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Day 485: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 8 Apr 2024

    67
    Let f(x)=4cos⁡3x+33cos⁡2x−10f(x) = 4\cos^{3}x+ 3\sqrt{3}\cos^{2}x- 10. The number of points of local maxima of ff in interval (0,2π)(0,2\pi) is:

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  2. Question 2

    Application of Integrals. Asked once: 3 Apr 2025

    75
    The area of the region bounded by the curve y=max⁡{∣x∣, x∣x−2∣}y=\max\{|x|,\ x|x-2|\}, the xx-axis and the lines x=−2x=-2 and x=4x=4 is equal to

  3. Question 3

    Binomial Theorem. Asked once: 6 Apr 2024

    86
    If the second, third and fourth terms in the expansion of (x+y)n(x + y)^{n} are 135,30 and 103\frac{10}{3}, respectively, then 6(n3+x2+y)6\left( n^{3}+x^{2}+ y \right) is equal to

  4. Question 4

    Complex Numbers. Asked once: 29 Jan 2025

    149
    Let integers a,b∈[−3,3]a,b \in \lbrack - 3,3\rbrack be such that a+b≠0a + b \neq 0. Then the number of all possible ordered pairs (a, b), for which ∣z−az+b∣=1\left| \frac{z - a}{z + b} \right|= 1 and ∣z+1ωω2ωz+ω21ω21z+ω∣=1,z∈C\left| \begin{matrix} z + 1 & \omega & \omega^{2} \\ \omega & z +\omega^{2} & 1 \\ \omega^{2} & 1 & z + \omega \end{matrix} \right|= 1,z \in C, where ω\omega and ω2\omega^{2} are the roots of x2+x+x^{2}+ x + 1=01 = 0, is equal to  ____\ \_\_\_\_

  5. Question 5

    Conic Sections. Asked once: 5 Apr 2026 S1

    60
    Let P be a moving point on the circle x2+y2−6x−8y+21=0x^{2}+y^{2}- 6x- 8y+ 21 = 0, Then, the maximum distance of P from the vertex of the parabola x2+6x+y+13=0x^{2}+ 6x+y+ 13 = 0 is equal to :

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