FOUNDATION X DPP : 1 MATHEMATICS Chapter 1: Number system Daily Practice Problems: 1 (Basics of Complex Number) 1. The collection of real numbers and imaginary numbers is known as: (a) Rational no (b) Irrational no (c) Complex no (d) None of these 2. A complex no consists of a real part and a/an : (a) Rational part (b) Irrational part (c) Imaginary part (d) None of these 3. For a complex no, z x iy, to be purely real : (a) Real part of z 0 (b) Imaginary part of z 0 (c) Real and imaginary part both should be zero (d) Complex no, z 0 4. 0 is a : (a) purely real complex no (b) purely imaginary complex no (c) purely real as well as purely imaginary complex no (d) Not a complex no 5. The real part in a complex no, z 5 5 (a) 5 (b) 5 (c) 1 (d) –1 6. The imaginary part in a complex no, z 9 16 is (a) 4i (b) 4i (c) 4 (d) –4 7. i i i i ? , where i 1 2 3 4 (a) –1 (b) 1 (c) 0 (d) Not defined 8. i is equal to (where i 1 ) 7 (a) i (b) i (c) 1 (d) –1 9. The number which can’t be represented on number line is (a) 2.5 (b) 1.3 (c) 3 (d) 5 10. 4 9 ? (a) –6 (b) 6i (c) 6 (d) 6i 11. Represent 4 16 in a ib form (a) 0 (b) 8 (c) 4 4i (d) 4 4i 12. The complex conjugate of 3 3 is (a) 3 3 (b) 3 3 (c) 3 3 (d) 3 3 13. The product of z 3 4i and its complex conjugate is (a) 16 (b) –16 (c) 25 (d) –7 Old ICC building, near Firoz Hospital, Sir Syed Nagar, Medical Road, Aligarh: 9997607607, 9997394458 FOUNDATION X DPP : 1 MATHEMATICS Chapter 1: Number system 3 14. i 2i i ? 1 8 1 1 1 1 3 (a) i (b) (c) i (d) i 256 256 256 256 15. 5 3i can be expressed in a ib form as 3 (a) 10 198i (b) 10 198i (c) 10 198i (d) 10 198i 16. The value of i457 is (a) 1 (b) – 1 (c) i (d) – i 1 i 1 3i 17. The standard form of is – 1 i (a) 3 i (b) 3 i (c) 1 i 3 (d) 1 i 3 18. If (x + iy) (2 – 3i) = 4 + i , then real values of x and y are – 13 14 5 14 (a) x 5, y 14 (b) x , y (c) x , y (d) None of these 5 13 13 13 1 19. The conjugate of is – 3 5i 1 1 34 (a) (3 5i ) (b) 3 + 5i (c) (d) 34 3 5i 3 5i ci 20. If a ib , where c is real, then a2 + b2 = ci (a) i (b) 1 (c) – 1 (d) 0 ANSWER KEY 1. c 2. c 3. b 4. c 5. b 6. d 7. c 8. b 9. d 10. b 11. c 12. d 13. c 14. a 15. b 16. c 17. a 18. c 19. a 20. b Old ICC building, near Firoz Hospital, Sir Syed Nagar, Medical Road, Aligarh: 9997607607, 9997394458
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