PYQ Vault

Day 68: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 3 times: 2021 Paper 19, 12 Apr 2023, 6 Apr 2024. This one: 6 Apr 2024 See all 3 of this type

    74
    The interval in which the function f(x)=xx,x>0f(x) =x^{x},x> 0, is strictly increasing is

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  2. Question 2

    Relations and Functions. This type asked 3 times: 2021 Paper 24, 25 Jan 2023, 6 Apr 2024. This one: 6 Apr 2024 See all 3 of this type

    166
    Let f(x)=17−sin⁡5xf(x) =\frac{1}{7 - \sin5x} be a function defined on RR. Then the range of the function f(x)f(x) is equal to:

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  3. Question 3

    Differentiation. This type asked 3 times: 25 Jun 2022, 4 Apr 2024, 5 Apr 2024. This one: 5 Apr 2024 See all 3 of this type

    77
    Let f(x)=x5+2x3+3x+1,x∈Rf(x) =x^{5}+ 2x^{3}+ 3x + 1,x \in R, and g(x)g(x) be a function such that g(f(x))=xg(f(x)) = x for all x∈Rx \in R. Then g(7)g′(7)\frac{g(7)}{g^{'}(7)} is equal to:

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  4. Question 4

    Limits and Continuity. This type asked 3 times: 2021 Paper 20, 8 Apr 2023, 5 Apr 2024. This one: 5 Apr 2024 See all 3 of this type

    176
    Let a>0a > 0 be a root of the equation 2x2+x−2=02x^{2}+ x - 2 = 0. If lim⁡x→1a16(1−cos⁡(2+x−2x2))(1−ax)2=α+β17\lim_{x \rightarrow\frac{1}{a}} \frac{16\left( 1 - \cos\left( 2 + x - 2x^{2} \right) \right)}{\left( 1 - ax \right)^{2}}= \alpha + \beta\sqrt{17}, where α,β∈Z\alpha,\beta \in Z then α+β\alpha + \beta is equal to
  5. Question 5

    Relations and Functions. This type asked 3 times: 2021 Paper 1, 26 Jun 2022, 5 Apr 2024. This one: 5 Apr 2024 See all 3 of this type

    161
    Let f, g:R→Rf,\text{ }g:R \rightarrow R be defined as: f(x)=∣x−1∣f(x) = |x - 1| and g(x)={ex,x≥0x+1,x≤0g(x) =\left\{ \begin{matrix} e^{x}, & x \geq 0 \\ x + 1, & x \leq 0 \end{matrix} \right.. Then the function f( g(x))f(\text{ }g(x)) is

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