The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has

  • [JEE MAIN 2014]
  • A

    no solution

  • B

    exactly one solution

  • C

    exactly two solution

  • D

    exactly four solution

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The number of real roots of the equation $\mathrm{e}^{4 \mathrm{x}}-\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}-\mathrm{e}^{\mathrm{x}}+1=0$ is equal to $.....$

  • [JEE MAIN 2021]

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Let $t$ be real number such that $t^2=a t+b$ for some positive integers $a$ and $b$. Then, for any choice of positive integers $a$ and $b, t^3$ is never equal to

  • [KVPY 2016]