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Day 112: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 2 times: 2021 Paper 3, 5 Apr 2024. This one: 5 Apr 2024 See all 2 of this type

    179
    Let a line perpendicular to the line 2x−y=102x - y = 10 touch the parabola y2=4(x−9)y^{2}= 4(x - 9) at the point PP. The distance of the point PP from the centre of the circle x2+y2−14x−8y+56=0x^{2}+y^{2}- 14x - 8y + 56 = 0 is

  2. Question 2

    Conic Sections. This type asked 2 times: 30 Jan 2024, 5 Apr 2024. This one: 5 Apr 2024 See all 2 of this type

    162
    Let the circle C1:x2+y2−2(x+y)+1=0C_{1}:x^{2}+y^{2}- 2(x + y) + 1 = 0 and C2C_{2} be a circle having centre at (−1,0)( - 1,0) and radius 2. If the line of the common chord of C1C_{1} and C2C_{2} intersects the yy-axis at the point PP, then the square of the distance of PP from the centre of C1C_{1} is:

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  3. Question 3

    Straight Lines. This type asked 2 times: 2021 Paper 23, 5 Apr 2024. This one: 5 Apr 2024 See all 2 of this type

    158
    Let A(−1,1)A( - 1,1) and B(2,3)B(2,3) be two points and PP be a variable point above the line ABAB such that the area of △PAB\bigtriangleup PAB is 10. If the locus of PP is ax+by=15ax + by = 15, then 5a+2b5a + 2b is:

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  4. Question 4

    Three Dimensional Geometry. This type asked 2 times: 26 Jun 2022, 5 Apr 2024. This one: 5 Apr 2024 See all 2 of this type

    80
    If the line 2−x3=3y−24λ+1=4−z\frac{2 - x}{3}=\frac{3y - 2}{4\lambda + 1}= 4 - z makes a right angle with the line x+33μ=1−2y6=5−z7\frac{x + 3}{3\mu}=\frac{1 - 2y}{6}=\frac{5 - z}{7}, then 4λ+9μ4\lambda + 9\mu is equal to :

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  5. Question 5

    Limits and Continuity. This type asked 2 times: 27 Jan 2024, 4 Apr 2024. This one: 4 Apr 2024 See all 2 of this type

    151
    If the function f(x)={72x−9x−8x+12−1+cos⁡x,x≠0alog⁡e2log⁡e3,x=0f(x) =\left\{ \begin{matrix} \frac{72^{x}-9^{x}-8^{x}+ 1}{\sqrt{2}-\sqrt{1 + \cos x}} & ,x \neq 0 \\ a\log_{e}2\log_{e}3 & ,x = 0 \end{matrix} \right. is continuous at x=0x = 0, then the value of a2a^{2} is equal to

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