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JEE Advanced

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is $3×10_{8}ms_{−1}.$ The final momentum of the object is

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Let $f(x)=∣1−x∣1−x(1+∣1−x∣) cos(1−x1 )$ for $x=1.$ Then: (A)$(lim)_{n→1_{−}}f(x)$ does not exist (B)$(lim)_{n→1_{+}}f(x)$ does not exist (C)$(lim)_{n→1_{−}}f(x)=0$ (D)$(lim)_{n→1_{+}}f(x)=0$

Let $f:RR$be a continuous odd function, which vanishes exactly at one point and $f(1)=21 ˙$Suppose that $F(x)=∫_{−1}f(t)dtforallx∈[−1,2]andG(x)=∫_{−1}t∣f(f(t))∣dtforallx∈[−1,2]I˙G(x)f(lim)_{x1}(F(x)) =141 ,$Then the value of $f(21 )$is

Let $f:RR$be a differentiable function such that $f(0),f(2π )=3andf_{prime}(0)=1.$If $g(x)=∫_{x}[f_{prime}(t)cosect−cottcosectf(t)]dtforx(0,2π ],$then $(lim)_{x0}g(x)=$

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the tune, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

The slope of the tangent to the curve $(y−x_{5})_{2}=x(1+x_{2})_{2}$at the point $(1,3)$is.

Let $△PQR$ be a triangle. Let $a=Q R,b=RP$ and $c=PQ$. If $∣a∣=12,∣∣ b∣∣ =43 $ and $b.c=24$, then which of the following is (are) true ?

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,

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