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Day 286: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    164
    Let QQ be the foot of perpendicular drawn from the point P(1,2,3)P(1,2,3) to the plane x+2y+z=14x + 2y + z = 14. If RR is a point on the plane such that ∠PRQ=60∘\angle PRQ =60^{\circ}, then the area of △PQR\bigtriangleup PQR is equal to:

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  2. Question 2

    Conic Sections. Asked once: 25 Jul 2022 (same type asked 3 times) See all 3 of this type

    163
    The tangents at the point A(1,3)A(1,3) and B(1,−1)B(1, - 1) on the parabola y2−2x−2y=1y^{2}- 2x - 2y = 1 meet at the point PP. Then the area (in unit  2\ ^{2} ) of the triangle PABPAB is:-

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  3. Question 3

    Vector Algebra. Asked once: 2021 Paper 26 (same type asked 3 times) See all 3 of this type

    72
    If vectors a→1=xi^−j^+k^{\overrightarrow{a}}_{1}= x\widehat{i}-\widehat{j}+\widehat{k} and a→2=i^+yj^+zk^{\overrightarrow{a}}_{2}=\widehat{i}+ y\widehat{j}+ z\widehat{k} are collinear, then aa possible unit vector parallel to the vector xi^+yj^+zk^x\widehat{i}+ y\widehat{j}+ z\widehat{k} is:

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  4. Question 4

    Application of Integrals. Asked once: 2021 Paper 25 (same type asked 3 times) See all 3 of this type

    81
    The area of the region bounded by the curve y=∣∣x−1∣−2∣y=\big||x-1|-2\big| and the line y=2y=2 is ____.

  5. Question 5

    Differentiation. Asked once: 2021 Paper 18 (same type asked 3 times) See all 3 of this type

    88
    If y=y(x)y=y(x) is an implicit function of xx such that log⁡e(x+y)=4xy\log_{e}(x+y) = 4xy, then d2ydx2\frac{d^{2}y}{dx^{2}} at x=0x= 0 is equal to