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JEE Advanced

The loss of kinetic energy during the above proces is

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

The circle $C_{1}:x_{2}+y_{2}=3,$ with centre at O, intersects the parabola $x_{2}=2y$ at the point P in the first quadrant. Let the tangent to the circle $C_{1}$ at P touches other two circles $C_{2}andC_{3}atR_{2}andR_{3},$ respectively. Suppose $C_{2}andC_{3}$ have equal radii $23 $ and centres at $Q_{2}$ and $Q_{3}$ respectively. If $Q_{2}$ and $Q_{3}$ lie on the y-axis, then (a)$Q2Q3=12$(b)$R2R3=46 $(c)area of triangle $OR2R3$ is $62 $(d)area of triangle $PQ2Q3is=42 $

If $f(x)∣cos(2x)cos(2x)sin(2x)−cosxcosx−sinxsinxsinxcosx∣,then:$$f_{prime}(x)=0$at exactly three point in $(−π,π)$$f_{prime}(x)=0$at more than three point in $(−π,π)$$f(x)$attains its maximum at $x=0$$f(x)$attains its minimum at $x=0$

The area enclosed by the curves$y=sinx+cosxandy=∣cosx−sinx∣$ over the interval $[0,2π ]$

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that $x_{1}+x_{2}+x_{3}$ is odd isThe probability that $x_{1},x_{2},x_{3}$ are in an aritmetic progression is

Let $p,q$be integers and let $α,β$be the roots of the equation, $x_{2}−x−1=0,$where $α=β$. For $n=0,1,2,,leta_{n}=pα_{n}+qβ_{n}˙$FACT : If $aandb$are rational number and $a+b5 =0,thena=0=b˙$If $a_{4}=28,thenp+2q=$7 (b) 21 (c) 14 (d) 12

Let $X$be a set with exactly 5 elements and $Y$be a set with exactly 7 elements. If $α$is the number of one-one function from $X$to $Y$and $β$is the number of onto function from $Y$to $X$, then the value of $5!1 (β−α)$is _____.

Let $n≥2$be integer. Take $n$distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$is