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Day 26: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Complex Numbers. This type asked 5 times: 2021 Paper 2, 2021 Paper 19, 29 Jul 2022, 24 Jan 2023, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 5 of this type

    67
    If z=32+i2,i=−1z =\frac{\sqrt{3}}{2}+\frac{i}{2},i =\sqrt{- 1}, then (z201−i)8\left( z^{201}- i \right)^{8} is equal to

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  2. Question 2

    Differential Equations. This type asked 5 times: 2021 Paper 5, 25 Jun 2022, 26 Jun 2022, 26 Jul 2022, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 5 of this type

    71
    If the solution curve y=f(x)y = f(x) of the differential equation (x2−4)y′−2xy+2x(4−x2)2=0, x>2\left( x^{2} - 4 \right)y' - 2xy + 2x\left( 4 - x^{2} \right)^{2} = 0,\ x > 2, passes through the point ( 3,15 ), then the local maximum value of f is ____\_\_\_\_

  3. Question 3

    Sequences and Series. This type asked 5 times: 2021 Paper 22, 1 Feb 2024, 4 Apr 2024, 7 Apr 2025, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 5 of this type

    74
    Suppose a,b,ca,b,c are in A.P. and a2,2 b2,c2a^{2},2{\text{ }b}^{2},c^{2} are in G.P. If a<b<ca < b < c and a+b+c=1a + b + c = 1, then 9(a2+b2+c2)9\left( a^{2} + b^{2} + c^{2} \right) is equal to ____\_\_\_\_.

  4. Question 4

    Complex Numbers. This type asked 5 times: 2021 Paper 25, 29 Jun 2022, 27 Jan 2024, 30 Jan 2024, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    71
    Let α=−1+i32\alpha = \frac{- 1 + i\sqrt{3}}{2} and β=−1−i32,i=−1\beta = \frac{- 1 - i\sqrt{3}}{2},i = \sqrt{- 1}. If (7−7α+9β)20+(9+7α−7β)20+(−7+9α+7β)20+(14+7α+7β)20=m10(7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + ( - 7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, then m is ____\_\_\_\_ .

  5. Question 5

    Conic Sections. This type asked 5 times: 14 Jun 2022, 28 Jun 2022, 25 Jul 2022, 13 Apr 2023, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    60
    If the line αx+2y=1\alpha x + 2y = 1, where α∈R\alpha \in R, does not meet the hyperbola x2−9y2=9x^{2}- 9y^{2}= 9, then a possible value of α\alpha is :

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