JEE MAIN Exponential Series Previous Year Questions (PYQs) – Page 1 of 2
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The sum of all the real roots of the equation $({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$ is
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Solution
The number of real roots of the equation ${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$ is :
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Solution
For $x\ge0$, the least value of $K$ for which $4^{,1+x}+4^{,1-x},\ \dfrac{K}{2},\ 16^{x}+16^{-x}$ are three consecutive terms of an A.P. is:
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Solution
The number of real roots of the equation ${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$ is :
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Solution
The number of solutions of the equation $e^{\sin x}-2e^{-\sin x}=2$ is:
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Solution
The sum of all real values of $x$ satisfying the equation
$(x^{2} - 5x + 5)^{x^{2} + 4x - 60} = 1$ is :
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Solution
Let $S=\Big\{x\in\mathbb{R}:(\sqrt3+\sqrt2)^{x}+(\sqrt3-\sqrt2)^{x}=10\Big\}$.
Then the number of elements in $S$ is:
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Solution
$ \text{The equation } e^{4x}+8e^{3x}+13e^{2x}-8e^{x}+1=0,\ x\in\mathbb{R}\ \text{ has:} $
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Solution
The sum $1+\dfrac{1+3}{2!}+\dfrac{1+3+5}{3!}+\dfrac{1+3+5+7}{4!}+\cdots$ up to $\infty$ terms is equal to
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Solution
The number of real roots of the equation ${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$ is :
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Solution
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and More.
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