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JEE Advanced

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength of the infrared region of the hydrogen spectrum to the nearest interger is

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A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the parabola $y_{2}=16x$ $0≤y≤6$ at the point art $F(x_{0},y_{0})$. The tangent to the parabola at $F(X_{0},Y_{0})$ intersects the y-axis at $G(0,y)$. The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum P) m= Q) = Maximum area of $△EFG$ is (R) $y_{0}=$ (S) $y_{1}=$

Let $g:R→R$ be a differentiable function with $g(0)=0,g_{′}(1)=0,g_{′}(1)=0$.Let $f(x)={∣x∣x g(x),0=0and0,x=0$ and $h(x)=e_{∣x∣}$ for all $x∈R$. Let $(foh)(x)$ denote $f(h(x))and(hof)(x)$ denote $h(f(x))$. Then which of thx!=0 and e following is (are) true?

Let $S$be the set of all non-zero real numbers such that the quadratic equation $αx_{2}−x+α=0$has two distinct real roots $x_{1}andx_{2}$satisfying the inequality $∣x_{1}−x_{2}∣<1.$Which of the following intervals is (are) a subset (s) of $S?$$(21 ,5 1 )$b. $(5 1 ,0)$c. $(0,5 1 )$d. $(5 1 ,21 )$

Let $F(x)=∫_{x}[2cos_{2}t.dt]$ for all $x∈R$ and $f:[0,21 ]→[0,∞)$ be a continuous function.For $a∈[0,21 ]$, if F'(a)+2 is the area of the region bounded by x=0,y=0,y=f(x) and x=a, then f(0) is

Let $a,b,c$be three non-zero real numbers such that the equation $3 acosx+2bsinx=c,x∈[−2π ,2π ]$, has two distinct real roots $α$and $β$with $α+β=3π $. Then, the value of $ab $is _______.

The common tangents to the circle $x_{2}+y_{2}=2$ and the parabola $y_{2}=8x$ touch the circle at $P,Q$ andthe parabola at $R,S$. Then area of quadrilateral $PQRS$ is

Suppose that the foci of the ellipse $9x_{2} +5y_{2} =1$are $(f_{1},0)and(f_{2},0)$where $f_{1}>0andf_{2}<0.$Let $P_{1}andP_{2}$be two parabolas with a common vertex at (0, 0) and with foci at $(f_{1}.0)and$(2f_2 , 0), respectively. Let$T_{1}$be a tangent to $P_{1}$which passes through $(2f_{2},0)$and $T_{2}$be a tangents to $P_{2}$which passes through $(f_{1},0)$. If $m_{1}$is the slope of $T_{1}$and $m_{2}$is the slope of $T_{2},$then the value of $(m121 +m22)$is

Let $αandβ$ be nonzero real numbers such that $2(cosβ−cosα)+cosαcosβ=1$ . Then which of the following is/are true? (a) $3 tan(2α )+tan(2β )=0$ (b) $3 tan(2α )−tan(2β )=0$ (c) $tan(2α )+3 tan(2β )=0$ (d) $tan(2α )−3 tan(2β )=0$