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## AIEEE Mathematics (2005)

Created by Quizmagic Team on Jan 09, 2013 07:03 PM.
`There are 25 questions of AIEEE Mathematics examination of year 2005 in this quiz.`
Top 5 Scores
 87 00:36 77 01:00 74 01:48 73 00:50 72 00:42
 Questions 25 Minutes 15 High Score 87 00:36 Quiz Played 144 times
Last played on Oct 20, 2016View comments
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### Sample Questions

Question 1
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thicknessthan melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is
 (1/36π) cm/min (5/6π) cm/min (1/54π) cm/min (1/18π) cm/min
Question 2
If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joiningthe centres of the spheres x2 + y2 + z2 + 6x − 8y − 2z = 13 and x2 + y2 + z2 − 10x + 4y −2z = 8, then a equals
 2 1 -2 -1
Question 3
If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is
 (-1/3, 7/3) (1/3, 7/3) (1, 7/3) (-1, 7/3)
Question 4
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in twodistinct points P and Q then the line 5x + by – a = 0 passes through P and Q for
 exactly two values of a exactly one value of a no value of a infinitely many values of a
Question 5
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally,then the equation of the locus of its centre is
 2ax + 2by – (a2 + b2 + p2 ) = 0 2ax + 2by – (a2 – b2 + p2 ) = 0 x2 + y2 – 2ax – 3by + (a2 – b2 – p2 ) = 0 x2 + y2 – 3ax – 4by + (a2 + b2 – p2 ) = 0
Question 6
An ellipse has OB as semi minor axis, F and F′ its focii and the angle FBF′ is a rightangle. Then the eccentricity of the ellipse is
 1/2 1/4 1/√3 1/√2
Question 7
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
 H/(A-B) H/2(A+B) H/(A+B) 2H/(A-B)
Question 8
The resultant R of two forces acting on a particle is at right angles to one of them andits magnitude is one third of the other force. The ratio of larger force to smaller one is
 8.4027777777777771E-2 0.12638888888888888 3 : 2√2 3 : √2
Question 9
The plane x + 2y – z = 4 cuts the sphere  x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius
 1 3 2 √2
Question 10
Let x1, x2, …,xn be n observations such that ∑x2i =400 and ∑xi =80. Then apossible value of n among the following is
 12 18 9 15