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AIEEE Latest Exam Pattern - AIEEE Sample Question with Solutions Page 15

(#M40027601) AIEEE QUESTION Mental Ability Keep an EYE

If α, β, γ are the roots of 2x^3
+ 3x^2
– 12x + 3 = 0.
Then the centroid of triangle whose vertices are
A = (α, β, γ), B = (β, γ, α), C = (γ, α, β) is

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(#M40027600) AIEEE QUESTION Mental Ability Keep an EYE

The perimeter of a ∆ABC is 6 times the
arithmetic mean of the sines of its angle. If the
side a is 1, then the angle A is

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(#M40027599) AIEEE QUESTION Mental Ability Keep an EYE

If x + y = k is a normal to the parabola y^2 = 12x,
p is the length of the perpendicular from the
focus of the parabola on this normal then
3k^3
+ 2p^2
is equal to -
(A) 2001 (B) 2021
(C) 2223 (D) 1213

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(#M40027598) AIEEE QUESTION Mental Ability Keep an EYE

If sin 3α = 4 sin α sin (x + α) sin (x – α) then
864 sin2
x + 3620 cos2
x is equal to -
(A) 1550 (B) 1650
(C) 1553 (D) 1653

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(#M40027597) AIEEE QUESTION Mental Ability Keep an EYE

If U is a universal set and A and B are its two
subsets such that n(U) = 700 and n(A) = 300,
n(B) = 200, n (A ∩ B) = 100 then n(AC
∩ BC
) =
(A) 100 (B) 300
(C) 400 (D) 600

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(#M40027596) AIEEE QUESTION Mental Ability Keep an EYE

If all the permutations of the letters in the word
'OBJECT' are arranged (and numbered serially)
in alphabetical order as in a dictionary, then the
717th word is -
(A) TOJECB (B) TOJEBC
(C) TOCJEB (D) TOJCBE

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(#M40027595) AIEEE QUESTION Mental Ability Keep an EYE

A student is allowed to select at most n books
from a collection of (2n + 1) books. If the total
number of ways in which he can select at least
one book is 63, then the value of n is -
(A) 2 (B) 3 (C) 4 (D) 5

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(#M40027594) AIEEE QUESTION Mental Ability Keep an EYE

n the expansion of ( 4 9 +6 8 )
500 the number of
terms which are integral is -
(A) 250 (B) 43
(C) 251 (D) 44

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(#M40027593) AIEEE QUESTION Mental Ability Keep an EYE

2m white counters and 2n red counters are
arranged in a straight line with (m + n) counters
on each side of a central mark. The number of
ways of arranging the counters, so that the
arrangements are symmetrical with respect to the
central mark, is

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(#M40027592) AIEEE QUESTION Mental Ability Keep an EYE

If F1 = (3, 0) and F2 = (–3, 0) and P is any point
on the curve 16x^2
+ 25y^2
= 400 then PF1 + PF2
equals -
(A) 8 (B) 6 (C) 10 (D) 12

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