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Day 47: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 4 times: 1 Feb 2023, 13 Apr 2023, 4 Apr 2024, 5 Apr 2024. This one: 5 Apr 2024 See all 4 of this type

    90
    Suppose ABAB is a focal chord of the parabola y2=12xy^{2}=12x of length ll and slope m<3m<\sqrt{3}. If the distance of the chord ABAB from the origin is dd, then l d2l\,d^{2} is equal to ____

  2. Question 2

    Matrices. This type asked 4 times: 2021 Paper 16, 27 Jul 2022, 8 Apr 2023, 4 Apr 2024. This one: 4 Apr 2024 See all 4 of this type

    175
    Let A be a 2×22 \times 2 symmetric matrix such that A[11]=[37]A\begin{bmatrix} 1 \\ 1 \end{bmatrix}=\begin{bmatrix} 3 \\ 7 \end{bmatrix} and the determinant of AA be 1. If A−1=αA+βIA^{- 1}= \alpha A + \beta I, where II is an identity matrix of order 2×22 \times 2, then α+β\alpha + \beta equals....

  3. Question 3

    Relations and Functions. This type asked 4 times: 2021 Paper 18, 11 Apr 2023, 30 Jan 2024, 4 Apr 2024. This one: 4 Apr 2024 See all 4 of this type

    82
    In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let mm and nn respectively be the least and the most number of students who studied all the three subjects. Then m+nm + n is equal to

  4. Question 4

    Conic Sections. This type asked 4 times: 2021 Paper 1, 2021 Paper 19, 28 Jun 2022, 31 Jan 2024. This one: 31 Jan 2024 See all 4 of this type

    64
    If one of the diameters of the circle x2+y2−10x+x^{2}+y^{2}- 10x+ 4y+13=04y+ 13 = 0 is a chord of another circle CC, whose centre is the point of intersection of the lines 2x+2x+ 3y=123y= 12 and 3x−2y=53x- 2y= 5, then the radius of the circle CC is

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  5. Question 5

    Differential Equations. This type asked 4 times: 2021 Paper 1, 2021 Paper 25, 27 Jan 2024, 31 Jan 2024. This one: 31 Jan 2024 See all 4 of this type

    158
    The temperature T(t)T(t) of a body at time t=0t = 0 is 160∘160^{\circ} FF and it decreases continuously as per the differential equation dTdt=−K(T−80)\frac{dT}{dt}= - K(T - 80), where KK is positive constant. If T(15)=120∘FT(15) =120^{\circ}F, then T(45)T(45) is equal to

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