AP EAMCET · Maths · Basic of Mathematics
If \(x=\frac{1}{2}\left(\sqrt{7}+\frac{1}{\sqrt{7}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal to
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
Given that, \(\begin{aligned} x & =\frac{1}{2}\left(\sqrt{7}+\frac{1}{\sqrt{7}}\right) \\ \Rightarrow \quad x^2 & =\frac{1}{4}\left(7+\frac{1}{7}+2\right)=\frac{1}{4}\left(\frac{64}{7}\right) \\ & =\frac{16}{7} \end{aligned}\) Now,…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The length of the latus rectum of \(16 x^2+25 y^2=400\) isAP EAMCET 2024 Easy
- The equation of a line which makes an angle of \(45^{\circ}\) with each of the pair of lines \(x y-x-y+1=0\) isAP EAMCET 2024 Easy
- If \(0 \leq x \leq 3\) and \(0 \leq y \leq 3\), then the number of solutions \((x, y)\) of the equation \(\left(\sqrt{\sin ^2 x-\sin x+\frac{1}{2}}\right) 2^{\sec ^2 y}=1\) isAP EAMCET 2025 Medium
- \[
\begin{aligned}
& \text { If } \int \cos x \cdot \cos 2 x \cdot \cos 5 x d x \\
& =A \sin 2 x+B \sin 4 x+C \sin 6 x+D \sin 8 x+k
\end{aligned}
\]
(where \(k\) is the arbitrary constant of integration), then \(\frac{1}{B}+\frac{1}{C}=\)AP EAMCET 2019 Hard - Let \(A\) and \(B\) be events with \(P(A)=\frac{1}{3}, P(B)=\frac{1}{4}\) and \(P(A \cup B)=\frac{1}{2}\). Then which of the following statement is incorrect?AP EAMCET 2021 Easy
- \(\int_0^3 \frac{3 x+1}{x^2+9} d x\) is equal to :AP EAMCET 2003 Medium
More PYQs from AP EAMCET
- By multiplying with \(e^{\int P d x}\) on both sides of the equation \(\frac{d y}{d x}+P(x) y=Q(x)\), the left side of the equation takes the form \(\frac{d}{d x}(y f(x))\), then \(f(x)=\)AP EAMCET 2022 Medium
- Shape of \(\mathrm{XeF}_4\) molecule isAP EAMCET 2021 Easy
- When a positively charged particle enters a uniform magnetic field with uniform velocity, its trajectory can be :
(1) a straight line
(2) a circle
(3) a helixAP EAMCET 2006 Easy - The chemicals and the reaction conditions required for the preparation of ethane areAP EAMCET 2005 Easy
- The combined equation of the diagonals of the square formed by the two pairs of straight lines given by \(x y+4 x-3 y-12=0\) and \(x y-3 x+4 y-12=0\) isAP EAMCET 2017 Hard
- In the preparation of baking soda, and in ratio is used to react with .AP EAMCET 2021 Medium