class 12

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JEE Advanced

The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by

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The function $f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣$has a local minimum or a local maximum at $x=$$−2$ (b) $−32 $ (c) 2 (d) $32 $

Let complex numbers $αandα1 $ lies on circle $(x−x_{0})_{2}(y−y_{0})_{2}=r_{2}and(x−x_{0})_{2}+(y−y_{0})_{2}=4r_{2}$ respectively. If $z_{0}=x_{0}+iy_{0}$ satisfies the equation $2∣z_{0}∣_{2}=r_{2}+2$ then $∣α∣$ is equal to (a) $2 1 $ (b) $21 $ (c) $7 1 $ (d) $31 $

Let $f:(0,∞)→R$ be a differentiable function such that $f_{′}(x)=2−xf(x) $ for all $x∈(0,∞)$ and $f(1)=1$, then

Let $f(x)=xsinπx$, $x>0$ Then for all natural numbers n, f\displaystyle{\left({x}\right)}{v}{a}{n}{i}{s}{h}{e}{s}{a}{t}

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 ______.

Let $f:R→Randg:R→R$ be respectively given by $f(x)=∣x∣+1andg(x)=x_{2}+1$. Define $h:R→R$ by $h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$.The number of points at which $h(x)$ is not differentiable is

Consider two straight lines, each of which is tangent to both the circle $x_{2}+y_{2}=21 $and the parabola $y_{2}=4x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O(0,0)$and whose semi-major axis is $OQ$. If the length of the minor axis of this ellipse is $2 $, then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is $2 1 $and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is $21 $and the length of the latus rectum is $21 $(c) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $42 1 (π−2)$(d) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $161 (π−2)$

Let $S_{n}=k=1∑4n (−1)2k(k+1) k_{2}˙$Then $S_{n}$can take value (s)$1056$b. $1088$c. $1120$d. $1332$