Page 20 - ISC-12

Single Correct Choice Type Jai Baba Ki17
◦
80. A man walks a distance of 3 units from the origin towards the north-east (N 45 E) direction. From
◦
there, he walks a distance of 4 units towards the north-west (N 45 W) direction to reach a point P.
Then the position of P in the Argand plane is
(A) 3e iπ/4 + 4i. (B) (3 − 4i)e iπ/4 . (C) (4 + 3i)e iπ/4 . (D) (3 + 4i)e iπ/4 .

[JEE 2007]

c
81. Let E denote the complement of an event E. Let E, F, G be pairwise independent events with
c
c
P(G) > 0 and P(E ∩ F ∩ G) = 0. Then P(E ∩ F |G) equals
c
c
c
c
(A) P(E ) + P(F ). (B) P(E ) − P(F ).
c
c
(C) P(E ) − P(F). (D) P(E) − P(F ).
[JEE 2007]
2
d x
82. equals
dy 2
2 −1 2 −1 −3
d y d y dy
(A) . (B) − .
dx 2 dx 2 dx
2 −2 2 −3
d y dy d y dy
(C) . (D) − .
dx 2 dx dx 2 dx
[JEE 2007]

p
dy 1 − y 2
83. The differential equation = determines a family of circles with
dx y
(A) variable radii and a fixed centre at (0, 1).
(B) variable radii and a fixed centre at (0, −1).

(C) fixed radius 1 and variable centres along the x-axis.
(D) fixed radius 1 and variable centres along the y-axis.

[JEE 2007]

~
~
~
84. Let ~a, b, ~c be unit vectors such that ~a + b + ~c = 0. Which one of the following is correct?
~
~
~
(A) ~a × b = b × ~c = ~c × ~a = 0.
~
~
~
(B) ~a × b = b × ~c = ~c × ~a 6= 0.
~
~
~
(C) ~a × b = b × ~c = ~a × ~c 6= 0.
~ ~
(D) ~a × b, b × ~c, ~c × ~a are mutually perpendicular.
[JEE 2007]
85. Let
x
f(x) =
n 1/n
(1 + x )
for n ≥ 2 and
g(x) = (f ◦ f ◦ · · · ◦ f)(x).
| {z }
n times