class 12

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JEE Advanced

Q. Which of the following is correct?

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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 $

Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her, is (A) $21 $ (B) $31 $ (C) $32 $ (D) $43 $

$L_{1}=x+3y−5=0,L_{2}=3x−ky−1=0,L_{3}=5x+2y−12=0$ are concurrent if k=

Let $f:(0,∞)R$ be given by $f(x)=∫_{x1}te_{−(t+t1)}dt ,$ then (a)$f(x)$ is monotonically increasing on $[1,∞)$(b)$f(x)$ is monotonically decreasing on $(0,1)$(c)$f(2_{x})$ is an odd function of $x$ on $R$

From a point $P(λ,λ,λ)$, perpendicular PQ and PR are drawn respectively on the lines $y=x,z=1$ and $y=−x,z=−1$.If P is such that $∠QPR$ is a right angle, then the possible value(s) of $λ$ is/(are)

Let $P$be a point in the first octant, whose image $Q$in the plane $x+y=3$(that is, the line segment $PQ$is perpendicular to the plane $x+y=3$and the mid-point of $PQ$lies in the plane $x+y=3)$lies on the z-axis. Let the distance of $P$from the x-axis be 5. If $R$is the image of $P$in the xy-plane, then the length of $PR$is _______.

There are five students $S_{1},S_{2},S_{3},S_{4}$and $S_{5}$in a music class and for them there are five seats $R_{1},R_{2},R_{3},R_{4}$and $R_{5}$arranged in a row, where initially the seat $R_{i}$is allotted to the student $S_{i},i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted five seats.The probability that, on the examination day, the student $S_{1}$gets the previously allotted seat $R_{1}$, and NONE of the remaining students gets the seat previously allotted to him/her is$403 $(b) $81 $(c) $407 $(d) $51 $

Suppose that $p ,q andr$ are three non-coplanar vectors in $R_{3}$. Let the components of a vector $s$ along $p ,q andr$ be 4, 3 and 5, respectively. If the components of this vector $s$ along $(−p +q +r),(p −q +r)and(−p −q +r)$ are x, y and z, respectively, then the value of $2x+y +z$ is