# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2013

### done AIEEE Solved Paper-2013 Total Questions - 30

• question_answer1) Distance between two parallel planes$2x+y$ $+2z=8$ and$4x+2y+4z+5=0\text{ }is:$     AIEEE Solevd Paper-2013

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

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

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

D)
$\frac{9}{2}$

• question_answer2) At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by$\frac{dp}{dx}=100-12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is:     AIEEE Solevd Paper-2013

A)
2500

B)
3000

C)
3500

D)
4500

• question_answer3) Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of$A\times B$ having 3 or more elements is:     AIEEE Solevd Paper-2013

A)
256

B)
220

C)
219

D)
211

• question_answer4) If the lines$\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$and$\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$are coplanar, then k can have:     AIEEE Solevd Paper-2013

A)
any value

B)
exactly one value

C)
exactly two values

D)
exactly three values

• question_answer5) If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$are the sides of a triangle ABC, then the length of the median through A is:     AIEEE Solevd Paper-2013

A)
$\sqrt{18}$

B)
$\sqrt{72}$

C)
$\sqrt{33}$

D)
$\sqrt{45}$

• question_answer6) The real number k for which the equation, $2{{x}^{3}}+3x+k=0$has two distinct real roots in [0, 1]     AIEEE Solevd Paper-2013

A)
lies between 1 and 2

B)
lies between 2 and 3

C)
lies between −1 and 0

D)
does not exist

• question_answer7) The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ??, is :     AIEEE Solevd Paper-2013

A)
$\frac{7}{81}(179-{{10}^{-20}})$

B)
$\frac{7}{9}(99-{{10}^{-20}})$

C)
$\frac{7}{81}(179+{{10}^{-20}})$

D)
$\frac{7}{9}(99+{{10}^{-20}})$

• question_answer8) A ray of light along$x+\sqrt{3}y=\sqrt{3}$gets reflected upon reaching x−axis, the equation of the reflected ray is:     AIEEE Solevd Paper-2013

A)
$y=x+\sqrt{3}$

B)
$\sqrt{3y}=x-\sqrt{3}$

C)
$y=\sqrt{3}x-\sqrt{3}$

D)
$\sqrt{3}y=x-1$

• question_answer9) The number of values of k, for which the system of equations: $(k+1)x+8y=4k$ $kx+(k+3)y=3k-1$ has no solution, is:     AIEEE Solevd Paper-2013

A)
in finite

B)
1

C)
2

D)
3

• question_answer10) If the equations${{x}^{2}}+2x+3=0$and$a{{x}^{2}}+bx+$ $c=0,\text{ }a,b,c\in R,$have a common root, then $a:b:c$ is     AIEEE Solevd Paper-2013

A)
1 : 2 : 3

B)
3 : 2 : 1

C)
1 : 3 : 2

D)
3 : 1 : 2

• question_answer11) The circle passing through (1, −2) and touching the axis of$x$at (3, 0) also passes through the point :     AIEEE Solevd Paper-2013

A)
(−5, 2)

B)
(2, −5)

C)
(5, −2)

D)
(−2, 5)

• question_answer12) If$x,y,z$are in A.P. and$ta{{n}^{-1}}x,ta{{n}^{-1}}y$and $ta{{n}^{-1}}z$ are also in A.P., then :     AIEEE Solevd Paper-2013

A)
$x=y=z$

B)
$2x=3y=6z$

C)
$6x=3y=2z$

D)
$6x=4y=3z$

• question_answer13) Consider: Statement − I:$(p\wedge \sim q)\wedge (\sim p\wedge q)$is a fallacy. Statement II:$(p\to q)\leftrightarrow (\sim q\to \sim p)$is a tautology.     AIEEE Solevd Paper-2013

A)
Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement I.

B)
Statement − I is true; Statement − II is true; Statement − II is not a correct explanation for Statement − I.

C)
Statement − I is true; Statement − II is false.

D)
Statement − I is false; Statement − II is true.

• question_answer14) If$\int f(x)dx=\psi (x),$ then$\int {{x}^{5}}f({{x}^{3}})dx$is equal to:     AIEEE Solevd Paper-2013

A)
$\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{2}}\psi ({{x}^{3}})dx} \right]+C$

B)
$\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-3\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C$

C)
$\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C$

D)
$\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx} \right]+C$

• question_answer15) $\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$is equal to:     AIEEE Solevd Paper-2013

A)
$-\frac{1}{4}$

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

C)
1

D)
2

• question_answer16) Statement − I: The value of the integral$\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}$is equal to $\frac{\pi }{6}$ Statement − II: $\int\limits_{a}^{b}{f(x)dx}\int\limits_{a}^{b}{f(a+b-x)dx}$     AIEEE Solevd Paper-2013

A)
Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement − I.

B)
Statement − I is true; Statement − II is true; Statement − II is a not a correct explanation for Statement − I.

C)
Statement − I is true; Statement − II is false.

D)
Statement − I is false; Statement − II is true.

• question_answer17) The equation of the circle passing through the foci of the ellipse$\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1,$and having centre at (0, 3) is :     AIEEE Solevd Paper-2013

A)
${{x}^{2}}+{{y}^{2}}-6y-7=0$

B)
${{x}^{2}}+{{y}^{2}}-6y+7=0$

C)
${{x}^{2}}+{{y}^{2}}-6y-5=0$

D)
${{x}^{2}}+{{y}^{2}}-6y+5=0$

• question_answer18) A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:     AIEEE Solevd Paper-2013

A)
$\frac{17}{{{3}^{5}}}$

B)
$\frac{13}{{{3}^{5}}}$

C)
$\frac{11}{{{3}^{5}}}$

D)
$\frac{10}{{{3}^{5}}}$

• question_answer19) The x−coordinate of the in centre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is:     AIEEE Solevd Paper-2013

A)
$2+\sqrt{2}$

B)
$2-\sqrt{2}$

C)
$1+\sqrt{2}$

D)
$1-\sqrt{2}$

• question_answer20) The term independent of x in expansion of ${{\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x}{x-{{x}^{1/2}}} \right)}^{10}}$is:     AIEEE Solevd Paper-2013

A)
4

B)
120

C)
210

D)
310

• question_answer21) The area (in square units) bounded by the curves$y=\sqrt{x},\text{ }2y-x+3=0,$x−axis, and lying in the first quadrant is:     AIEEE Solevd Paper-2013

A)
9

B)
36

C)
18

D)
$\frac{27}{4}$

• question_answer22) Let${{T}_{n}}$be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If${{T}_{n+1}}-{{T}_{n}}=1$then the value of n is:     AIEEE Solevd Paper-2013

A)
7

B)
5

C)
10

D)
8

• question_answer23) If z is a complex number of unit modulus and argument $\theta$, then $\arg \left( \frac{1+z}{1+z} \right)$ equals:     AIEEE Solevd Paper-2013

A)
$-\theta$

B)
$\frac{\pi }{2}-\theta$

C)
$\theta$

D)
$\pi -\theta$

• question_answer24) ABCD is a trapezium such that AB and CD are parallel and$BC\bot CD$. If$\angle ADB=\theta ,\text{ }BC=p$ and$CD=q,$then AB is equal to:     AIEEE Solevd Paper-2013

A)
$\frac{({{p}^{2}}\text{+}{{q}^{2}})sin\theta }{p\,cos\,\theta +q\,sin\,\theta }$

B)
$\frac{{{p}^{2}}+{{q}^{2}}cos}{p\,cos\,\theta +q\,sin\,\theta }$

C)
$\frac{{{p}^{2}}+{{q}^{2}}}{{{p}^{2}}cos\,\theta +{{q}^{2}}sin\,\theta }$

D)
$\frac{({{p}^{2}}+{{q}^{2}})\sin \theta }{{{(pcos\,\theta +qsin\,\theta )}^{2}}}$

• question_answer25) If$P=\left[ \begin{matrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \\ \end{matrix} \right]$is the ad joint of$3\times 3$matrix A and $|A|=4,$ then $\alpha$ is equal to:     AIEEE Solevd Paper-2013

A)
4

B)
11

C)
5

D)
0

• question_answer26) The intercepts on x−axis made by tangents to the curve,$y=\int\limits_{0}^{x}{|t|}dt,x\in R,$which are parallel to the line$y=2x,$are equal to     AIEEE Solevd Paper-2013

A)
$\pm 1$

B)
$\pm 2$

C)
$\pm 3$

D)
$\pm 4$

• question_answer27) Given: A circle,$2{{x}^{2}}+2{{y}^{2}}=5$and a parabola, ${{y}^{2}}=4\sqrt{5}x.$ Statement − I: An equation of a common tangent to these curves is$y=x+5.$ Statement − II: If the line,$y=mx+\frac{\sqrt{5}}{m}(m\ne 0)$is their common tangent, then ?m? satisfies${{m}^{4}}-3{{m}^{2}}+2=0.$     AIEEE Solevd Paper-2013

A)
Statement−I is true; Statement−II is true; Statement − II is a correct explanation for Statement − I.

B)
Statement−I is true; Statement−II is true; Statement − II is not a correct explanation for Statement − I.

C)
Statement−I is true; Statement−II is false.

D)
Statement−I is false; Statement−II is true.

• question_answer28) If$y=sec(ta{{n}^{-1}}x),$then$\frac{dy}{dx}$at$x=1$is equal to:     AIEEE Solevd Paper-2013

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

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

C)
1

D)
$\sqrt{2}$

• question_answer29) The expression$\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$can be written as:     AIEEE Solevd Paper-2013

A)
$sinA\text{ }cosA+1$

B)
$secA\text{ }cosecA+1$

C)
$tanA+cotA$

D)
$secA+cosecA$

• question_answer30) All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?     AIEEE Solevd Paper-2013

A)
mean

B)
median

C)
mode

D)
variance