Page 24 - ISC-12

Multiple Correct Choices Type

Each question in this section is a multiple choice question with four choices (A),
(B), (C) and (D), out of which more than one choices are correct.

1. Let P 1 : 2x + y − z = 3 and P 2 : x + 2y + z = 2 be two planes. Then, which of the following
statement(s) is(are) TRUE?

(A) The line of intersection of P 1 and P 2 has direction ratios 1, 2, −1.
(B) The line
3x − 4 1 − 3y z
= =
9 9 3
is perpendicular to the line of intersection of P 1 and P 2 .
◦
(C) The acute angle between P 1 and P 2 is 60 .
(D) If P 3 is the plane passing through the point (4, 2, −2) and perpendicular to the line of
2
intersection of P 1 and P 2 , then the distance of the point (2, 1, 1) from the plane P 3 is √ .
3
[JEE 2018]

2 0 2
2. For every twice integrable function f : R → [−2, 2] with (f(0)) + (f (0)) = 85, which of the
following statement(s) is(are) TRUE?

(A) There exist r, s ∈ R, where r < s, such that f is one-one on the open interval (r, s).
0
(B) There exists x 0 ∈ (−4, 0) such that |f (x 0 )| ≤ 1.
(C) lim f(x) = 1.
x→∞
00
0
(D) There exists α ∈ (−4, 4) such that f(α) + f (α) = 0 and f (α) 6= 0.
[JEE 2018]

3. Let f : R → R and g : R → R be two non-constant differentiable functions. If
0
0

f (x) = e (f(x)−g(x)) g (x) for all x ∈ R
and f(1) = g(2) = 1, then which of the following statement(s) is(are) TRUE?
(A) f(2) < 1 − log 2. (B) f(2) > 1 − log 2.
e
e
(C) g(1) > 1 − log 2. (D) g(1) < 1 − log 2.
e
e
[JEE 2018]

4. Let f : [0, ∞) → R be a continuous function such that
x
Z
f(x) = 1 − 2x + e x−t f(t) dt
0
for all x ∈ [0, ∞). Then, which of the following statement(s) is(are) TRUE?