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Day 157: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 31 Jan 2023 (same type asked 5 times) See all 5 of this type

    151
    The equation e4x+8e3x+13e2x−8ex+1=0,x∈Re^{4x}+ 8e^{3x}+ 13e^{2x}- 8e^{x}+ 1 = 0,x \in R has:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 30 Jan 2023 (same type asked 5 times) See all 5 of this type

    85
    If the equation of the plane passing through the point (1,1,2)(1,1,2) and perpendicular to the line x−3y+x - 3y + 2z−1=0=4x−y+z2z - 1 = 0 = 4x - y + z is Ax+By+Cz=1Ax + By + Cz = 1, then 140(C−B+A)140(C - B + A) is equal to

  3. Question 3

    Three Dimensional Geometry. Asked once: 8 Apr 2023 (same type asked 5 times) See all 5 of this type

    162
    For a,b∈Za,b \in Z and ∣a−b∣≤10|a - b| \leq 10, let the angle between the plane P:ax+y−z=bP:ax + y - z = b and the line l:x−1=al:x - 1 = a −y=z+1- y = z + 1 be cos⁡−1(13)\cos^{- 1}\left( \frac{1}{3} \right). If the distance of the point (6,−6,4)(6, - 6,4) from the plane PP is 363\sqrt{6}, then a4+b2a^{4}+b^{2} is equal to

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  4. Question 4

    Conic Sections. Asked once: 2021 Paper 26 (same type asked 5 times) See all 5 of this type

    65
    If the locus of the mid-point of the line segment from the point (3,2)(3,2) to a point on the circle, x2+y2=1x^{2}+y^{2}= 1 is a circle of the radius rr, then rr is equal to:

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  5. Question 5

    Conic Sections. Asked once: 29 Jun 2022 (same type asked 5 times) See all 5 of this type

    79
    Let the tangent to the circle C1:x2+y2=2C_{1}:x^{2}+y^{2}= 2 at the point M(−1,1)M( - 1,1) intersect the circle C2C_{2} : (x−3)2+(y−2)2=5(x - 3)^{2}+ (y - 2)^{2}= 5, at two distinct points AA and BB. If the tangents to C2C_{2} at the points AA and BB intersect at NN, then the area of the triangle ANB is equal to:

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