Practice Questions

Q62.The equation |𝑧- 𝑖| = | 𝑧- 1 | , 𝑖= √-1, represents: 1 (1) a circle of radius (2) a circle of radius 1 2 (3) the line through the origin with slope 1 (4) the line through the origin with slope -1 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q62.If both the roots of the quadratic equation x2 −mx + 4 = 0 are real and distinct and they lie in the interval (1, 5), then m lies in the interval: Note: In the actual JEE paper interval was [1, 5] (1) (−5, −4) (2) (3, 4) (3) (5, 6) (4) (4, 5)

Q62.If a > 0 and z = (1+i)2a−i √25 (1) −15 −35 i (2) −35 −15 i (3) 1 5 −35 i (4) −15 + 53 i

Q62.If z z α (α ∈R) is a purely imaginary number and |z| = 2, then a value of α is : + (1) 1 (2) 12 (3) √2 (4) 2

Q62.If 𝛼 and 𝛽 be the roots of the equation 𝑥2 - 2𝑥+ 2 = 0, then the least value of 𝑛 for which 𝛼 𝑛= 1 is 𝛽 (1) 5 (2) 4 (3) 2 (4) 3

Q62.Let z ∈C be such that |z| < 1. If ω = 5(1−z)5+3z , then: JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) 5Re(ω) > 1 (2) 5Im(ω) < 1 (3) 5Re(ω) > 4 (4) 4Im(ω) > 5

Q62.Let z = 5 5 + . If R(z) and I(z) respectively denote the real and imaginary parts of z, ( √32 + 2i ) ( √32 −i2 ) then (1) I(z) = 0 (2) R(z) < 0 and I(z) > 0 (3) R(z) > 0 and I(z) > 0 (4) R(z) = −3

Q62.If 𝑧 and 𝜔 are two complex numbers such that 𝑧𝜔= 1 and 𝑎𝑟𝑔𝑧- 𝑎𝑟𝑔( 𝜔) = 2, then: (1) 𝑧¯ω = 1 - 𝑖 (2) ¯𝑧𝜔= 𝑖 √2 (3) 𝑧¯ω = -1 + 𝑖 (4) ¯𝑧ω = - 𝑖 √2

Q62.Let 𝐴= 𝜃∈- 𝜋 𝜋: 3 + 2𝑖 sin𝜃 is purely imaginary . Then the sum of the elements in 𝐴 is: 2, 1 - 2𝑖 sin𝜃 5𝜋 (1) (2) π 6 (3) 2𝜋 (4) 3𝜋 3 4

Q62.Let z be a complex number such that |z| + z = 3 + i ( where i = √−1) Then |z| is equal to : (1) √34 (2) 5 3 3 (3) √41 (4) 5 4 4

Q62.All the points in the set S = { α+iα−i , α ∈R}, i = √−1 lie on a (1) straight line whose slope is −1 (2) circle whose radius is √2 (3) circle whose radius is 1 (4) straight line whose slope is 1 JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper

Q62.Let z1 and z2 be two complex numbers satisfying |z1| = 9 and |z2 −3 −4i| = 4. Then the minimum value of |z1 −z2| is : (1) 2 (2) √2 (3) 0 (4) 1

Q62.The number of integral values of 𝑚 for which the equation, 1 + 𝑚2𝑥2 - 21 + 3𝑚𝑥+ 1 + 8𝑚= 0 has no real root, is (1) 2 (2) 3 (3) Infinitely many (4) 1 𝑖

Q62.Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If z = 3z1 + 2z2 then maximum 2z2 3z1 value of |z| is Note: In actual paper value of |z| was asked. Hence, none of the options given were correct. So we have modified the question as well as options. (1) 7 (2) 9 2 2 (3) 5 (4) 1 2 2 √172

Q62.Let z ∈C with Im(z) = 10 and it satisfies 22 z+nz−n = 2i −1 for some natural number n. Then (1) n = 20 and Re(z) = 10 (2) n = 40 and Re(z) = 10 (3) n = 20 and Re(z) = −10 (4) n = 40 and Re(z) = −10

Q62.Let (−2 −13 i) 3 = x+iy27 (i = √−1), (1) 91 (2) -85 (3) 85 (4) -91

Q63.If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r can not be equal to: (1) 3 (2) 3 4 2 (3) 5 (4) 7 4 4

Q63.Let a1, a2, … , a10 be a G.P. If a1a3 = 25, then a5a9 equals : (1) 54 (2) 4 (52) (3) 53 (4) 2 (52)

Q63.Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys 𝐴 and 𝐵, who refuse to be the members of the same JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper team, is: (1) 300 (2) 200 (3) 500 (4) 350

Q63.The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + … upto 11th term is: (1) 945 (2) 916 (3) 946 (4) 915

Q63.Let z0 be a root of quadratic equation, x2 + x + 1 = 0. If z = 3 + 6iz810 −3iz930 , then arg (z) is equal to: (1) 0 (2) π4 (3) π (4) π 6 3

Q63.If 19 th term of a non-zero A.P. is zero, then its (49th term): (29th term) is: (1) 4: 1 (2) 1: 3 (3) 3: 1 (4) 2: 1 2 n where q is a real number + + … +

Q63.Suppose that 20 pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is: (1) 170 (2) 180 (3) 210 (4) 190

Q63.The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is: (1) 220 (2) 221 (3) 220 + 1 (4) 220 - 1

Q63.A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then: (1) m = n = 68 (2) n = m –8 (3) m = n = 78 (4) m + n = 68 A is