AIEEE Question Bank Download
 

From which website I can do download the question bank of All India engineering entrance examination because I have need of this for do prepation of its current engineering entrance exam because I do participate in this

Re: AIEEE Question Bank Download
 

All India engineering entrance examination question paper is uploaded in the below now you can see file like this and download it from here as free of cost.

1. The equation esin x – e–sin x – 4 = 0 has
(1) infinite number of real roots (2) no real roots
(3) exactly one real root (4) exactly four real roots
1. 2
Sol. esin x – e–sin x = 4 esin x = t
t – 1
t
= 4
t2 – 4t – 1 = 0 t =
4 16 4
2
± +
t =
4 2 5
2
±
t = 2 5 ±
esin x = 2 ± 5 –1 £ sin x £ 1 1
e
£ esin x £ e
esin x = 2 + 5 not possible
esin x = 2 – 5 not possible \ hence no solution
2. Let ˆ ˆa and b be two unit vectors. If the vectors ˆ ˆ ˆ ˆ c a 2b and d 5a 4b = + = -

are perpendicular to each other,
then the angle between ˆ ˆa and b is
(1)
6
p (2)
2
p
(3)
3
p (4)
4
p
2. 3
Sol. c d 0 × =


2 2 5 a 6a b 8 b 0 + × - =


1
6a b 3 a b
2
× = × =

( ) a b
3
p × =

3. A spherical balloon is filled with 4500p cubic meters of helium gas. If a leak in the balloon causes the gas
to escape at the rate of 72p cubic meters per minute, then the rate (in meters per minute) at which the
radius of the balloon decreases 49 minutes after the leakage began is
(1)
9
7
(2)
7
9
(3)
2
9
(4)
9
2
3. 3
Sol. v = 2 4
r
3
p
After 49 minutes volume = 4500p – 49 (72p) = 972p
4
3
pr3 = 972p r3 = 729 r = 9
v =
4
3
pr3 2 dv 4 dr
3r
dt 3 dt
= p 72p = 4p 2 dr
r
dt
dr 72 2
dt 4 9 9 9