PYQ Vault
EbooksTutor

Day 617: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 3

    74
    If Rolle's theorem holds for the function f(x)=x3−ax2+bx−4,x∈[1,2]f(x) =x^{3}- ax^{2}+ bx - 4,x \in \lbrack 1,2\rbrack with f′(43)=0f^{'}\left( \frac{4}{3} \right)= 0, then ordered pair (a,b)(a,b) is equal to :

    Tap an option to check your answer.

  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 5

    71
    Let a complex number z,∣z∣≠1z,|z| \neq 1, satisfy log⁡12(∣z∣+11(∣z∣−1)2)≤2\log_{\frac{1}{\sqrt{2}}}\left( \frac{|z| + 11}{(|z| - 1)^{2}} \right)\leq 2. Then, the largest value of ∣z∣|z| is equal to

    Tap an option to check your answer.

  3. Question 3

    Conic Sections. Asked once: 5 Apr 2024

    73
    Let the line 2x+3y−k=0,k>02x + 3y - k = 0,k > 0, intersect the xx-axis and yy-axis at the points AA and BB, respectively. If the equation of the circle having the line segment ABAB as a diameter is x2+y2−3x−2y=0x^{2}+y^{2}- 3x - 2y = 0 and the length of the latus rectum of the ellipse x2+9y2=k2x^{2}+ 9y^{2}=k^{2} is mn\frac{m}{n}, where mm and nn are coprime, then 2 m+n2\text{ }m + n is equal to

    Tap an option to check your answer.

  4. Question 4

    Definite Integration. Asked once: 25 Jan 2023

    72
    The minimum value of the function f(x)=∫02e∣x−t∣dtf(x) =\int_{0}^{2} e^{|x - t|}dt is:

    Tap an option to check your answer.

  5. Question 5

    Sequences and Series. Asked once: 28 Jul 2022

    86
    For p,q∈Rp,q \in R, consider the real valued function f(x)=(x−p)2−q,x∈Rf(x) = (x - p)^{2}- q,x \in R and q>0q > 0. Let a1,a2,a3a_{1},a_{2},a_{3} and a4a_{4} be in an arithmetic progression with mean pp and positive common difference. If ∣f(ai)∣=500\left| f\left( a_{i} \right) \right|= 500 for all i=1,2,3,4i = 1,2,3,4, then the absolute difference between the roots of f(x)=0f(x) = 0 is