Mathematics · 2021
JEE Main · 27 July 2021, Shift 2 · Q75
Let α= max_x ∈ R {8^2 sin 3 x · 4^4 cos 3 x} and β= min_x ∈ R {8^2 sin 3 x · 4^4 cos 3 x}. If 8 x^2+ b x+ c =0 is a quadratic equation whose roots…
Let $\displaystyle \alpha=\max _{x \in \mathbf{R}}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $\displaystyle \beta=\min _{x \in \mathbf{R}}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$.
If $\displaystyle 8 x^2+\mathrm{b} x+\mathrm{c}=0$ is a quadratic equation whose roots are $\displaystyle \alpha^{1 / 5}$ and $\displaystyle \beta^{1 / 5}$, then the value of $\displaystyle \mathrm{c}-\mathrm{b}$ is equal to:
Official answer
(1)
$\displaystyle 42$
More from Trigonometric Identities
- Let (π)/2<θ<π and cot θ=-1/(2 √2). Then the value of sin ((15 θ)/2)( cos 8 θ+ sin 8 θ)+ cos ((15 θ)/2)( cos 8 θ- sin 8 θ) is equal to2026
- If (cos^2 48^°- sin^2 12^°)/(sin^2 24^°- sin^2 6^°)=(α+β √5)/2, where α, β ∈ N, then α+β is equal to ____2026
- If L= sin^2((π)/16)- sin^2((π)/8) and M= cos^2((π)/16)- sin^2((π)/8), then:2020
- Let tan A, tan B, where A, B ∈(-(π)/2, (π)/2), be the roots of the quadratic equation x^2-2 x-5=0. Then 20 sin^2((A+B)/2) is equal to:2026
- If the line x=y=z intersects the line x sin A+y sin B+z sin C-18=0=x sin 2 A+y sin 2 B+z sin 2 C-9, where A, B, C are the angles of a triangle A B C,…2023
- For the functions f(θ)=α tan^2 θ+β cot^2 θ, and g(θ)=α sin^2 θ+β cos^2 θ, α>β>0, let min_0<θ<(π)/2 f(θ)= max_0<θ<π g(θ). If the first term of a G.P.…2026
- Let cos (α+β)=-1/10 and sin (α-β)=3/8, where 0<α<(π)/3 and 0<β<(π)/4. If tan 2 α=(3(1-r √5))/(√11(s+√5)), r, s ∈ N, then r+s is equal to ____.2026
- If tan A is equal to the integral solution of the inequality 4 x^2-24 x+35<0 and sin B is equal to the slope of the angle bisector of the second…2021
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.