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JEE Advanced

A thin uniform annular disc of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

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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 :

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 $

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

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 w = ($3 +2ι )$ and $P={w_{n}:n=1,2,3,…..},$ Further $H_{1}={z∈C:Re(z)>21 }andH_{2}={z∈c:Re(z)<−21 }$ Where C is set of all complex numbers. If $z_{1}∈P∩H_{1},z_{2}∈P∩H_{2}$ and O represent the origin, then $∠Z_{1}OZ_{2}$ =

Let $a,b,xandy$ be real numbers such that $a−b=1andy=0.$ If the complex number $z=x+iy$ satisfies $Im(z+1az+b )=y$ , then which of the following is (are) possible value9s) of x? (a)$−1−1−y_{2} $ (b) $1+1+y_{2} $(c)$−1+1−y_{2} $ (d) $−1−1+y_{2} $

Consider the circle $x_{2}+y_{2}=9$ and the parabola $y_{2}=8x$. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.

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 $x=0$