# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2009

### done AIEEE Solved Paper-2009 Total Questions - 30

• question_answer1) Let a, b, c be such that$b(a+c)\ne 0$. If $\left| \begin{matrix} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \\ \end{matrix} \right|+\left| \begin{matrix} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ {{(-1)}^{n+2}}a & {{(-1)}^{n+1}}b & {{(-1)}^{n}}c \\ \end{matrix} \right|=0,$ then the value of n is     AIEEE  Solved  Paper-2009

A)
zero

B)
any even integer

C)
any odd integer

D)
any integer

• question_answer2) If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ... , 1 + 100d from their mean is 255, then the d is equal to     AIEEE  Solved  Paper-2009

A)
10.0

B)
20.0

C)
10.1

D)
20.2

• question_answer3) If the roots of the equation$b{{x}^{2}}+cx+a=0$be imaginary, then for all real values of$x,$the expression$3{{b}^{2}}{{x}^{2}}+6bcx+2{{c}^{2}}$is     AIEEE  Solved  Paper-2009

A)
greater than 4ab

B)
less than 4ab

C)
greater than -4ab

D)
less than -4ab

• question_answer4) Let A and B denote the statements $A:\text{ }cos\,\alpha +cos\beta +cos\,\gamma =0$ $B:\text{ }sin\,\alpha +sin\,\beta +sin\,\gamma =0$ If$cos(\beta \gamma )+cos(\gamma \alpha )+cos(\alpha \beta )=3/2,$ then     AIEEE  Solved  Paper-2009

A)
A is true and B is false

B)
A is false and B is true

C)
both A and B are true

D)
both A and B are false

• question_answer5) The lines$p({{p}^{2}}+1)xy+q=0$and ${{({{p}^{2}}+1)}^{2}}x+({{p}^{2}}+1)y+2q=0$are perpendicular to a common line for     AIEEE  Solved  Paper-2009

A)
no value of p

B)
exactly one value of p

C)
exactly two values of p

D)
more than two values of p

• question_answer6) If A, B and C are three sets such that $A\cap B=A\cap C$and$A\cup B=A\cup C,$then     AIEEE  Solved  Paper-2009

A)
$A=B$

B)
$A=C$

C)
$B=C$

D)
$A\cap B=\phi$

• question_answer7) If $\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$are non-coplanar vectors and p, q are real numbers, then the equality$[3\overrightarrow{u},\text{ }p\overrightarrow{v},p\overrightarrow{w}]-[p\overrightarrow{v},\overrightarrow{w},q\overrightarrow{u}]-[2\overrightarrow{w},q\overrightarrow{v},q\overrightarrow{u}]=0$holds for     AIEEE  Solved  Paper-2009

A)
exactly one value of (p, q)

B)
exactly two values of (p, q)

C)
more than two but not all values of (p, q)

D)
all values of (p, q)

• question_answer8) Let the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$lie in the plane$x+3y\alpha z+\beta =0.$Then $(\alpha ,\,\,\beta )$ equals     AIEEE  Solved  Paper-2009

A)
(6, - 17)

B)
(-6, 7)

C)
(5, -15)

D)
(-5, 5)

• question_answer9) From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is     AIEEE  Solved  Paper-2009

A)
less than 500

B)
at least 500 but less than 750

C)
at least 750 but less than 1000

D)
at least 1000

• question_answer10) $\int\limits_{0}^{\pi }{[\cot x]dx,}$where [.] denotes the greatest integer function, is equal to   AIEEE  Solved  Paper-2009 v

A)
$\pi /2$

B)
1

C)
$-1$

D)
$-\pi /2$

• question_answer11) For real$x,$let$f(x)={{x}^{3}}+5x+1,$then     AIEEE  Solved  Paper-2009

A)
f is one-one but not onto R

B)
f is onto R but not one-one

C)
f is one-one and onto R

D)
f is neither one-one nor onto R

• question_answer12) In a binomial distribution $B\left( n,p=\frac{1}{4} \right),$if  the probability of at least one success is greater than or equal to$\frac{9}{10}$, then n is greater than     AIEEE  Solved  Paper-2009

A)
$\frac{1}{\log _{10}^{4}-\log _{10}^{3}}$

B)
$\frac{1}{\log _{10}^{4}+\log _{10}^{3}}$

C)
$\frac{9}{\log _{10}^{4}-\log _{10}^{3}}$

D)
$\frac{4}{\log _{10}^{4}-\log _{10}^{3}}$

• question_answer13) If P and Q are the points of intersection of the circles${{x}^{2}}+{{y}^{2}}+3x+7y+2p5=0$and ${{x}^{2}}+{{y}^{2}}+2x+2y{{p}^{2}}=0,$then there is a circle passing through P, Q and (1, 1) for     AIEEE  Solved  Paper-2009

A)
all values of p

B)
all except one value of p

C)
all except two values of p

D)
exactly one value of p

• question_answer14) The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines of the vector are     AIEEE  Solved  Paper-2009

A)
6, -3, 2

B)
$\frac{6}{5},\frac{-3}{5},\frac{2}{5}$

C)
$\frac{6}{7},\frac{-3}{7},\frac{2}{7}$

D)
$\frac{-6}{7},\frac{-3}{7},\frac{2}{7}$

• question_answer15) If$\left| Z-\frac{4}{z} \right|=2,$then the maximum value of |Z| is equal to     AIEEE  Solved  Paper-2009

A)
$\sqrt{3}+1$

B)
$\sqrt{5}+1$

C)
2

D)
$2+\sqrt{2}$

• question_answer16) Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) is equal to$\frac{1}{3}$. Then the circumcentre of the triangle ABC is at the point     AIEEE  Solved  Paper-2009

A)
(0, 0)

B)
$\left( \frac{5}{4},0 \right)$

C)
$\left( \frac{5}{2},0 \right)$

D)
$\left( \frac{5}{3},0 \right)$

• question_answer17) The remainder left out when${{8}^{2n}}{{(62)}^{2n+1}}$ is divided by 9 is     AIEEE  Solved  Paper-2009

A)
0

B)
2

C)
7

D)
8

• question_answer18) The ellipse${{x}^{2}}+4{{y}^{2}}=4$is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is     AIEEE  Solved  Paper-2009

A)
${{x}^{2}}+16{{y}^{2}}=16$

B)
${{x}^{2}}+12{{y}^{2}}=16$

C)
$4{{x}^{2}}+48{{y}^{2}}=48$

D)
$4{{x}^{2}}+64{{y}^{2}}=48$

• question_answer19) The sum to infinity of the series $1+\frac{2}{3}+\frac{6}{{{3}^{2}}}+\frac{10}{{{3}^{3}}}\frac{14}{{{3}^{4}}}+....$is

A)
2

B)
3

C)
4

D)
6

• question_answer20) The differential equation which represents the family of curves$y={{c}_{1}}{{e}^{{{C}_{2}}x}},$where${{c}_{1}}$and ${{c}_{2}}$are arbitrary constants, is     AIEEE  Solved  Paper-2009

A)
$y'={{y}^{2}}$

B)
$y''=y'y$

C)
$yy''=y'$

D)
$yy''={{(y')}^{2}}$

• question_answer21) One ticket is selected at random from 50 tickets numbered 00, 01, 02, ... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals     AIEEE  Solved  Paper-2009

A)
1/14

B)
1/7

C)
5/14

D)
1/50

• question_answer22) Let y be an implicit function of x defined by ${{x}^{2x}}2{{x}^{x}}coty1=0.$Then y?(1) equals     AIEEE  Solved  Paper-2009

A)
-1

B)
1

C)
$log\text{ }2$

D)
$\text{ }log2$

• question_answer23) The area of the region bounded by the parabola${{(y2)}^{2}}=x1,$the tangent to the parabola at the point (2, 3) and the x-axis is

A)
3

B)
6

C)
9

D)
12

• question_answer24) Given$P(x)={{x}^{4}}+a{{x}^{3}}+cx+d$such that$x=0$is the only real root of$P'(x)=0$. If $P(1)<P(1),$then in the interval [-1, 1].     AIEEE  Solved  Paper-2009

A)
P(-1) is the minimum and P(1) is the maximum of P

B)
P(-1) is not minimum but P(1) is the maximum of P

C)
P(-1) is the minimum but P(1) is not the maximum of P

D)
neither P(-1) is the minimum nor P(1) is the maximum of P

• question_answer25) The shortest distance between the line $yx=1$and the curve$x={{y}^{2}}$is     AIEEE  Solved  Paper-2009

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

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

C)
$\frac{3\sqrt{2}}{5}$

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

• question_answer26) Directions: Questions No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let $f(x)={{(x+1)}^{2}}1,\text{ }x\ge 1$ Statement - 1: The set$\{x:f(x)={{f}^{-1}}(x)\}$ $=\{0,\text{ }1\}$. Statement - 2: f is a bijection.     AIEEE  Solved  Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement 1: The variance of first n even natural numbers is $\frac{{{n}^{2}}-1}{4}$ Statement 2: The sum of first n natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first n natural numbers is$\frac{n(n+1)(2n+1)}{6}$     AIEEE  Solved  Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice.   Statement 1:$\tilde{\ }(p\leftrightarrow \tilde{\ }q)$is equivalent to$p\leftrightarrow q$ Statement 2:$\tilde{\ }(p\leftrightarrow \tilde{\ }q)$is a tautology     AIEEE  Solved  Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a 2 × 2 matrix Statement 1: adj (adj A) = A Statement 2:$|adj\text{ }A|=|A|$     AIEEE  Solved  Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let$f(x)=x|x|$and$g(x)=sinx$ Statement 1: gof is differentiable at$x=0$and its derivative is continuous at that point Statement 2: gof is twice differentiable at$x=0$

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

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

C)
(c) Statement-1 is true, statement-2 is false.

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