Page 4 - ISC-12

Single Correct Choice Type

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

1. For any positive integer n, define f n : (0, ∞) → R as
n
X −1 1
f n (x) = tan for all x ∈ (0, ∞)
1 + (x + j)(x + j − 1)
j=1
π π
−1
Here, the inverse trigonometric function tan x assumes values in − , .
2 2
Then, which of the following statement(s) is(are) TRUE?
5 10
P 2 P 0 2
(A) tan (f j (0)) = 55. (B) 1 + f (0) sec (f j (0)) = 10.
j
j=1 j=1
1
(C) For any fixed positive integer n, lim tan (f n (x)) = .
x→∞ n
2
(D) For any fixed positive integer n, lim sec (f n (x)) = 1.
x→∞
[JEE 2018]

2. The equation of the plane passing through (1, 1, 1) and perpendicular to the planes 2x + y − 2z = 5
and 3x − 6y − 2z = 7, is

(A) 14x + 2y − 15z = 1. (B) 14x − 2y + 15z = 27.

(C) 14x + 2y + 15z = 31. (D) −14x + 2y + 15z = 3.
[JEE 2017]

3. Let O be the origin and let PQR be an arbitrary triangle. The point S is such that
−→ −→ −→ −→ −→ −→ −→ −→ −→ −→ −→ −→
OP · OQ + OR · OS = OR · OP + OQ · OS = OQ · OR + OP · OS

Then the triangle PQR has S as its
(A) centroid. (B) circumcentre. (C) incentre. (D) orthocenter.

[JEE 2017]

4. If y = y(x) satisfies the differential equation
! −1
r
√ q √ q √
8 x 9 + x dy = 4 + 9 + x dx, x > 0
√
and y(0) = 7, then y(256) =

(A) 3. (B) 9. (C) 16. (D) 80.

[JEE 2017]