Solved papers for JEE Main & Advanced AIEEE Solved Paper-2006
done AIEEE Solved Paper-2006 Total Questions - 40
question_answer1) If the roots of the quadratic equation \[{{x}^{2}}+px+q=0\]are tan\[30{}^\circ \]and tan\[15{}^\circ \] respectively, then the value of\[2+q-p\]is
AIEEE Solved Paper-2006
question_answer3) Let W denotes the words in the English dictionary. Define the relation R by \[R=\{(x,y)\in W\times W|\] the words\[x\]and y have atleast one letter in common}. Then, R is
AIEEE Solved Paper-2006
question_answer4) The number of values of\[x\]in the interval \[[0,3\pi ]\]satisfying the equation \[2\text{ }si{{n}^{2}}x+5\text{ }sin\text{ }x-3=0\]is
AIEEE Solved Paper-2006
question_answer5) If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B),\]then which of the following will be always true?
AIEEE Solved Paper-2006
question_answer7) If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c}),\] where \[\vec{a},\,\vec{b}\] and \[\vec{c}\] are any three vectors such that \[\vec{a}.\vec{b}\ne 0,\vec{b}.\vec{c}\ne 0,\] then \[\vec{a}\] and \[\vec{c}\] are
AIEEE Solved Paper-2006
A)
inclined at an angle of\[\frac{\pi }{6}\]between them b
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B)
perpendicular
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C)
parallel
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D)
inclined at an angle of\[\frac{\pi }{3}\]between them
question_answer8) All the values of m for which both roots of the equation \[{{x}^{2}}-2mx+{{m}^{2}}-1=0\]are greater than -2 but less than 4 lie in the interval
AIEEE Solved Paper-2006
question_answer9) ABC is a triangle, right singled at A. The resultant of the forces acting along \[\overrightarrow{AB},\,\overrightarrow{AC}\] with magnitudes\[\frac{1}{AB}\]and\[\frac{1}{AC}\]respectively is the force along \[\overrightarrow{AD},\] where D is the foot of the perpendicular from A to BC. The magnitude of the resultant is
AIEEE Solved Paper-2006
question_answer10) Suppose, a population A has 100 observations 101, 102,..., 200 and another population B has 100 observations 151, 152, .... 250. If\[{{V}_{A}}\]and\[{{V}_{B}}\]represent the variances of the two populations respectively, then\[\frac{{{V}_{A}}}{{{V}_{B}}}\]is
AIEEE Solved Paper-2006
question_answer13) The locus of the vertices of the family of parabolas\[y=\frac{{{a}^{3}}{{x}^{2}}}{3}+\frac{{{a}^{2}}x}{2}-2a\]is
AIEEE Solved Paper-2006
question_answer14) A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
AIEEE Solved Paper-2006
question_answer15) The value of a, for which the points A, B, C with position vectors\[2\hat{i}-\hat{j}+\hat{k},\hat{i}-3\hat{j}-5\hat{k}\]and \[a\hat{i}-3\hat{j}+\hat{k}\] respectively are the vertices of a right angled triangle with \[C=\frac{\pi }{2}\]are
AIEEE Solved Paper-2006
question_answer18) At an election, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is
AIEEE Solved Paper-2006
question_answer19) If the expansion in powers of\[x\]of the function \[\frac{1}{(1-ax)(1-bx)}\]is\[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{2}}{{x}^{3}}+....,\]then\[{{a}_{n}}\]is
AIEEE Solved Paper-2006
question_answer20) For natural numbers m, n, if \[{{(1-y)}^{m}}{{(1+y)}^{n}}=1+{{a}_{1}}y+{{a}_{2}}{{y}^{2}}+.....\]and\[{{a}_{1}}={{a}_{2}}=10,\]then (m, n) is
AIEEE Solved Paper-2006
question_answer21) A particle has two velocities of equal magnitude inclined to each other at an angle \[\theta \]. If one of them is halved, the angle between the- other and the original resultant velocity is bisected by the new resultant. Then, 0 is
AIEEE Solved Paper-2006
question_answer22) At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is atmost one phone call during a 10 min time period, is
AIEEE Solved Paper-2006
question_answer23) A body falling .from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If \[g=10m/{{s}^{2}},\]then the height above the point P from where the body began to fall is
AIEEE Solved Paper-2006
question_answer26) Let \[{{a}_{1}},{{a}_{2}},{{a}_{3}},....\] be terms of an AP. If \[\frac{{{a}_{1}}+{{a}_{2}}+.....+{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+....{{a}_{q}}}=\frac{{{p}^{2}}}{{{q}^{2}}},\] \[p\ne q,\]then\[\frac{{{a}_{6}}}{{{a}_{21}}}\]equals
AIEEE Solved Paper-2006
question_answer30) A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length\[x\]. The maximum area enclosed by the park is
AIEEE Solved Paper-2006
question_answer31) If\[(a,\text{ }{{a}^{2}})\]falls inside the angle made by the lines \[y=\frac{x}{2},\text{ }x>0\]and\[y=3x,\text{ }x>0,\]then a belongs to
AIEEE Solved Paper-2006
question_answer33) If the lines\[3x-4y-7=0\]and\[2x-3y-5=0\]are two diameters of a circle of area\[49\,\pi \,sq\]units, the equation of the circle is
AIEEE Solved Paper-2006
question_answer35) The differential equation whose solution is \[A{{x}^{2}}+B{{y}^{2}}=1,\]where A and B are arbitrary constants, is of
AIEEE Solved Paper-2006
question_answer36) The value of \[\int_{I}^{a}{[x]\,f'\,(x)\,dx,\,\,a>1,}\] where\[[x]\] denotes the greatest integer not exceeding \[x,\]is
AIEEE Solved Paper-2006
question_answer37) Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid-points of the chords of the circle C 'that subtend an angle of\[\frac{2\pi }{3}\]at its centre, is
AIEEE Solved Paper-2006
question_answer38) If\[{{a}_{1}},{{a}_{2}},....{{a}_{n}}\]are in HP, then the expression\[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}+,....+{{a}_{n-1}}{{a}_{n}}\]is equal to
AIEEE Solved Paper-2006
question_answer39) If\[{{z}^{2}}+z+1=0,\]where z is complex number, then the value of \[{{\left( z+\frac{1}{z} \right)}^{2}}+{{\left( {{z}^{2}}+\frac{1}{{{z}^{2}}} \right)}^{2}}+{{\left( {{z}^{3}}+\frac{1}{{{z}^{3}}} \right)}^{2}}\] \[+......+{{\left( {{z}^{6}}+\frac{1}{{{z}^{6}}} \right)}^{2}}\]is
AIEEE Solved Paper-2006