x}_{1}}+2{{x}_{2}}+{{x}_{3}}=3$ $2{{x}_{1}}+3{{x}_{2}}+{{x}_{3}}=3$ $3{{x}_{1}}+5{{x}_{2}}+2{{x}_{3}}=1$ The system has       AIEEE  Solved  Paper-2010

A)
Infinite number of solutions

B)
Exactly 3 solutions

C)
a unique solution

D)
No solution

• question_answer5)   There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is -       AIEEE  Solved  Paper-2010

A)
3

B)
36

C)
66

D)
108

• question_answer6)   Let$f:(1,1)\to R$be a differentiable function with$f(0)=1$and$f'(0)=1.$Let$~g(x)=$ $=[f{{(2f(x)+2]}^{2}}$Then$g'(0)=$       AIEEE  Solved  Paper-2010

A)
4

B)
-4

C)
0

D)
-2

• question_answer7) Let$f:R\to R$be a positive increasing function with $\underset{x\to \infty }{\mathop{\lim }}\,\frac{f(3x)}{f(x)}=1$.Then $\underset{x\to \infty }{\mathop{\lim }}\,\frac{f(2x)}{f(x)}=$       AIEEE  Solved  Paper-2010

A)
1

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

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

D)
3

• question_answer8) Let$p(x)$be a function defined on R such that $p'(x)=p'(1x),$for all$x\in [0,1],p(0)=1$and$p(1)=41.$ Then $\int\limits_{0}^{1}{p(x)}dx$equals -       AIEEE  Solved  Paper-2010

A)
$\sqrt{41}$

B)
21

C)
41

D)
42

• question_answer9)   A person is to count 4500 currency notes. Let ${{a}_{n}}$denote the number of notes he counts in the${{n}^{th}}$minute. If${{a}_{1}}={{a}_{2}}=....={{a}_{10}}=150$and${{a}_{10}},{{a}_{11}},...$are in an AP with common difference ? 2, then the time taken by him to count all notes is -       AIEEE  Solved  Paper-2010

A)
24 minutes

B)
34 minutes

C)
125 minutes

D)
135 minutes

• question_answer10) The equation of the tangent to the curve$y=x+\frac{4}{{{x}^{2}}},$that is parallel to the x ? axis, is -       AIEEE  Solved  Paper-2010

A)
y = 0

B)
y = 1

C)
y = 2

D)
y = 3

• question_answer11)   The area bounded by the curves$y=cos\text{ }x$and$y=sin\text{ }x$between the ordinates $x=0$and$x=\frac{3\pi }{2}$is -       AIEEE  Solved  Paper-2010

A)
$4\sqrt{2}-2$

B)
$4\sqrt{2}+2$

C)
$4\sqrt{2}-1$

D)
$4\sqrt{2}+1$

• question_answer12)    Solution of the differential equation$cos\text{ }x\text{ }dy=$ $y(sin\text{ }xy)dx,$ $0<x<\frac{\pi }{2}$is -       AIEEE  Solved  Paper-2010

A)
$sec\text{ }x=(tan\text{ }x+c)y$

B)
$y\text{ }sec\text{ }x=tan\text{ }x+c$

C)
$y\text{ }tan\text{ }x=sec\text{ }x+c$

D)
$tan\text{ }x=(sec\text{ }x+c)y$

• question_answer13)   Let$\overrightarrow{a}=\hat{j}-\hat{k}$and$\overrightarrow{c}=\hat{i}-\hat{j}-\hat{k}$Then the vector $\overrightarrow{b}$satisfying$\overrightarrow{a}\times \overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and$\overrightarrow{a}.\overrightarrow{b}=3$is -       AIEEE  Solved  Paper-2010

A)
$-\hat{i}+\hat{j}-2\hat{k}$

B)
$2\hat{i}-\hat{j}+2\hat{k}$

C)
$\hat{i}-\hat{j}-2\hat{k}$

D)
$\hat{i}+\hat{j}-2\hat{k}$

• question_answer14)   If the vectors $\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k},\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}$and $\overrightarrow{c}=\lambda \hat{i}-\hat{j}+\mu \hat{k}$are mutually orthogonal, then $(\lambda ,\mu )=$       AIEEE  Solved  Paper-2010

A)
(-3, 2)

B)
(2, -3)

C)
(-2, 3)

D)
(3, -2)

• question_answer15)   If two tangents drawn from a point P to the parabola${{y}^{2}}=4x$are at right angles, then the locus of P is       AIEEE  Solved  Paper-2010

A)
$x=1$

B)
$2x+1=0$

C)
$x=1$

D)
$2x1=0$

• question_answer16)   The line L given by $\frac{x}{5}+\frac{y}{b}=1$passes through the point (13, 32). The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$.Then the distance between L and K is -       AIEEE  Solved  Paper-2010

A)
$\frac{23}{\sqrt{15}}$

B)
$\sqrt{17}$

C)
$\frac{17}{\sqrt{15}}$

D)
$\frac{23}{\sqrt{17}}$

• question_answer17) A line AB in three dimensional space makes angles$45{}^\circ$and$120{}^\circ$with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle$\theta$with the positive z-axis, then$\theta$equals -       AIEEE  Solved  Paper-2010

A)
$30{}^\circ$

B)
$45{}^\circ$

C)
$60{}^\circ$

D)
$75{}^\circ$

• question_answer18)   Let S be a non- empty subset of R. Consider the following statement: P: There is a rational number$x\in S$such that$x>0$ Which of the following statements is the negation of the statement P?       AIEEE  Solved  Paper-2010

A)
There is a rational number$x\in S$such that $x\le 0$

B)
There is no rational number$x\in S$such that $x\le 0$

C)
Every rational number$x\in S$satisfies $x\le 0$

D)
$x\in S$and$x\le 0$ $\Rightarrow$$x$is not rational

• question_answer19)   Let $\cos (\alpha +\beta )=\frac{4}{5}$and let,$sin(\alpha -\beta )=\frac{5}{13}$where$0\le \alpha ,\beta \le \frac{\pi }{4}$.Then tan$2\alpha =$         AIEEE  Solved  Paper-2010

A)
$\frac{25}{16}$

B)
$\frac{56}{33}$

C)
$\frac{19}{12}$

D)
$\frac{20}{7}$

• question_answer20) The circle${{x}^{2}}+{{y}^{2}}=4x+8y+5$intersects the line$3x4y=m$at two distinct points if       AIEEE  Solved  Paper-2010

A)
$85<m<35$

B)
$35<m<15$

C)
$15<m<65$

D)
$35<m<85$

• question_answer21)   For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is -       AIEEE  Solved  Paper-2010

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

B)
$\frac{11}{2}$

C)
$6$

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

• question_answer22)   An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is -       AIEEE  Solved  Paper-2010

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

B)
$\frac{2}{7}$

C)
$\frac{1}{21}$

D)
$\frac{2}{23}$

• question_answer23)   For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is -       AIEEE  Solved  Paper-2010

A)
There is a regular polygon with $\frac{r}{R}=\frac{1}{2}$

B)
There is a regular polygon with $\frac{r}{R}=\frac{1}{\sqrt{2}}$

C)
There is a regular polygon with $\frac{r}{R}=\frac{2}{3}$

D)
There is a regular polygon with $\frac{r}{R}=\frac{\sqrt{3}}{2}$

• question_answer24)   The number of$3\times 3$non - singular matrices, with four entries as 1 and all other entries as 0, is -       AIEEE  Solved  Paper-2010

A)
Less than 4

B)
5

C)
6

D)
at least 7

• question_answer25)   Let$f:R\to R$be defined by $f(x)=\left\{ \begin{matrix} k-2x, & if & x\le -1 \\ 2x+3, & if & x>-1 \\ \end{matrix} \right.$ If$f$has a local minimum at$x=1,$then a possible value of k is       AIEEE  Solved  Paper-2010

A)
1

B)
0

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

D)
$-1$

• question_answer26) Directions: Questions number 86 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is$\frac{1}{85}$ Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is $(\pm 1,\pm 2,\pm 3,\pm 4,\pm 5\}$ Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.       AIEEE  Solved  Paper-2010

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

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

C)
Statement -1 is true, Statement -2 is false.

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

• question_answer27) Directions: Questions number 87 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let ${{S}_{1}}=\sum\limits_{j=1}^{10}{j{{(j-1)}^{10}}}{{C}_{j}},{{S}_{2}}=\sum\limits_{j=1}^{10}{{{j}^{10}}{{C}_{j}}}$and ${{S}_{3}}=\sum\limits_{j=1}^{10}{{{j}^{2}}^{10}{{C}_{j}}}$ Statement ? 1: ${{S}_{3}}=55\times {{2}^{9}}.$ Statement ? 2:${{S}_{1}}=90\times {{2}^{8}}$and${{S}_{2}}=10\times {{2}^{8}}.$ Statement ? 1 (Assertion) and Statement ? 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.       AIEEE  Solved  Paper-2010

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

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

C)
Statement -1 is true, Statement -2 is false.

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

• question_answer28) Directions: Questions number 88 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement - 1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane$xy+z=5.$ Statement - 2: The plane$xy+z=5$bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.     AIEEE  Solved  Paper-2010

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

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

C)
Statement -1 is true, Statement -2 is false.

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

• question_answer29) Directions: Questions number 89 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let$f:R\to R$be a continuous function defined by $f(x)=\frac{1}{{{e}^{x}}+2{{e}^{-x}}}$ Statement - 1: $f(c)=\frac{1}{3},$for some$c\in R$. Statement - 2: $0<f(x)\le \frac{1}{2\sqrt{2}},$for all $x\in R$. Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.     AIEEE  Solved  Paper-2010

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

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

C)
Statement -1 is true, Statement -2 is false.

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

• question_answer30) Directions: Questions number 90 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a $2\times 2$ matrix with non zero entries and let${{A}^{2}}=I,$where I is$2\times 2$identity matrix. Define Tr(A) = sum of diagonal elements of A and $|A|=$determinant of matrix A. Statement - 1 : Tr(A) = 0 Statement - 2 : $|A|=1$ Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.     AIEEE  Solved  Paper-2010

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

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

C)
Statement -1 is true, Statement -2 is false.

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