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JEE Advanced

The value of n in the molecular formula $Be_{n}Al_{2}Si_{6}O_{18}$ is

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Let $f_{1}:R→R,f_{2}:(−2π ,2π )→Rf_{3}:(−1,e_{2π}−2)→R$and $f_{4}:R→R$be functions defined by\displaystyle{{f}_{{1}}{\left({x}\right)}}={\sin{{\left(\sqrt{{{1}-{e}^{{-{{x}}}}^{2}}}\right)}}},(ii) $f_{2}(x)={tan_{−1}x∣sinx∣ ifx=01ifx=0,$where the inverse trigonometric function $tan_{−1}x$assumes values in $(2π ,2π )$,(iii) $f_{3}(x)=[sin((g)_{e}(x+2))]$, where, for $t∈R$, $[t]$denotes the greatest integer less than or equal to $t$,(iv) $f_{4}(x)={x_{2}sin(x1 )ifx=00ifx=0$.LIST-I LIST-IIP. The function $f_{1}$is 1. NOT continuous at $x=0$Q. The function $f_{2}$is 2. continuous at $x=0$and NOTR. The function $f_{2}$is differentiable at $x=0$S. The function $f_{2}$is 3. differentiable at $x=0$and itsis NOT continuous at $x=0$4. differentiable at $x=0$and itsderivative is continuous at $x=0$The correct option is$P→2;Q→3;R→1;S→4$(b) $P→4;Q→1;R→2;S→3$(c) $P→4;Q→2;R→1;S→3$(d) $P→2;Q→1;R→4;S→3$

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2x+y−2z=5$ and $3x−6y−2z=7$ , is (A) $14x+2y+15z=3$ (B) $14x+2y−15z=1$ (C) $14x+2y+15z=31$ (D) $14x−2y+15z=27$

Let $u^=u_{1}i^+u_{2}j^ +u_{3}k^$ be a unit vector in be a unit vector in $R_{3}andw^=6 1 (i^+j^ +2k^)$.Given that there exists vector $v^$ in $R_{3}$ such that $∣u^×v∣=1andw^.(u^×v)=1$. Which of the following statement(s) is(are) correct?

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 _______.

A curve passes through the point $(1,6π )$ . Let the slope of the curve at each point $(x,y)$ be $xy +sec(xy ),x>0.$ Then the equation of the curve is

Let $f:R0,1 $ be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? $e_{x}−∫_{0}f(t)sintdt$ (b) $f(x)+∫_{0}f(t)sintdt$(c)$x−∫_{0}f(t)costdt$ (d) $x_{9}−f(x)$

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 of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

Let P be the point on parabola $y_{2}=4x$ which is at the shortest distance from the center S of the circle $x_{2}+y_{2}−4x−16y+64=0$ let Q be the point on the circle dividing the line segment SP internally. Then