class 12

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JEE Advanced

Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follow arrhenius equation 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 $V_{r}$ denote the sum of the first' ' terms of an arithmetic progression (A.P.) whose first term is'r and the common difference is $(2r−1)$. Let $T_{r}=V_{r+1}−V_{r}−2$ and $Q_{r}=T_{r+1}−T_{r}$ for $r=1,2,…….$ The sum $V_{1}+V_{2}+……+V_{n}$ is

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?

Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let $x$be the number of such words where no letter is repeated; and let $y$be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, $9xy =$

For a non-zero complex number $z$, let $arg(z)$denote theprincipal argument with $π<arg(z)≤π$Then, whichof the following statement(s) is (are) FALSE?$arg(−1,−i)=4π ,$where $i=−1 $(b) The function $f:R→(−π,π],$defined by $f(t)=arg(−1+it)$for all $t∈R$, iscontinuous at all points of $R$, where $i=−1 $(c) For any two non-zero complex numbers $z_{1}$and $z_{2}$, $arg(z_{2}z_{1} )−arg(z_{1})+arg(z_{2})$is an integer multiple of $2π$(d) For any three given distinct complex numbers $z_{1}$, $z_{2}$and $z_{3}$, the locus of the point $z$satisfying the condition $arg((z−z_{3})(z_{2}−z_{1})(z−z_{1})(z_{2}−z_{3}) )=π$, lies on a straight line

Let $f:[0,2]→R$ be a function which is continuous on [0,2] and is differentiable on (0,2) with $f(0)=1$$Let:F(x)=∫_{0}f(t )dtforx∈[0,2]I˙fF_{prime}(x)=f_{prime}(x)$ . for all $x∈(0,2),$ then $F(2)$ equals (a)$e_{2}−1$ (b) $e_{4}−1$(c)$e−1$ (d) $e_{4}$

Let $f:R→R,g:R→Randh:R→R$ be the differential functions such that $f(x)=x_{3}+3x+2,g(f(x))=xandh(g(g(x)))=x,forallx∈R.Then$ (a)g'(2)=$151 $ (b)h'(1)=666 (c)h(0)=16 (d)h(g(3))=36

Let $f:(0,π)→R$be a twice differentiable function such that $(lim)_{t→x}t−xf(x)sint−f(x)sinx =sin_{2}x$for all $x∈(0,π)$. If $f(6π )=−12π $, then which of the following statement(s) is (are) TRUE?$f(4π )=42 π $(b) $f(x)<6x_{4} −x_{2}$for all $x∈(0,π)$(c) There exists $α∈(0,π)$such that $f_{prime}(α)=0$(d) $f(2π )+f(2π )=0$