Solved papers for JEE Main & Advanced AIEEE Solved Paper-2012

done AIEEE Solved Paper-2012 Total Questions - 30

• question_answer1) The equation ${{e}^{\sin x}}-{{e}^{-\sin x}}-4=0$ has:   AIEEE  Solved  Paper-2012

A)
infinite number of real roots

B)
no real roots

C)
exactly one real root

D)
exactly four real roots

• question_answer2) Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2\hat{b}$ and $\vec{d}=5\hat{a}-4\hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is:   AIEEE  Solved  Paper-2012

A)
$\frac{\pi }{6}$

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

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

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

• question_answer3) A spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:   AIEEE  Solved  Paper-2012

A)
$\frac{9}{7}$

B)
$\frac{7}{9}$

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

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

• question_answer4) Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + .... + (361 + 380 + 400) is 8000. Statement-2: $\sum\limits_{k=1}^{n}{({{k}^{3}}-{{(k-1)}^{3}}={{n}^{3}}}$, for any natural number n.   AIEEE  Solved  Paper-2012

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) The negation of the statement ?If I become a teacher, then I will open a school? is:   AIEEE  Solved  Paper-2012

A)
I will become a teacher and I will not open a school.

B)
Either I will not become a teacher or I will not open a school.

C)
Neither I will become a teacher nor I will open a school

D)
I will not become a teacher or I will open a school.

• question_answer6) If the integral $\int{\frac{5\tan x}{\tan x-2}dx=x+a\,\ell n\left| \sin x-2\cos x \right|+k}$, then a is equal to:   AIEEE  Solved  Paper-2012

A)
$-1$

B)
$-2$

C)
1

D)
2

• question_answer7) Statement-1: An equation of a common tangent to the parabola ${{y}^{2}}=16\sqrt{3}x$ and the ellipse $2{{x}^{2}}+{{y}^{2}}=4$ is $y=2x+2\sqrt{3}$. Statement-2: If the line $mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola ${{y}^{2}}=16\sqrt{3}x$ and the ellipse $2{{x}^{2}}+{{y}^{2}}=4$, then m satisfies${{m}^{4}}+2{{m}^{2}}=24$.   AIEEE  Solved  Paper-2012

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_answer8) Let $A=\left( \begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \\ \end{matrix} \right)$. If ${{\mu }_{1}}$ and ${{\mu }_{2}}$ are column matrices such that A{{u}_{1}}\left( \begin{align} & 1 \\ & 0 \\ & 0 \\ \end{align} \right) and A{{u}_{2}}\left( \begin{align} & 0 \\ & 1 \\ & 0 \\ \end{align} \right), then ${{u}_{1}}+{{u}_{2}}$ is equal to:   AIEEE  Solved  Paper-2012

A)
\left( \begin{align} & -1 \\ & 1 \\ & 0 \\ \end{align} \right)

B)
\left( \begin{align} & -1 \\ & 1 \\ & -1 \\ \end{align} \right)

C)
\left( \begin{align} & -1 \\ & -1 \\ & 0 \\ \end{align} \right)

D)
\left( \begin{align} & 1 \\ & -1 \\ & -1 \\ \end{align} \right)

• question_answer9) If n is a positive integer, then ${{\left( \sqrt{3}+1 \right)}^{2n}}-{{\left( \sqrt{3}-1 \right)}^{2n}}$ is:   AIEEE  Solved  Paper-2012

A)
an irrational number

B)
an odd positive integer

C)
an even positive integer

D)
a rational number other than positive integers

• question_answer10) If 100 times the 100th term of an AP with non zero common  difference equals the 50 times its 50th term, then the 150th term of this AP is :   AIEEE  Solved  Paper-2012

A)
-150

B)
150 times its 50th term

C)
150

D)
zero

• question_answer11) In a $\Delta PQR$, if $3\sin P+4\cos Q=6$ and $4\sin Q+3\cos P=1$, then the angle R is equal to:   AIEEE  Solved  Paper-2012

A)
$\frac{5\pi }{6}$

B)
$\frac{\pi }{6}$

C)
$\frac{\pi }{4}$

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

• question_answer12) A equation of a plane parallel to the plane $x-2y+2z-5=0$and at a unit distance from the origin is:     AIEEE  Solved  Paper-2012

A)
$x-2y+2z-3=0$

B)
$x-2y+2z+1=0$

C)
$x-2y+2z-1=0$

D)
$x-2y+2z+5=0$

• question_answer13) If the line $2x+y=k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals :   AIEEE  Solved  Paper-2012

A)
$\frac{29}{5}$

B)
5

C)
6

D)
$\frac{11}{5}$

• question_answer14) Let ${{x}_{1}},{{x}_{2}},\,....\,,{{x}_{n}}$ be n observations, and let $\overline{x}$ be their arithmetic mean and ${{\sigma }^{2}}$ be the variance Statement-1: Variance of $2{{x}_{1}},2{{x}_{2}},\,......,\,2{{x}_{n}}$ is $4{{\sigma }^{2}}$. Statement-2: Arithmetic mean $2{{x}_{1}},2{{x}_{2}},\,......,\,2{{x}_{n}}$ is $4\overline{x}$.   AIEEE  Solved  Paper-2012

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_answer15) The population p(t) at time t of a certain mouse species satisfies the differential equation$\frac{dp(t)}{dt}=0.5\,p(t)-450$If $p(0)=850$, then the time at which the population becomes zero is :   AIEEE  Solved  Paper-2012

A)
$2\,\ell n18$

B)
$\ell n\,9$

C)
$\frac{1}{2}\ell n\,18$

D)
$\ell n\,18$

• question_answer16) Let a, $b\in R$ be such that the function f given by $f(x)=\ell n\left| x \right|+b{{x}^{2}}+ax,\,x\ne 0$ has extreme values at $x=-1$ and $x=2$. Statement-1: f has local maximum at $x=-1$ and at $x=2$. Statement-2: $a=\frac{1}{2}$ and $b=\frac{-1}{4}$.   AIEEE  Solved  Paper-2012

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_answer17) The area bounded between the parabolas ${{x}^{2}}=\frac{y}{4}$ and ${{x}^{2}}=9y$ and the straight line $y=2$is:   AIEEE  Solved  Paper-2012

A)
$20\sqrt{2}$

B)
$\frac{10\sqrt{2}}{3}$

C)
$\frac{20\sqrt{2}}{3}$

D)
$10\sqrt{2}$

• question_answer18) Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:   AIEEE  Solved  Paper-2012

A)
880

B)
629

C)
630

D)
879

• question_answer19) If f : $R\to R$ is a function defined by $f(x)=[x]\cos \left( \frac{2x-1)}{2} \right)\pi$, where $[x]$ denotes the greatest integer function, then f is:   AIEEE  Solved  Paper-2012

A)
continuous for every real $x$.

B)
discontinuous only at $x=0$.

C)
discontinuous only at non-zero integral values of $x$.

D)
continuous only at $x=0$.

• question_answer20) If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then k is equal to :   AIEEE  Solved  Paper-2012

A)
$-1$

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

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

D)
0

• question_answer21) Three numbers are chosen at random without replacement from {1, 2, 3, ..., 8}. The probability that their minimum is 3, given that their maximum is 6, is :   AIEEE  Solved  Paper-2012

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

B)
$\frac{1}{5}$

C)
$\frac{1}{4}$

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

• question_answer22) If $z\ne 1$ and $\frac{{{z}^{2}}}{z-1}$ is real, then the point represented by the complex number z lies :   AIEEE  Solved  Paper-2012

A)
either on the real axis or on a circle passing through the origin.

B)
on a circle with centre at the origin.

C)
either on the real axis or on a circle not passing through the origin.

D)
on the imaginary axis.

• question_answer23) Let P and Q be $3\times 3$ matrices $P\ne Q$. If ${{P}^{3}}={{Q}^{3}}$ and ${{P}^{2}}={{Q}^{2}}$, then determinant of $({{P}^{2}}={{Q}^{2}})$ is equal to :   AIEEE  Solved  Paper-2012

A)
$-2$

B)
1

C)
0

D)
$-1$

• question_answer24) If $g(x)=\int\limits_{0}^{x}{\cos 4t\,\,dt}$, then $g(x+\pi )$ equals   AIEEE  Solved  Paper-2012

A)
$\frac{g(x)}{g(\pi )}$

B)
$g(x)+g(\pi )$

C)
$g(x)-g(\pi )$

D)
$g(x).\,g(\pi )$

• question_answer25) The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is :   AIEEE  Solved  Paper-2012

A)
$\frac{10}{3}$

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

C)
$\frac{6}{5}$

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

• question_answer26) Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is :   AIEEE  Solved  Paper-2012

A)
${{5}^{2}}$

B)
${{3}^{5}}$

C)
${{2}^{5}}$

D)
${{5}^{3}}$

• question_answer27) An ellipse is drawn by taking a diameter of the circle ${{(x-1)}^{2}}+{{y}^{2}}=1$ as its semi-minor axis and a diameter of the circle ${{x}^{2}}+{{(y-2)}^{2}}=4$ is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :   AIEEE  Solved  Paper-2012

A)
$4{{x}^{2}}+{{y}^{2}}=4$

B)
${{x}^{2}}+4{{y}^{2}}=8$

C)
$4{{x}^{2}}+{{y}^{2}}=8$

D)
${{x}^{2}}+4{{y}^{2}}=16$

• question_answer28) Consider the function, $f(x)=\left| x-2 \right|+\left| x-5 \right|,x\in R$. Statement-1: $f'(4)=0$ Statement-2: $f$ is continuous in [2, 5], differentiable in (2, 5) and $f(2)=f(5)$.   AIEEE  Solved  Paper-2012

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 corect explanation for Statement-1.

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

• question_answer29) A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. if the area of the triangle OPQ is least, then the slope of the line PQ is :   AIEEE  Solved  Paper-2012

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

B)
$-4$

C)
$-2$

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

• question_answer30) Let ABCD be a parallelogram such that $\overrightarrow{AB}=\vec{q},\,\,\overrightarrow{AD}=\vec{p}$ and $\angle BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\vec{r}$ is given by :   AIEEE  Solved  Paper-2012

A)
$\vec{r}=3\vec{q}-\frac{3(\vec{p}.\,\vec{q})}{(\vec{p}.\,\vec{p})}\vec{p}$

B)
$\vec{r}=-\vec{q}+\left( \frac{\vec{p}.\,\vec{q}}{\vec{p}.\,\vec{p}} \right)\vec{p}$

C)
$\vec{r}=\vec{q}-\left( \frac{\vec{p}.\,\vec{q}}{\vec{p}.\,\vec{p}} \right)\vec{p}$

D)
$\vec{r}=-3\vec{q}+\frac{3(\vec{p}.\,\vec{q})}{(\vec{p}.\,\vec{p})}\vec{p}$

Study Package

AIEEE Solved Paper-2012

You need to login to perform this action.
You will be redirected in 3 sec