Relations and Functions

JEE Main · Mathematics · 17 past questions

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1. Q1 2026 2 Apr Shift 1

   If the domain of the function $f(x)=\sqrt{\log_{(0.6)}\left(\left|\dfrac{2x-5}{x^2-4}\right|\right)}$ is…

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2. Q2 2026 4 Apr Shift 1

   Let $[\cdot]$ denote the greatest integer function. If the domain of the function…

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3. Q3 2026 4 Apr Shift 1

   The number of functions $f:\{1,2,3,4\}\to\{a,b,c\}$, which are not onto, is…

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4. Q4 2026 4 Apr Shift 2

   For the function $f: [1,\infty) \to [1,\infty)$ defined by $f(x) = (x-1)^4 + 1$, among the two statements…

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5. Q5 2026 4 Apr Shift 2

   Let for some $\alpha\in\mathbb R$, $f:\mathbb R\to\mathbb R$ be a function satisfying…

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6. Q6 2026 5 Apr Shift 1

   Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that…

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7. Q7 2026 5 Apr Shift 1

   Let $A=\{1,2,3,4,5,6\}$. The number of one-one functions $f:A\to A$ such that $f(1)\ge3$, $f(3)\le4$ and…

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8. Q8 2026 5 Apr Shift 2

   Let $A = \{1, 4, 7\}$ and $B = \{2, 3, 8\}$. Then the number of elements, in the relation…

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9. Q9 2026 6 Apr Shift 1

   Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\to\{1,e,e^2,e^3\}$ and…

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10. Q10 2026 6 Apr Shift 2

    Let $f: \mathbf{R} \to \mathbf{R}$ be defined as $f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}$. Then $f$ is…

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11. Q11 2026 6 Apr Shift 2

    Let $f: \mathbb{R} \to \mathbb{R}$ be such that $f(xy) = f(x)f(y)$, for all $x, y \in \mathbb{R}$ and…

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12. Q12 2026 6 Apr Shift 2

    $Let R = {(x, y) \in N \times N : \log_e(x+y) \le 2}. Then the minimum number of elements, required to be…$

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13. Q13 2026 6 Apr Shift 2

    Let $f(x) = \begin{cases} x^3+8 ; & x<0 \\ x^2-4; & x\ge 0 \end{cases}$ and…

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14. Q14 2026 8 Apr Shift 2

    Consider the relation R on the set {-2, -1, 0, 1, 2} defined by (a, b) ∈ R if and only if 1+ab > 0. Then…

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15. Q15 2026 8 Apr Shift 2

    Let $f:(1,\infty)\to\mathbb{R}$ be a function defined as $f(x)=\dfrac{x-1}{x+1}$. Let $f^{i+1}(x)=f(f^i(x))$…

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16. Q16 2026 8 Apr Shift 2

    Let $\dfrac{x^2}{f(a^2+7a+3)} + \dfrac{y^2}{f(3a+15)} = 1$ represent an ellipse with major axis along y-axis…

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17. Q17 2026 8 Apr Shift 2

    Let $f$ be a polynomial function such that…

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