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Day 74: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 3 times: 2021 Paper 5, 29 Jan 2023, 1 Feb 2023. This one: 1 Feb 2023 See all 3 of this type

    175
    The point of intersection CC of the plane 8x+y+2z=08x+y+2z=0 and the line joining the points A(−3,−6,1)A(-3,-6,1) and B(2,−4,−3)B(2,-4,-3) divides the line segment ABAB internally in the ratio 14:314:3. If a,b,ca,b,c (where ∣a∣,∣b∣,∣c∣|a|,|b|,|c| are coprime) are the direction ratios of the perpendicular from the point CC on the line 1−x1=y+42=z+23\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}, then ∣a+b+c∣|a+b+c| is equal to

  2. Question 2

    Application of Integrals. This type asked 3 times: 28 Jun 2022, 29 Jun 2022, 30 Jan 2023. This one: 30 Jan 2023 See all 3 of this type

    83
    Let α\alpha be the area of the larger region bounded by the curve y2=8xy^{2}= 8x and the lines y=xy = x and x=2x = 2, which lies in the first quadrant. Then the value of 3α3\alpha is equal to

  3. Question 3

    Matrices. This type asked 3 times: 2021 Paper 2, 28 Jul 2022, 25 Jan 2023. This one: 25 Jan 2023 See all 3 of this type

    167
    Let A, B, C be 3×33 \times 3 matrices such that AA is symmetric and BB and CC are skew-symmetric. Consider the statements (S1) A13 B26−B26 A13A^{13}{\text{ }B}^{26}-B^{26}{\text{ }A}^{13} is symmetric (S2) A26C13−C13 A26A^{26}C^{13}-C^{13}{\text{ }A}^{26} is symmetric Then,

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  4. Question 4

    Conic Sections. This type asked 3 times: 2021 Paper 10, 2021 Paper 20, 24 Jan 2023. This one: 24 Jan 2023 See all 3 of this type

    82
    Let a tangent to the curve 9x2+16y2=1449x^{2}+ 16y^{2}= 144 intersect the coordinate axes at the points AA and BB. Then, the minimum length of the line segment ABAB is

  5. Question 5

    Straight Lines. This type asked 3 times: 26 Jul 2022, 27 Jul 2022, 24 Jan 2023. This one: 24 Jan 2023 See all 3 of this type

    176
    The equations of the sides AB,BCAB,BC and CACA of a triangle ABCABC are: 2x+y=0,x+py=21a,(a≠0)2x + y = 0,x + py = 21a,(a \neq 0) and x−y=3x - y = 3 respectively. Let P(2,a)P(2,a) be the centroid of △ABC\bigtriangleup ABC. Then (BC)2(BC)^{2} is equal to