PYQ Vault
EbooksTutor

Day 442: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 6 Apr 2026 S1

    70
    Let e be the base of natural logarithm and let f:{1,2,3,4}→{1,e,e2,e3}f:\{ 1,2,3,4\} \rightarrow\left\{ 1,e,e^{2},e^{3} \right\} and g:{1,e,e2,e3}→{1,12,13,14}g:\left\{ 1,e,e^{2},e^{3} \right\}\rightarrow\left\{ 1,\frac{1}{2},\frac{1}{3},\frac{1}{4} \right\} be two bijective functions such that ff is strictly decreasing and g is strictly increasing. If ϕ(x)=[f−1{ g−1(12)}]x\phi(x) =\left\lbrack f^{- 1}\left\{ {\text{ }g}^{- 1}\left( \frac{1}{2} \right) \right\} \right\rbrack^{x}, then the area of the region R={(x,y):x2≤y≤ϕ(x)R =\left\{ (x,y):x^{2}\leq y \leq\phi(x) \right., 0≤x≤1}0 \leq x \leq 1\} is :

    Tap an option to check your answer.

  2. Question 2

    Binomial Theorem. Asked once: 6 Apr 2026 S1

    58
    If the coefficients of the middle terms in the binomial expansions of (1+αx)26(1 +\alpha x)^{26} and (1−αx)28(1 -\alpha x)^{28}, α≠0\alpha\neq 0, are equal, then the value of α\alpha is:

    Tap an option to check your answer.

  3. Question 3

    Complex Numbers. Asked once: 4 Apr 2026 S2

    52
    Let S={z∈C:z2+4z+16=0}S =\left\{ z \in\mathbb{C}:z^{2}+ 4z + 16 = 0 \right\}. Then ∑z∈S∣z+3i∣2\sum_{z \in S} |z +\sqrt{3}i|^{2} is equal to :

    Tap an option to check your answer.

  4. Question 4

    Conic Sections. Asked once: 8 Apr 2026 S2

    70
    Let x2f(a2+7a+3)+y2f(3a+15)=1\frac{x^{2}}{f\left( a^{2}+ 7a+ 3 \right)}+\frac{y^{2}}{f(3a+ 15)}= 1 represent an ellipse with major axis along y-axis, where ff is a strictly decreasing positive function on RR. If the set of all possible values of aa is R−[α,β]R - \lbrack\alpha,\beta\rbrack, then α2+β2\alpha^{2}+\beta^{2} is equal to :

    Tap an option to check your answer.

  5. Question 5

    Definite Integration. Asked once: 8 Apr 2026 S2

    66
    The value of the integral ∫02x(x2+x+1)(x+1)(x4+x2+1)dx\int_{0}^{2} \frac{\sqrt{x\left( x^{2}+x+ 1 \right)}}{(\sqrt{x+ 1})\left( \sqrt{x^{4}+x^{2}+ 1} \right)}dx is equal to :

    Tap an option to check your answer.