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JEE Advanced

$A+B+CEx.No1.2.3.4. →[A]0.20.20.20.3 Product[B]0.10.20.10.1 [C]0.10.10.20.1 Rate of reaction6×10_{−5}6×10_{−5}1.2×10_{−4}9×10_{−5} $ When [A] =0.15 [B]=0.25 [C]=0.15 Rate of reaction is $Y×10_{−5}M/s$ Find Y.

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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

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 $x=0$

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes $P_{1}:x+2y−z+1=0$ and $P_{2}:2x−y+z−1=0$, Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane $P_{1}$. Which of the following points lie(s) on M?

For every pair of continuous functions $f,g:[0,1]→R$ such that $max{f(x):x∈[0,1]}=max{g(x):x∈[0,1]}$ then which are the correct statements

Let RS be the diameter of the circle $x_{2}+y_{2}=1,$ where S is the point $(1,0)$ Let P be a variable apoint (other than $RandS$) on the circle and tangents to the circle at $SandP$ meet at the point Q.The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. then the locus of E passes through the point(s)- (A) $(31 ,3 1 )$ (B) $(41 ,21 )$ (C) $(31 ,−3 1 )$ (D) $(41 ,−21 )$

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) $dy_{1}dm =31 fory_{1}>0$

Let $a$ and $b$ be two unit vectors such that $a.b=0$ For some $x,y∈R$, let $c=xa+yb+(a×b$ If $(∣c∣=2$ and the vector $c$ is inclined at same angle $α$ to both $a$ and $b$ then the value of $8cos_{2}α$ is

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is