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Single choice Objective ('–1' negative marking) Q.2, 4, 5, 6 (4 marks 3 min.) [16, 12] Multiple choice objective ('–1' negative marking) Q.3 (6 marks 5 min.) [6, 5] Subjective Questions ('–1' negative marking) Q.1 (4 marks 5 min.) [4, 5] 1. ABCD is a quadrilateral and E the point of intersection of the lines joining the middle points of opposite      sides . Show that the resultant of OA , OB , OC and OD is equal to 4 OE , where O is any point. 2. P, Q have position vectors → a & b  relative to the origin 'O' & X, Y divide PQ internally and externally  respectively in the ratio 2 : 1 . Vector XY = 3 → → 4 → → 5 → → 4 → → (A) b  a (B) a  b (C) b  a (D*) b  a 3. P is a point on the line through the point A whose position vector is a and the line is parallel to the vector b . If PA = 6 , the position vector of P is : → 6 → b 6 (A) a + 6 b (B*) a + → b (C*) b a – 6 → | b | (D) b + → a a → → → → → → → → 4. Let a , b , c be three unit vectors such that a  b  c = 1 and a  b . If c makes angles ,  with → → respectively then cos + cos is equal to a , b (A) 3/2 (B) 1 (C*) – 1 (D) 1/2 5. → ˆ (ˆi  →  → ˆ (ˆj → (→ ˆ)(kˆ  → = (A*) 0 (B) r (C) 2 r (D) 3 r → → → → → 6. If →  ˆi  ˆj, b  2ˆj – kˆ and →  →  b → →  b  →  b r then is equal to a (A*) 1 (ˆi  3ˆj  kˆ) r (B) a a, r a 1 ˆi – 3ˆj  kˆ (C) → r 1 (ˆi – ˆj  kˆ) (D) none of these Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5 (4 marks 3 min.) [20, 15] Match the Following (no negative marking) (2 × 4) Q.6 (8 marks 8 min.) [8, 8] 1. If → → are nonzero and noncollinear vectors then , → → → →  → → → →  → → → → = (A) →  → (B*) →  → (C) →  → (D) →  → 2. A vector → of magnitude 20 parallel to the bisector of the angle between → a  7i  4 j  4k and → ˆ ˆ ˆ is b  2i  j  2k (A) ± 20 2ˆi  7ˆj  kˆ 3 (B) ± 3 ˆi  7ˆj  2kˆ 20 (C) ± 20 ˆi  2ˆj  7kˆ 3 (D*) ± 20 ˆi  7ˆj  2kˆ 3 3. Let the centre of the parallelopiped formed by   PA  ‸i  2 ‸j  2 k‸ ;  PB  4 ‸i  3‸j  k‸ ; PC  3‸i  5 ‸j  k‸ is given by the position vector (7, 6, 2) . Then the position vector of the point P is: (A*) (3, 4, 1) (B) (6, 8, 2) (C) (1, 3, 4) (D) (2, 6, 8) 4. If Lim x  – rx)  2 , then (A*) q = 4r (B) q = 2r (C) q = r (D) q = 6r 5. The number log4 2 + (2000)6 3 log (2000)6 can be written as m where m and n are relatively prime n positive integers, then (m + n) equals (A) 4 (B) 5 (C) 6 (D*) 7 6. Match the column Column - I Column - II (A) If → → → are three mutually perpendicular vectors where (p) 3 a, b, c 4 → → → 1 → → → → → → a  b  2 and c  1 , then [a  b 12 b  c c  a] is (B) If → → are two unit vectors inclined at  , then (q) 0 a, b 3 → → → → →

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