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
doneclear
B)
Neither R nor S is an equivalence relation
doneclear
C)
S is an equivalence relation but R is not an equivalence relation
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
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
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
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
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
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
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
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
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 \[x\le 0\]
doneclear
B)
There is no rational number\[x\in S\]such that \[x\le 0\]
doneclear
C)
Every rational number\[x\in S\]satisfies \[x\le 0\]
doneclear
D)
\[x\in S\]and\[x\le 0\] \[\Rightarrow \]\[x\]is not rational
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
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
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 \[\frac{r}{R}=\frac{1}{2}\]
doneclear
B)
There is a regular polygon with \[\frac{r}{R}=\frac{1}{\sqrt{2}}\]
doneclear
C)
There is a regular polygon with \[\frac{r}{R}=\frac{2}{3}\]
doneclear
D)
There is a regular polygon with \[\frac{r}{R}=\frac{\sqrt{3}}{2}\]
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
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
doneclear
B)
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
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
doneclear
B)
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
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
doneclear
B)
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
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
doneclear
B)
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
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
doneclear
B)
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.