##### JEE Questions

Welcome to the BYJU’S JEE questions and answers page! Students and aspirants can access a huge library of questions covering all the important topics that are included in the JEE syllabus. The questions and answers have been prepared by a group of experienced subject matter experts. Students will find questions framed from Physics, Maths and Chemistry subjects.

The JEE questions and answers discussed here will give a much clearer idea of many JEE topics such as gravitation, thermodynamics, atomic structure, chemical bonding, binomial theorem, quadratic equation, etc. The questions have further been answered in an informative and easy to understand manner.

Alternatively, the questions are very important from an examination point of view and can help in quick revision of the different topics. Additionally, students can also clear their doubts and confusion by referring to these questions regarding any concept or topic. Students will find questions that are both conceptual and descriptive including definitions, principles, formulas, examples of, properties of, and types.

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Answer: Solution: Given z = (√3/2 +i/2)5+(√3/2 -i/2)5 = (cos π/6 +i sin π/6)5+(cos π/6 -i sin π/6)5 = 2 cos 5π/6  = -√3 => Re(z) <0, Im (z) = 0 Hence option...
Answer: Solution: Given z = (11-3i)/(1+i) Multiply numerator and denominator with (1-i) z = (11-3i)(1-i)/(1+i)(1-i) = (11-3i-11i-3)/(1+1) = (8-14i)/2 = 4-7i z-ia = 4-7i-ia z-ia real means...
Answer: In Mathematics, geometric mean and harmonic mean are the two different types of mean to calculate the average of the given values. The procedure to calculate the geometric and harmonic mean are...
Answer: Solution: Given (z-1)/(2z+1) = 4  (z-1)/(2z+1) = (x+iy-1)/(2(x+iy)+1) = ((x-1)+iy)/(2x+1)+2iy Multiply numerator and denominator with (2x+1)-2iy) =...
Answer: In Mathematics, the word “Inverse” refers to the opposite operation. It means that the operation reverses the process of other operations.  For example, the inverse of the...
Answer: Solution: Given |(z-1)/(z+1)| = 1 z = x+iy Put z in given equation |x+iy-1)/(x+iy+1)| = 1 √((x-1)2+y2) = √((x+1)2+y2) Squaring both sides (x-1)2+y2 = (x+1)2+y2 (x+1)2-(x-1)2 =...
Answer: In probability, independent events are the events that are not affected by previous events. To calculate the probability of two independent events, multiply the probability of one event by the...
Answer: Solution: Let A = z, B = iz, C = z+iz |AB| = |iz-z| |BC| = z |AC| = iz |AC| = |BC|  P is the centre of AB P = (z+iz)/2 Area of triangle ABC = ½ |AB×PC| = ½...
Answer: A heat engine is a device that converts heat to work. It takes heat from a reservoir then does work such as lifting weight and moving a piston and finally discharges heat energy into the sink...
Answer: Solution: |4-3i| = √(42+32) = √25 = 5 When tripled, magnitude = 3(5) = 15 (eiπ )3(4-3i) = (cos π+i sin π)(12-9i) = (-1+0)(12-9i) = -12+9i Hence option (1) is the answer...
Answer: In Maths, a matrix is defined as a rectangular array of numbers, which are arranged in rows and columns. Each number in the array is called the element or the entity of a matrix. The array of...
Answer: Solution: Given |z + 8| + |z - 8|= 16 Let z = x+iy |x+iy+8|+|x-iy-8| = 16 √(x+8)2+y2 = 16-√((x-8)2+y2) x2+64+16x+y2 = 256+x2+64-16x+y2-32√((x-3)2+y2) 32x =...
Answer: Solution: When the point (4,1) undergoes reflection, it becomes (1,4) After translation through a distance of 2 units (1+4)+(2,0) = (3,4) After rotation, coordinates are (√2, 7√2)...
Answer: Solution: Given x = (-3+i√3)/2 = (-1+i√3)/2-(1/1) = ω-1 [since ω = (-1+i√3)/2] (x2+3x2)2(x2+3x+1) (x2+3x2)2(x2+3x+1) =...
Answer: Solution: Let Z = ((1+i)/√2)2/3 = ((1/√2)+(i/√2))2/3 Z = (cos (π/4) + i sin (π/4))2/3 Z = cos (8k+1)π/6 + i sin (8k+1)π/6 Substitute k = 1, we get Z = cos...
Answer: Solution: Given √(x+iy) = ±(a+ib) Squaring both sides (x+iy) = (a+ib)2 = a2+2aib-b2 = a2-b2+2aib Comparing real and imaginary part x = a2-b2 y = 2ab -x-iy = -a2+b2-i2ab =...
Answer: (1) (2) (3) (4) Solution: (-1+√(3i))/2 = ω We know ω3n = 1 (-½)+√(3i)/2)1000 = ω1000 = ω3(333) ω = ω Hence option (4) is the answer...
Answer: Solution: 1+ z+ z3 + z4 = 0 => (1+z)+z3(1+z) = 0 => (1+z3)(1+z) = 0 z = -1 z3 = -1 z = -1, - ω, -ω2 are cube roots of unity So these are the vertices of an equilateral...
Answer: Solution: Given condition | z +1 - i| ≤ 1 | z - (-1+i)| ≤ 1 This will represent a circle with centre (-1,1) and radius is unity. This lies in the second quadrant. The point (0,1) i.e...
Answer: Solution: Given z1 ≠ z2 and |z1| = |z2| The numerator is purely imaginary and the denominator is purely real. Im(z) and Re(z) are real numbers. So (z2+z1)/(z1-z2) is purely imaginary...
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