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Day 45: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 4 times: 29 Jul 2022, 25 Jan 2023, 8 Apr 2023, 24 Jan 2025. This one: 24 Jan 2025 See all 4 of this type

    65
    Let circle CC be the image of x2+y2−2x+4y−4=0x^{2}+y^{2}- 2x + 4y - 4 = 0 in the line 2x−3y+5=02x - 3y + 5 = 0 and AA be the point on CC such that OA is parallel to xx-axis and A lies on the right hand side of the centre OO of CC. If B(α,β)B(\alpha,\beta), with β<4\beta < 4, lies on CC such that the length of the arc AB is (1/6)th (1/6)^{\text{th~}} of the perimeter of C , then β−3α\beta -\sqrt{3}\alpha is equal to

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  2. Question 2

    Application of Integrals. This type asked 4 times: 29 Jul 2022, 29 Jan 2023, 29 Jan 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    71
    If the area of the larger portion bounded between the curves x2+y2=25x^{2}+y^{2}= 25 and y=∣x−1∣y = |x - 1| is 14(bπ+c)\frac{1}{4}(b\pi + c), b,c∈Nb,c \in N, then b+cb + c is equal to ___\_\_\_

  3. Question 3

    Application of Integrals. This type asked 4 times: 2021 Paper 5, 26 Jul 2022, 6 Apr 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    133
    If the area of the region {(x,y):−1≤x≤1,0≤y≤a+e∣x∣−e−x,a>0}\left\{ (x,y): - 1 \leq x \leq 1,0 \leq y \leq a +e^{|x|}-e^{- x},a > 0 \right\} is e2+8e+1e\frac{e^{2}+ 8e + 1}{e}, then the value of a is :

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  4. Question 4

    Permutations and Combinations. This type asked 4 times: 2021 Paper 22, 1 Feb 2023, 8 Apr 2023, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    62
    The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is

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  5. Question 5

    Probability. This type asked 4 times: 2021 Paper 7, 2021 Paper 20, 25 Jun 2022, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    70
    One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

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