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Day 50: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 4 times: 2021 Paper 18, 2021 Paper 20, 29 Jun 2022, 31 Jan 2023. This one: 31 Jan 2023 See all 4 of this type

    65
    A wire of length 20 m20\text{ }m is to be cut into two pieces. A piece of length l1l_{1} is bent to make a square of area A1A_{1} and the other piece of length l2l_{2} is made into a circle of area A2A_{2}. If 2A1+3A22A_{1}+ 3A_{2} is minimum then (πl1):l2\left( \pi l_{1} \right):l_{2} is equal to:

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  2. Question 2

    Application of Integrals. This type asked 4 times: 2021 Paper 3, 2021 Paper 24, 2021 Paper 26, 29 Jan 2023. This one: 29 Jan 2023 See all 4 of this type

    162
    The area of the region A={(x,y):∣cos⁡x−sin⁡x∣≤y≤sin⁡x,0≤x≤π2}A =\left\{ (x,y):|\cos x - \sin x| \leq y \leq \sin x,0 \leq x \leq\frac{\pi}{2} \right\} is

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  3. Question 3

    Permutations and Combinations. This type asked 4 times: 2021 Paper 26, 14 Jun 2022, 26 Jun 2022, 29 Jan 2023. This one: 29 Jan 2023 See all 4 of this type

    171
    The total number of 4 -digit numbers whose greatest common divisor with 54 is 2 , is

  4. Question 4

    Conic Sections. This type asked 4 times: 2021 Paper 8, 2021 Paper 13, 27 Jul 2022, 28 Jul 2022. This one: 28 Jul 2022 See all 4 of this type

    87
    For the hyperbola H:x2−y2=1H:x^{2}-y^{2}= 1 and the ellipse E:x2a2+y2b2=1,a>b>0E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1,a > b > 0, let the (1) eccentricity of EE be reciprocal of the eccentricity of HH, and (2) the line y=52x+Ky =\sqrt{\frac{5}{2}}x + K be a common tangent of EE and HH. Then 4(a2+b2)4\left( a^{2}+b^{2} \right) is equal to

  5. Question 5

    Complex Numbers. This type asked 4 times: 2021 Paper 18, 2021 Paper 22, 26 Jun 2022, 29 Jun 2022. This one: 29 Jun 2022 See all 4 of this type

    152
    Let arg(z)arg(z) represent the principal argument of the complex number zz. Then, ∣z∣=3|z| = 3 and arg(z−1)−arg(z - 1) - arg(z+1)=π4arg(z + 1) =\frac{\pi}{4} intersect:

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