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Day 612: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 11

    57
    Let ' aa ' be a real number such that the function f(x)=ax2+6x−15,x∈Rf(x) =ax^{2}+ 6x- 15,x\in R is increasing in (−∞,34)\left( - \infty,\frac{3}{4} \right) and decreasing in (34,∞)\left( \frac{3}{4},\infty \right). Then the function g(x)=ax2−6x+15,x∈Rg(x) =ax^{2}- 6x+ 15,x\in R has aa :

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  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 9

    85
    Let z1,z2z_{1},z_{2} be the roots of the equation z2+az+12=0z^{2}+az+12=0 and z1,z2z_{1},z_{2} form an equilateral triangle with the origin. Then the value of ∣a∣|a| is

  3. Question 3

    Conic Sections. Asked once: 6 Apr 2024

    75
    A circle in inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are mm and nn, respectively, then m+n2m+n^{2} is equal to

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  4. Question 4

    Definite Integration. Asked once: 29 Jan 2023

    152
    The value of the integral ∫12(t4+1t6+1)dt\int_{1}^{2} \left( \frac{t^{4}+ 1}{t^{6}+ 1} \right)dt is

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  5. Question 5

    Matrices. Asked once: 2021 Paper 3

    89
    Let A=[xyzyzxzxy]A =\begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix}, where x,yx,y and zz are real numbers such that x+y+z>0x + y + z > 0 and xyz=2xyz = 2. If A2=I3A^{2}=I_{3}, then the value of x3+y3+z3x^{3}+y^{3}+z^{3} is