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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
doneclear
B)
P(-1) is not minimum but P(1) is the maximum of P
doneclear
C)
P(-1) is the minimum but P(1) is not the maximum of P
doneclear
D)
neither P(-1) is the minimum nor P(1) is the maximum of P
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
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
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
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
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
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
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
doneclear
B)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
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
doneclear
B)
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.