JEE Main Algebra — Numbers & Matrices – Topic Test

Topics in this test

Difficulty: 15 medium · 15 hard

Algebra — Numbers & Matrices MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

1. Q1. If a complex number z satisfies |z| = 1 and arg z = π/3, then z + 1/z equals:

   यदि एक सम्मिश्र संख्या z, |z| = 1 और arg z = π/3 को संतुष्ट करती है, तो z + 1/z बराबर है:

   • A. 1
   • B. 1/2
   • C. 2
   • D. √3
   Solution

   Here z = cos(π/3) + i sin(π/3) and 1/z = z̄ = cos(π/3) − i sin(π/3), so z + 1/z = 2cos(π/3) = 2 · (1/2) = 1.

   यहाँ z = cos(π/3) + i sin(π/3) और 1/z = z̄ = cos(π/3) − i sin(π/3), अतः z + 1/z = 2cos(π/3) = 2 · (1/2) = 1 है।

2. Q2. Match List I (complex number) with List II (its modulus). List I: A. 3 + 4i; B. 5 + 12i; C. 8 + 6i; D. 7 + 24i. List II: 1. 13; 2. 5; 3. 25; 4. 10.

   सूची I (सम्मिश्र संख्या) का सूची II (उसका मापांक) के साथ मिलान कीजिए। सूची I: A. 3 + 4i; B. 5 + 12i; C. 8 + 6i; D. 7 + 24i। सूची II: 1. 13; 2. 5; 3. 25; 4. 10।

   • A. A-2, B-1, C-4, D-3
   • B. A-2, B-1, C-3, D-4
   • C. A-3, B-1, C-4, D-2
   • D. A-1, B-2, C-3, D-4
   Solution

   |3+4i| = 5, |5+12i| = 13, |8+6i| = 10, and |7+24i| = 25, giving A-2, B-1, C-4, D-3.

   |3+4i| = 5, |5+12i| = 13, |8+6i| = 10, और |7+24i| = 25, जिससे A-2, B-1, C-4, D-3 प्राप्त होता है।

3. Q3. In the Argand plane, the equation |z − i| = |z − 1| represents:

   आर्गंड तल में, समीकरण |z − i| = |z − 1| निरूपित करता है:

   • A. the line x + y = 1 / रेखा x + y = 1
   • B. the line y = −x / रेखा y = −x
   • C. the line y = x + 1 / रेखा y = x + 1
   • D. the line y = x / रेखा y = x
   Solution

   The equation is the locus of points equidistant from (0, 1) and (1, 0), i.e. the perpendicular bisector of the segment joining them, which is the line y = x.

   यह समीकरण उन बिंदुओं का बिंदुपथ है जो (0, 1) और (1, 0) से समान दूरी पर हैं, अर्थात् इन्हें मिलाने वाले खंड का लंब समद्विभाजक, जो रेखा y = x है।

Frequently asked questions

More tests in the JEE Main 2027 Mock Test Series

• Basic Concepts & Atomic Structure – Topic TestFree
• Bonding & Periodicity – Topic Test
• Inorganic — p/d/f Block & Coordination – Topic Test
• Organic — Biomolecules & Practical – Topic Test
• Organic — Functional Groups – Topic Test
• Organic — Fundamentals & Hydrocarbons – Topic Test
• Physical Chemistry — Electrochemistry & Kinetics – Topic Test
• Physical Chemistry — Energetics & Equilibrium – Topic Test
• Algebra — Combinatorics & Series – Topic Test
• Coordinate Geometry – Topic Test
• Differential Calculus – Topic Test
• Integral Calculus & Differential Equations – Topic Test
• Probability & Statistics – Topic Test
• Sets, Relations, Functions & Trigonometry – Topic Test
• Vectors & 3D Geometry – Topic Test
• Electrostatics and Current Electricity – Topic Test
• Magnetism, EMI and EM Waves – Topic Test
• Mechanics – Topic Test
• Modern Physics – Topic Test
• Optics – Topic Test
• Oscillations and Waves – Topic Test
• Properties of Matter & Heat – Topic Test
• Units, Measurement & Experimental Skills – Topic Test
• Basic Concepts & Atomic Structure: Atomic Structure – Chapter Test
• Basic Concepts & Atomic Structure: Some Basic Concepts in Chemistry – Chapter Test
• Bonding & Periodicity: Chemical Bonding and Molecular Structure – Chapter Test
• Bonding & Periodicity: Classification of Elements and Periodicity in Properties – Chapter Test
• Inorganic — p/d/f Block & Coordination: Coordination Compounds – Chapter Test
• Inorganic — p/d/f Block & Coordination: d- and f-Block Elements – Chapter Test
• Inorganic — p/d/f Block & Coordination: p-Block Elements – Chapter Test

See the full JEE Main 2027 Mock Test Series → · JEE Main: pattern, notification & syllabus →