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JEE Advanced

$XeF_{4}$ and $XeF_{6}$ are expected to be

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Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

In R', consider the planes $P_{1},y=0$ and $P_{2}:x+z=1$. Let $P_{3}$, be a plane, different from $P_{1}$, and $P_{2}$, which passes through the intersection of $P_{1}$, and $P_{2}$. If the distance of the point $(0,1,0)$ from $P_{3}$, is $1$ and the distance of a point $(α,β,γ)$ from $P_{3}$ is $2$, then which of the following relation is (are) true ?

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}

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) $2a,8,1$

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of $nm $ is ____

Let $P=⎣⎡ 1416 014 001 ⎦⎤ $and $I$ be the identity matrix of order $3$. If $Q=[q_{()}ij]$ is a matrix, such that $P_{50}−Q=I$, then $q_{21}q_{31}+q_{32} $ equals

Consider the hyperbola $H:x_{2}−y_{2}=1$ and a circle S with centre $N(x_{2},0)$ Suppose that H and S touch each other at a point $(P(x_{1},y_{1})$ with $x_{1}>1andy_{1}>0$ The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle $ΔPMN$ then the correct expression is (A) $dx_{1}dl =1−3x_{1}1 $ for $x_{1}>1$ (B) $dx_{1}dm =3(x _{1}−1)x_{!} )forx_{1}>1$ (C) $dx_{1}dl =1+3x_{1}1 forx_{1}>1$ (D) $dy_{1}dm =31 fory_{1}>0$

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 $