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Day 109: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 2 times: 14 Jun 2022, 23 Jan 2025. This one: 23 Jan 2025 See all 2 of this type

    134
    A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of 81 cm3/min81{\text{ }cm}^{3}/min and the thickness of the ice-cream layer decreases at the rate of 14π cm/min\frac{1}{4\pi}\text{ }cm/min. The surface area (in cm2cm^{2} ) of the chocolate ball (without the ice-cream layer) is :

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  2. Question 2

    Probability. This type asked 2 times: 2021 Paper 24, 23 Jan 2025. This one: 23 Jan 2025 See all 2 of this type

    135
    A board has 16 squares as shown in the figure : Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

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  3. Question 3

    Statistics. This type asked 2 times: 30 Jan 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 2 of this type

    66
    Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12 . If the number of students whose marks are less than 12 is 18 , then the total number of students is

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  4. Question 4

    Straight Lines. This type asked 2 times: 8 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 2 of this type

    147
    Let A(6,8),B(10cos⁡α,−10sin⁡α)A(6,8),B(10\cos\alpha, - 10\sin\alpha) and C (−10sin⁡α,10cos⁡α)( - 10\sin\alpha,10\cos\alpha), be the vertices of a triangle. If L(a,9)L(a,9) and G(h,k)G(h,k) be its orthocenter and centroid respectively, then (5a−3h+6k+100sin⁡2α)(5a - 3h + 6k + 100\sin2\alpha) is equal to ______\_\_\_\_\_\_

  5. Question 5

    Complex Numbers. This type asked 2 times: 28 Jun 2022, 9 Apr 2024. This one: 9 Apr 2024 See all 2 of this type

    82
    The sum of the square of the modulus of the elements in the set
    {z=a+ib:a,b∈Z,z∈C,∣z−1∣≤1,∣z−5∣≤∣z−5i∣}\mathbf{\{ z = a + ib:a,b \in Z,z \in C,|z - 1| \leq 1,|z - 5| \leq |z - 5i|\}}
    is