Page 49 - ISC-12

2Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

3. Which of the following options is the only CORRECT combination?
(A) (I) (i) (P). (B) (II) (ii) (Q).

(C) (III) (iii) (R). (D) (IV) (iv) (S).

4. Which of the following options is the only CORRECT combination?
(A) (I) (ii) (R). (B) (II) (iii) (S).

(C) (III) (iv) (P). (D) (IV) (i) (S).

5. Which of the following options is the only INCORRECT combination?
(A) (I) (iii) (P). (B) (II) (iv) (Q). (C) (III) (i) (R). (D) (II) (iii) (P).

[JEE 2017]

Paragraph for Question Nos. 6 and 7

−−→ −−→ −→ −→ −→ −→
Let O be the origin, and OX, OY , OZ be three unit vectors in the directions of the sides QR, RP, PQ,
respectively, of a triangle PQR.

−−→

6. OX × OY =
−−→
(A) sin (P + Q). (B) sin 2R. (C) sin (P + R). (D) sin (Q + R).

7. If the triangle PQR varies, then the minimum value of

cos (P + Q) + cos (Q + R) + cos (R + P)
is
5 3 3 5
(A) − . (B) − . (C) . (D) .
3 2 2 3

[JEE 2017]

Paragraph for Question Nos. 8 and 9

Football teams T 1 and T 2 have to play two games against each other. It is assumed that the outcomes of
the two games are independent. The probabilities of T 1 winning, drawing and losing a game against T 2 are
1 1 1
, and , respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a
2 6 3
game. Let X and Y denote the total points scored by teams T 1 and T 2 , respectively, after two games.

8. P(X > Y ) is

1 5 1 7
(A) . (B) . (C) . (D) .
4 12 2 12

9. P(X = Y ) is
11 1 13 1
(A) . (B) . (C) . (D) .
36 3 36 2

[JEE 2016]