AP EAMCET · Maths · Basic of Mathematics

$\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}$ is equal to

A $1$
B $2$
C $3$
D $4$

Verified Solution

Answer & Solution

Correct Answer

(B) $2$

Step-by-step Solution

Detailed explanation

Now,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If $\left|\begin{array}{ccc}a+b+2 c & a & b \\ c & 2 a+b+c & b \\ c & a & a+2 b+c\end{array}\right|=2$, then $a^3+b^3+c^3-3 a b c=$

AP EAMCET 2019 Easy
If $(1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad$ then $\sum_{r=1}^{15} r \frac{a_r}{a_r-1}$ is equal to

AP EAMCET 2005 Hard
The radius of a circle whose center is $(2,1)$ and one of the chords is a diameter of the circle $x^2+y^2-2 x-6 y+6=0$, is units.

AP EAMCET 2021 Medium
$\int e^{-2 x}\left(\frac{1-\sin 2 x}{1+\cos 2 x}\right) d x=$

AP EAMCET 2023 Medium
$\lim_{x \to 1} \frac{(1 - x) (1 - x^{2}) \dots \dots (1 - x^{2 n})}{{\{(1 - x) (1 - x^{2}) \dots \dots (1 - x^{n})\}}^{2}} = \underline{}, \forall n \in N$

AP EAMCET 2021 Hard
The sum of all the coefficients in the binomial expansion of $(1+2 x)^n$ is 6561. Let $R=(I+2 x)^n=I+F$, where $I \in N$ and $0 < F < \mathrm{l}$.
If $x=\frac{1}{\sqrt{2}}$, then $1-\frac{F}{1+(\sqrt{2}-1)^4}=$

AP EAMCET 2019 Medium

Explore more questions on app

From AP EAMCET

The distance from the origin to the image of $(1,1)$ with respect to the line $x+y+5=0$ is

AP EAMCET 2016 Easy
The oxidation state of phosphorus in cyclo-tri-meta phosphoric acid is

AP EAMCET 2020 Medium
Which one of the following reactions is not feasible ?

AP EAMCET 2025 Medium
The diagonals $\mathrm{AC}$ and $\mathrm{BD}$ of a rhombus $\mathrm{ABCD}$ intersect at the point $(3,4)$. If $\mathrm{BD}=2 \sqrt{2}, \mathrm{~A}=(1,2), \mathrm{B}=(\alpha, \beta)$,$D=(\gamma, \delta)$ and $\alpha < \delta < \gamma < \beta$, then $\beta+\gamma-\delta=$

AP EAMCET 2023 Medium
The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y=3 x-0.8 x^2$. The time of flight of the projectile is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ ).

AP EAMCET 2024 Easy
Two blocks of masses m and 2 m are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

AP EAMCET 2024 Medium

Explore more questions on app

\(\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}\) is equal to

Answer & Solution

Step-by-step Solution

See the Complete Solution