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Day 584: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2021 Paper 9

    70
    A vector a→\overrightarrow{a} has components 3p3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, a→\overrightarrow{a} has components p+1p + 1 and 10\sqrt{10}, then a value of pp is equal to:

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  2. Question 2

    Application of Derivatives. Asked once: 29 Jun 2022

    156
    Let f:R→Rf:R \rightarrow R be a function defined by f(x)=(x−3)n1(x−5)n2,n1,n2∈Nf(x) = (x - 3)^{n_{1}}(x - 5)^{n_{2}},n_{1},n_{2}\in N. Then, which of the following is NOT true?

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  3. Question 3

    Application of Integrals. Asked once: 25 Jul 2022

    73
    Let the locus of the centre (α,β),β>0(\alpha,\beta),\beta > 0, of the circle which touches the circle x2+(y−1)2=1x^{2}+ (y - 1)^{2}= 1 externally and also touches the xx-axis be LL. Then the area bounded by LL and the line y=4y = 4 is:

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  4. Question 4

    Complex Numbers. Asked once: 27 Jul 2022

    63
    Let the minimum value v0v_{0} of v=∣z∣2+∣z−3∣2+∣z−6i∣2v = |z|^{2}+ |z - 3|^{2}+ |z - 6i|^{2}, z∈Cz \in C is attained at z=z0z =z_{0}. Then ∣2z02−z‾03+3∣2+v02\left| 2z_{0}^{2}-{\overline{z}}_{0}^{3}+ 3 \right|^{2}+v_{0}^{2} is equal to

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  5. Question 5

    Conic Sections. Asked once: 28 Jan 2025

    52
    Let ABCDABCD be a trapezium whose vertices lie on the parabola y2=4xy^{2}= 4x. Let the sides ADAD and BCBC of the trapezium be parallel to yy-axis. If the diagonal AC is of length 254\frac{25}{4} and it passes through the point (1,0)(1,0), then the area of ABCDABCD is :

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