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 distinct real roots of the equation $|\mathrm{x}||\mathrm{x}+2|-5|\mathrm{x}+1|-1=0$ is....................

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Let $\alpha, \beta ; \alpha>\beta$, be the roots of the equation $x^2-\sqrt{2} x-\sqrt{3}=0$. Let $P_n=\alpha^n-\beta^n, n \in N$. Then $(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}$ is equal to :

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