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JEE Advanced

The work function $(ϕ)$ of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

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

Let $P$be a point in the first octant, whose image $Q$in the plane $x+y=3$(that is, the line segment $PQ$is perpendicular to the plane $x+y=3$and the mid-point of $PQ$lies in the plane $x+y=3)$lies on the z-axis. Let the distance of $P$from the x-axis be 5. If $R$is the image of $P$in the xy-plane, then the length of $PR$is _______.

Let $f:(0,∞)→R$ be a differentiable function such that $f_{′}(x)=2−xf(x) $ for all $x∈(0,∞)$ and $f(1)=1$, then

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

Let m and n be two positive integers greater than 1.If $α→0lim α_{m}e_{cosα_{n}}−e =−(2e )$ then the value of $nm $ is

Let $a,b,c$be three non-zero real numbers such that the equation $3 acosx+2bsinx=c,x∈[−2π ,2π ]$, has two distinct real roots $α$and $β$with $α+β=3π $. Then, the value of $ab $is _______.

Consider the cube in the first octant with sides OP,OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where $O(0,0,0)$ is the origin. Let $S(21 ,21 ,21 )$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If $p =SP,q =SQ ,r=SR$ and $t=ST$ then the value of $∣(p ×q )×(r×(t)∣is$

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)