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Day 578: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 14 Jun 2022

    76
    Let a^,b^\widehat{a},\widehat{b} be unit vectors. If c→\overrightarrow{c} be a vector such that the angle between a^\widehat{a} and c→\overrightarrow{c} is π12\frac{\pi}{12}, and b^=c→+2(c→×a^)\widehat{b}=\overrightarrow{c}+ 2(\overrightarrow{c}\times\widehat{a}), then ∣6c→∣2|6\overrightarrow{c}|^{2} is equal to

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  2. Question 2

    Application of Derivatives. Asked once: 25 Jul 2022

    179
    Let the area enclosed by the xx-axis, and the tangent and normal drawn to the curve 4x3−4x^{3}- 3xy2+6x2−5xy−8y2+9x+14=03xy^{2}+ 6x^{2}- 5xy - 8y^{2}+ 9x + 14 = 0 at the point (−2,3)( - 2,3) be AA. Then 8 A8\text{ }A is equal to

  3. Question 3

    Application of Integrals. Asked once: 25 Jan 2023

    161
    Let TT and CC respectively be the transverse and conjugate axes of the hyperbola 16x2−y2+64x+4y+44=016x^{2}-y^{2}+ 64x + 4y + 44 = 0. Then the area of the region above the parabola x2=y+4x^{2}= y + 4, below the transverse axis TT and on the right of the conjugate axis CC is:

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  4. Question 4

    Complex Numbers. Asked once: 28 Jul 2022

    178
    Let z=a+ib,b≠0z = a + ib,b \neq 0 be complex numbers satisfying z2=z‾⋅21−∣z∣z^{2}=\overline{z}\cdot2^{1 - |z|}. Then the least value of nn ∈N\in N, such that zn=(z+1)nz^{n}= (z + 1)^{n}, is equal to

  5. Question 5

    Conic Sections. Asked once: 29 Jan 2025

    150
    Let y2=12xy^{2}= 12x the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP) (SQ)=1474(SQ) =\frac{147}{4}. Let CC be the circle described taking PQPQ as a diameter. If the equation of a circle CC is 64x2+64y2−αx−643y=β64x^{2}+ 64y^{2}- \alpha x - 64\sqrt{3}y = \beta, then β−α\beta - \alpha is equal to  _____\ \_\_\_\_\_ -