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JEE Advanced

Which of the following is/are correct regarding root mean square speed $(U_{rms})$ & average translation K.E. $(E_{av})$ of molecules in a gas at equilibrium

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Let $f:[a,b]1,∞ $be a continuous function and let $g:RR$be defined as$g(x)={0ifxbThen$$g(x)$is continuous but not differentiable at a$g(x)$is differentiable on $R$$g(x)$is continuous but nut differentiable at $b$$g(x)$is continuous and differentiable at either $a$or $b$but not both.

Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

Perpendiculars are drawn from points on the line $2x+2 =−1y+1 =3z $ to the plane $x+y+z=3$ The feet of perpendiculars lie on the line (a) $5x =8y−1 =−13z−2 $ (b) $2x =3y−1 =−5z−2 $ (c) $4x =3y−1 =−7z−2 $ (d) $2x =−7y−1 =5z−2 $

The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

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) $y_{1}=$

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is :

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

The common tangents to the circle $x_{2}+y_{2}=2$ and the parabola $y_{2}=8x$ touch the circle at $P,Q$ andthe parabola at $R,S$. Then area of quadrilateral $PQRS$ is