1. If x = √-16, then

2. If z_1 = 2 + 3i and z_2 = =3 -2 i, then z_1 - z_2 is equal to

3. If z ≠ 0 is a complex number, then

Q. no 4 to 8 . Study Based Questions

A complex number z is purely real if and only if z¯ = z and is purely imaginary if and only if z¯ = -z. Based on the above information, answer the following questions.

(i) If 3+2i sinθ/1-2i sinθ is purely real, then θ is equal to

5. If x and y are real numbers and the complex number (2+i)x-i/4 + i + (1-i) y + 2i/4i is purely real,  the relation between x and y is

6. If z be a complex number satisfying | Re(z) |+| Im (z) |= 4, then |z| cannot be

7. The smallest positive integer (n) for which (1+i)^2n = (1-i)^2n is

8. If z_₁ and z_2 are complex numbers such that |z_1 - z_2/z_1 + z_2| =1, then

9. The solution set of 2x - 1/3 ≥ (3x-2/4)- (2-x/5) is

10. The set of values of x satisfying 2≤ (x-3) < 4 is

11. In an experiment, a solution of hydrochloric acid is to be kept between 30°C and 35°C. The range of temperature in degree Fahrenheit, if conversion formula is given by C = 5/9 (F-32), where C and F represent temperature in degree Celsius and degree Fahrenheit respectively, is between

12. The number of ways in which three girls and nine boys can be seated in two vans, each having numbered seats 3 in the front and 4 at the back, such that 3 girls always sit together in a back row on adjacent seats, is

13. Match the following columns and choose the correct option from the codes given below.

14. 8th term from the end of the sequence  12,4, 4/3, 4/9,...., 20th term is

15. Which term of the sequence 3, 6, 12, .... is 768?

16. The sum of the GP 3, 6, 12,.... upto 10 terms is

17. If the first and fourth term of a GP are 2 and 54, respectively then the sum of first seven terms is

18. The length of three unequal edges of a rectangular solid block are in GP. The volume of the Hock is 216 cm³ and the total surface area is 252 cm². The length of the longest edges is

19. The distance between the points (6, - 4) and (3,0) is

20. The coordinates of a point which divides the line. segment joining A (1, 3) and B (-3, 9) internally in the ratio 1: 3, are given by

21. The angle between the X-axis and the line joining the points (4,-2) and (5, - 3) is

22. The equation of the line which have slope -2 and cuts-off an intercept -6 on X-axis, is

23. Seven persons are to be seated in a row. The probability that two particular persons sit next to each other, is

24. P and Q are two condidates seeking admission in NEET. The probability that P is selected is 0.5 and the probability that both P and Q are selected is at most 0.3. Then, the probability of Q being selected is

25. 4 cards are drawn from a well-shuffled deck of 52 cards. Thus, the probability of obtaining 3 diamonds and one spade is