# Solved papers for JEE Main & Advanced AIEEE Paper (Held On 11 May 2011)

### done AIEEE Paper (Held On 11 May 2011) Total Questions - 30

• question_answer1) Let f be a function defined by $f(x)={{(x-1)}^{2}}+1,(x\ge 1).$ Statement -1 : The set$\{x:f(x)={{f}^{-1}}(x)\}=\{1,2\}.$ Statement - 2 : f is a bisection and ${{f}^{-1}}(x)=1+\sqrt{x-1},x\ge 1.$     AIEEE  Solved  Paper (Held On 11 May  2011)

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_answer2) If $\omega \ne 1$ is the complex cube root of unity and matrix $H=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right],$then ${{H}^{70}}$is equal to -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$0$

B)
$-H$

C)
${{H}^{2}}$

D)
$H$

• question_answer3) Let [.] denote the greatest integer function then the value of $\int\limits_{0}^{1.5}{x[{{x}^{2}}]dx}$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$0$

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

C)
$\frac{3}{4}$

D)
$\frac{5}{4}$

• question_answer4) The curve that passes through the point (2, 3), and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$2y-3x=0$

B)
$y=\frac{6}{x}$

C)
${{x}^{2}}+{{y}^{2}}=13$

D)
${{\left( \frac{x}{2} \right)}^{2}}+{{\left( \frac{y}{3} \right)}^{2}}=2$

• question_answer5) A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standard deviation of gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (ingm) of fishes are respectively:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
32,2

B)
32,4

C)
28,2

D)
28,4

• question_answer6) The lines x + y = | a | and ax - y = 1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$(0,\infty )$

B)
$[1,\infty )$

C)
$(-1,\infty )$

D)
$(-1,1]$

• question_answer7) If the vector $p\,\hat{i}+\hat{j}+\hat{k},\hat{i}+q\,\hat{j}+\hat{k}$and $\,\hat{i}+\hat{j}+r\,\hat{k}$$(p\ne q\ne r\ne 1)$ are coplanar, then the value of pqr - (p+q+r) is-     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
2

B)
0

C)
-1

D)
-2

• question_answer8) The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along a straight line x = y = z is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$10\sqrt{3}$

B)
$5\sqrt{3}$

C)
$3\sqrt{10}$

D)
$3\sqrt{5}$

• question_answer9) Let $\vec{a},\vec{b},\vec{c}$be three non-zero vectors which are pairwise non-collinear. If $\vec{a}+3\vec{b}$is collinear with $\vec{c}$ and $\vec{b}+2\vec{c}$is collinear with $\vec{a}+3\vec{b}+6\vec{c}$ is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\vec{a}$

B)
$\vec{c}$

C)
$\vec{0}$

D)
$\vec{a}+\vec{c}$

• question_answer10) lf A(2,-3) and B(-2,1) are two vertices of a triangle and third vertex moves on the line $2x+3y=9,$ then the locus of the centroid of the triangle is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$xy=1$

B)
$2x+3y=1$

C)
$2x+3y=3$

D)
$2x3y=1$

• question_answer11) There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$N\le 100$

B)
$100<N\le 140$

C)
$140<N\le 190$

D)
$N>190$

• question_answer12) Define F(x) as the product of two real functions ${{f}_{1}}(x)=x,x\in R,$and ${{f}_{2}}(x)=\left\{ \begin{matrix} \sin \frac{1}{x}, & if\,x\ne 0\, \\ 0, & if\,x=0 \\ \end{matrix} \right.$as follows: $F(x)=\left\{ \begin{matrix} {{f}_{1}}(x).{{f}_{2}}(x), & if\,x\ne 0\, \\ 0, & if\,x=0 \\ \end{matrix} \right.$ Statement -1 : F(x) is continuous on R. Statement - 2 : ${{f}_{1}}(x)$ and ${{f}_{2}}(x)$ are continuous on R     AIEEE  Solved  Paper (Held On 11 May  2011) .

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_answer13) Statement -1 : For each natural number $n,{{(n+1)}^{7}}-{{n}^{7}}-1$is divisible by 7. Statement - 2 : For each natural number $n,{{n}^{7}}-n$is divisible by 7.     AIEEE  Solved  Paper (Held On 11 May  2011)

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_answer14) The equation of the circle passing through the point (1,0) and (0,1) and having the smallest radius is -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
${{x}^{2}}+{{y}^{2}}-2x-2y+1=0$

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

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

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

• question_answer15) The equation of the hyperbola whose foci are (-2, 0) and (2, 0) and eccentricity is 2 is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
${{x}^{2}}-3{{y}^{2}}=3$

B)
$3{{x}^{2}}-{{y}^{2}}=3$

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

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

• question_answer16) If the trivial solution is the only solution of the system of equations $x-ky+z=0$ $kx+3y-kz=0$ $3x+y-z=0$ then the set of all values of k is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
R-{2,-3}

B)
R-{2}

C)
R-{-3}

D)
{2,-3}

• question_answer17) Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4,3). Rahul made a mistake in writing down coefficient of x to get roots (3,2). The correct roots of equation are :           AIEEE  Solved  Paper (Held On 11 May  2011)

A)
6,1

B)
4,3

C)
-6,-1

D)
-4,-3

• question_answer18) Let ${{a}_{n}}$ be the ${{n}^{th}}$ term of an A.P. If $\sum\limits_{r=1}^{100}{{{a}_{2r}}=\alpha }$ and $\sum\limits_{r=1}^{100}{{{a}_{2r}}-1=\beta },$ then the common difference of the A.P. is     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\alpha -\beta$

B)
$\frac{\alpha -\beta }{100}$

C)
$\beta -\alpha$

D)
$\frac{\alpha -\beta }{200}$

• question_answer19) Consider the differential equation ${{y}^{2}}dx+\left( x-\frac{1}{y} \right)dy=0.$If y  = 1, then x is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$4-\frac{2}{y}-\frac{{{e}^{\frac{1}{y}}}}{e}$

B)
$3-\frac{1}{y}+\frac{{{e}^{\frac{1}{y}}}}{e}$

C)
$1+\frac{1}{y}-\frac{{{e}^{\frac{1}{y}}}}{e}$

D)
$1-\frac{1}{y}+\frac{{{e}^{\frac{1}{y}}}}{e}$

• question_answer20) Let $f:R\to [0,\infty )$ be such that $\underset{x\to 5}{\mathop{\lim }}\,f(x)$ exists and $\underset{x\to 5}{\mathop{\lim }}\,\frac{{{(f(x))}^{2}}-9}{\sqrt{|x-5|}}=0$ Then $\underset{x\to 5}{\mathop{\lim }}\,f(x)$equals:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
0

B)
1

C)
2

D)
3

• question_answer21) Statement-1 : Determinant of a skew-symmetric matrix of order 3 is zero. Statement - 2 : For any matrix $A,\det {{(A)}^{T}}=\det (A)$ and $\det (-A)=-det(A).$ Where det denotes the determinant of matrix B. Then :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Both statements are true

B)
Both statements are false

C)
Statement-1 is false and statement-2

D)
Statement-1 is true and statement-2 is false

• question_answer22) The possible values of $\theta \in (0,\pi )$such that $\sin (\theta )+sin(4\theta )+sin(7\theta )=0$are :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{\pi }{4},\frac{5\pi }{12},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}$

B)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{35\pi }{36}$

C)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}$

D)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{4\pi }{9},\frac{\pi }{2},\frac{3\pi }{4},\frac{8\pi }{9}$

• question_answer23) The area bounded by the curves ${{y}^{2}}=4x$and ${{x}^{2}}=4y$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{32}{3}$

B)
$\frac{16}{3}$

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

D)
0

• question_answer24) Let f be a function defined by - $f(x)=\left\{ \begin{matrix} \frac{\tan x}{x} & ,x\ne 0 \\ 1 & ,x=0 \\ \end{matrix} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ne 0$ Statement -1 : x = 0 is point of minima of f Statement-2 : f'(0) =0.     AIEEE  Solved  Paper (Held On 11 May  2011)

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_answer25) The only statement among the following that is a tautology is -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$A\wedge (A\vee B)$

B)
$A\vee (A\wedge B)$

C)
$[A\wedge (A\to B)]\to B$

D)
$B\to [A\wedge (A\to B)]$

• question_answer26) Let A, B, C be pariwise independent events with P > 0 and $P(A\cap B\cap C)=0.$ Then $P({{A}^{c}}\cap {{B}^{c}}/C).$     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$P(1)-P({{B}^{c}})$

B)
$P({{A}^{c}})+P({{B}^{c}})$

C)
$P({{A}^{c}})-P({{B}^{c}})$

D)
$P({{A}^{c}})-P(B)$

• question_answer27) Let for $a\ne {{a}_{1}}\ne 0,$ $f(x)=a{{x}^{2}}+bx+c,g9x)={{a}_{1}}{{x}^{2}}+{{b}_{1}}x+{{c}_{1}}$and$p(x)=f(x)-g(x).$ If p(x) = 0 only for x = -1 and p(-2) = 2, then the value of p is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
3

B)
9

C)
6

D)
18

• question_answer28) The length of the perpendicular drawn from the point (3, -1,11) to the line $\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\sqrt{29}$

B)
$\sqrt{33}$

C)
$\sqrt{53}$

D)
$\sqrt{66}$

• question_answer29) Consider the following relation R on the set of real square matrices of order 3. $R=\{(A,B)|A={{P}^{-1}}BP$for some invertible matrix P}. Statement -1 : R is equivalence relation. Statement - 2 : For any two invertible $3\times 3$ matrices M and N,${{(MN)}^{-1}}={{N}^{-1}}{{M}^{-1}}.$     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Statement-1 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) If function f(x) is differentiate at x = a, then $\underset{x\to a}{\mathop{\lim }}\,\frac{{{x}^{2}}f(a)-{{a}^{2}}f(x)}{x-a}$is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$-{{a}^{2}}f'(a)$

B)
$af(a)-{{a}^{2}}f\,'(a)$

C)
$2af(a)-{{a}^{2}}f\,'(a)0$

D)
$2af(a)+{{a}^{2}}f'(a)$