PYQ Vault
EbooksTutor

Day 462: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 4 Apr 2026 S2

    75
    Let ff be a twice differentiable function such that f(x)=∫0xtan⁡(t−x)dt−∫0xf(t)tan⁡tdt,x∈(−π2,π2)f(x) = \int_{0}^{x} \tan(t - x)dt - \int_{0}^{x} f(t)\tan tdt,x \in \left( - \frac{\pi}{2},\frac{\pi}{2} \right) .Then f′′(π6)+12f′(−π6)+f(π6)f^{''}\left( \frac{\pi}{6} \right) + 12f'\left( - \frac{\pi}{6} \right) + f\left( \frac{\pi}{6} \right) is equal to ____\_\_\_\_ .

  2. Question 2

    Determinants. Asked once: 8 Apr 2024

    153
    If α≠a,β≠b,γ≠c\alpha \neq a,\beta \neq b,\gamma \neq c and ∣αbcaβcabγ∣=0\left| \begin{matrix} \alpha & b & c \\ a & \beta & c \\ a & b & \gamma \end{matrix} \right|= 0, then aα−a+bβ−b+γγ−c\frac{a}{\alpha - a}+\frac{b}{\beta - b}+\frac{\gamma}{\gamma - c} is equal to :

    Tap an option to check your answer.

  3. Question 3

    Differential Equations. Asked once: 11 Apr 2023

    74
    Let f:[2,4]→Rf:\lbrack 2,4\rbrack \rightarrow\mathbb{R} be a differentiable function such that (xlog⁡ex)f′(x)+(log⁡ex)f(x)+f(x)≥1\left( x\log_{e}x \right)f^{'}(x) +\left( \log_{e}x \right)f(x) +f(x) \geq 1, x∈[2,4]x \in \lbrack 2,4\rbrack with f(2)=12f(2) =\frac{1}{2} and f(4)=14f(4) =\frac{1}{4}. Consider the following two statements: (A): f(x)≤1f(x) \leq 1, for all x∈[2,4]x \in \lbrack 2,4\rbrack (B): f(x)≥18f(x) \geq\frac{1}{8}, for all x∈[2,4]x\in \lbrack 2,4\rbrack Then,

    Tap an option to check your answer.

  4. Question 4

    Differentiation. Asked once: 6 Apr 2024

    163
    Suppose for a differentiable function h,h(0)=0h,h(0) = 0, h(1)=1h(1) = 1 and h′(0)=h′(1)=2h^{'}(0) =h^{'}(1) = 2. If g(x)=h(ex)eh(x)g(x) = h\left( e^{x} \right)e^{h(x)}, then g′(0)g^{'}(0) is equal to:

    Tap an option to check your answer.

  5. Question 5

    Indefinite Integration. Asked once: 4 Apr 2025

    147
    If ∫ (1+x2+x)10(1+x2−x)9dx=\int_{}^{}\ \frac{\left( \sqrt{1 + x^{2}} + x \right)^{10}}{\left( \sqrt{1 + x^{2}} - x \right)^{9}}dx =
    1m((1+x2+x)n(n1+x2−x))+C where C\frac{1}{m}\left( \left( \sqrt{1 + x^{2}} + x \right)^{n}\left( n\sqrt{1 + x^{2}} - x \right) \right) + C\text{~where~}C
    is the constant of integration and m,n∈Nm,n \in N, then m+nm + n is equal to.