Question 1: Palette 1/7

AP-EAPCET 2025 MCQ

The equation $x^{\frac{3}{4}\left(\log _2 x\right)^2+\log _2 x-\frac{5}{4}}=\sqrt{2}$ has

A

no real roots

B

only one real solution

C

exactly two real solutions

D

exactly three real solutions

Question 2: Palette 2/7

AP-EAPCET 2024 MCQ

$\cosh (\log 4)$ is equal to

A

$\frac{8}{17}$

B

$\frac{17}{8}$

C

0

D

$\frac{9}{8}$

Question 3: Palette 3/7

AP-EAPCET 2024 MCQ

$\cosh 1 + 2 = $

A

$\log(2 + \sqrt{3})$

B

$\log(2 + \sqrt{5})$

C

$\log(2 - \sqrt{5})$

D

$\log(2 + \sqrt{2})$

Question 4: Palette 4/7

AP-EAPCET 2022 MCQ

$4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2 x-1} \Rightarrow x=$

A

$\frac{5}{2}$

B

$\frac{1}{2}$

C

$\frac{3}{2}$

D

$\frac{7}{2}$

Question 5: Palette 5/7

AP-EAPCET 2022 MCQ

$\left\{x \in R / \frac{\sqrt{|x|^2-2|x|-8}}{\log \left(2-x-x^2\right)}\right.$ is a real number $\}=$

A

$(-\infty,-4] \cup[4, \infty)$

B

$\phi$

C

$(-1,2)$

D

$(-\infty,-4] \cup(-1,2) \cup[4, \infty)$

Question 6: Palette 6/7

AP-EAPCET 2022 MCQ

If $4+6\left(e^{2 x}+1\right) \tanh x=11 \cosh x+11 \sinh x$ then $x=$

A

$\log _{10}$

B

$\log 4$

C

$\log 5$

D

$\log 2$

Question 7: Palette 7/7

AP-EAPCET 2022 MCQ

If $4^x-3^{x-1 / 2}=3^{x+1 / 2}-2^{2 x-1}$, then the value of $x$ is

A

$7 / 2$

B

$5 / 2$

C

$1 / 2$

D

$3 / 2$