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JEE Advanced

The pair(s) of reagents that yield paramagnetic species is/are

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The value of $(((g)_{2}9)_{2})_{(log)((log)9)1}×(7 )_{(log)71}$is ________.

Â·If the normals of the parabola $y_{2}=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x−3)_{2}(y+2)_{2}=r_{2}$ , then the value of $r_{2}$ is

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?

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,

In a triangle PQR, P is the largest angle and $cosP=31 $. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Let $f:R→(0,∞)$ and $g:R→R$ be twice differentiable functions such that f" and g" are continuous functions on R. suppose $f_{prime}(2)=g(2)=0,f(2)=0$ and $g_{′}(2)=0$, If $x→2lim f_{′}(x)g_{′}(x)f(x)g(x) =1$ then

Let $f[0,1]→R$ (the set of all real numbers be a function.Suppose the function f is twice differentiable, $f(0)=f(1)=0$,and satisfies $f_{′}(x)–2f_{′}(x)+f(x)≤e_{x},x∈[0,1]$.Which of the following is true for $0<x<1?$

Let $F(x)=∫_{x}[2cos_{2}t.dt]$ for all $x∈R$ and $f:[0,21 ]→[0,∞)$ be a continuous function.For $a∈[0,21 ]$, if F'(a)+2 is the area of the region bounded by x=0,y=0,y=f(x) and x=a, then f(0) is