question_answer2) At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by\[\frac{dp}{dx}=100-12\sqrt{x}\]. If the firm employs 25 more workers, then the new level of production of items is:
AIEEE Solevd Paper-2013
question_answer3) Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of\[A\times B\] having 3 or more elements is:
AIEEE Solevd Paper-2013
question_answer4) If the lines\[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\]and\[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\]are coplanar, then k can have:
AIEEE Solevd Paper-2013
question_answer5) If the vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\]and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\]are the sides of a triangle ABC, then the length of the median through A is:
AIEEE Solevd Paper-2013
question_answer8) A ray of light along\[x+\sqrt{3}y=\sqrt{3}\]gets reflected upon reaching x−axis, the equation of the reflected ray is:
AIEEE Solevd Paper-2013
question_answer9) The number of values of k, for which the system of equations: \[(k+1)x+8y=4k\] \[kx+(k+3)y=3k-1\] has no solution, is:
AIEEE Solevd Paper-2013
question_answer10) If the equations\[{{x}^{2}}+2x+3=0\]and\[a{{x}^{2}}+bx+\] \[c=0,\text{ }a,b,c\in R,\]have a common root, then \[a:b:c\] is
AIEEE Solevd Paper-2013
question_answer16) Statement − I: The value of the integral\[\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}\]is equal to \[\frac{\pi }{6}\] Statement − II: \[\int\limits_{a}^{b}{f(x)dx}\int\limits_{a}^{b}{f(a+b-x)dx}\]
AIEEE Solevd Paper-2013
A)
Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement − I.
doneclear
B)
Statement − I is true; Statement − II is true; Statement − II is a not a correct explanation for Statement − I.
question_answer17) The equation of the circle passing through the foci of the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1,\]and having centre at (0, 3) is :
AIEEE Solevd Paper-2013
question_answer18) A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:
AIEEE Solevd Paper-2013
question_answer19) The x−coordinate of the in centre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is:
AIEEE Solevd Paper-2013
question_answer20) The term independent of x in expansion of \[{{\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x}{x-{{x}^{1/2}}} \right)}^{10}}\]is:
AIEEE Solevd Paper-2013
question_answer21) The area (in square units) bounded by the curves\[y=\sqrt{x},\text{ }2y-x+3=0,\]x−axis, and lying in the first quadrant is:
AIEEE Solevd Paper-2013
question_answer22) Let\[{{T}_{n}}\]be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If\[{{T}_{n+1}}-{{T}_{n}}=1\]then the value of n is:
AIEEE Solevd Paper-2013
question_answer23) If z is a complex number of unit modulus and argument \[\theta \], then \[\arg \left( \frac{1+z}{1+z} \right)\] equals:
AIEEE Solevd Paper-2013
question_answer24) ABCD is a trapezium such that AB and CD are parallel and\[BC\bot CD\]. If\[\angle ADB=\theta ,\text{ }BC=p\] and\[CD=q,\]then AB is equal to:
AIEEE Solevd Paper-2013
question_answer26) The intercepts on x−axis made by tangents to the curve,\[y=\int\limits_{0}^{x}{|t|}dt,x\in R,\]which are parallel to the line\[y=2x,\]are equal to
AIEEE Solevd Paper-2013
question_answer27) Given: A circle,\[2{{x}^{2}}+2{{y}^{2}}=5\]and a parabola, \[{{y}^{2}}=4\sqrt{5}x.\] Statement − I: An equation of a common tangent to these curves is\[y=x+5.\] Statement − II: If the line,\[y=mx+\frac{\sqrt{5}}{m}(m\ne 0)\]is their common tangent, then ?m? satisfies\[{{m}^{4}}-3{{m}^{2}}+2=0.\]
AIEEE Solevd Paper-2013
A)
Statement−I is true; Statement−II is true; Statement − II is a correct explanation for Statement − I.
doneclear
B)
Statement−I is true; Statement−II is true; Statement − II is not a correct explanation for Statement − I.
question_answer30) All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
AIEEE Solevd Paper-2013