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JEE Advanced

In following reaction the value of K is $5×10_{−4}S_{−1}$ $2N_{2}O_{5}→Δ2N_{2}O_{4}+O_{2}$ Initial pressure was 1 atm, while the final pressure was 1.45 atm at time $y×10_{3}sec$ calculate y

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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

For each positive integer $n$, let $y_{n}=n1 ((n+1)(n+2)n+n˙ )_{n1}$For $x∈R$let $[x]$be the greatest integer less than or equal to $x$. If $(lim)_{n→∞}y_{n}=L$, then the value of $[L]$is ______.

A box $B_{1}$, contains 1 white ball, 3 red balls and 2 black balls. Another box $B_{2}$, contains 2 white balls, 3 red balls and 4 black balls. A third box $B_{3}$, contains 3 white balls, 4 red balls and 5 black balls.

If $2x−y+1=0$ is a tangent to the hyperbola $a_{2}x_{2} −16y_{2} =1$ then which of the following CANNOT be sides of a right angled triangle? (a)$a,4,2$ (b) $a,4,1$(c)$2a,4,1$ (d) $2a,8,1$

Solve $(g)_{0.2}∣x−3∣≥0.$

Let $f:R→R$and $g:R→R$be two non-constant differentiable functions. If $f_{prime}(x)=(e_{(f(x)−g(x))})g_{prime}(x)$for all $x∈R$, and $f(1)=g(2)=1$, then which of the following statement(s) is (are) TRUE?$f(2)<1−(g)_{e}2$(b) $f(2)>1−(g)_{e}2$(c) $g(1)>1−(g)_{e}2$(d) $g(1)<1−(g)_{e}2$

Which of the following values of $α$satisfying the equation $∣∣ (1+α)_{2}(1+2α)_{2}(1+3α)_{2}(2+α)_{2}(2+2α)_{2}(2+3α)_{2}(3+α)_{2}(3+2α)_{2}(3+3α)_{2}∣∣ =−648α?$$−4$b. $9$c. $−9$d. $4$

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,