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JEE Main

A long metallic bar is carrying heat from one its ends to the other end under steady-state. The variation of temperature $θ$ along the length x of the bar from its end is best described by which of the following figure.

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Let A be a $2×2$ matrix with real entries. Let I be the $2×2$identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that $A_{2}=I$.Statement 1: If $A=I$and $A=−I$, then det $A=−1$.Statement 2: If $A=I$and $A=−I$, then $tr(A)=0$.

It is given that the events A and B are such that $P(A)=41 ,P(BA )=21 andp(AB )=32 ˙$ Then P(B) is:

In a binomial distribution $B(n,p=41 )$, if the probability of at least one success is greater than or equal to $109 $, then n is greater than

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A student measuring the focal length of convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by the student should look like

Calculate the wavelength (in nanometer) associated with a proton moving at $1.0×10_{3}ms_{−1}$ (Mass of proton $=1.67×10_{−27}kgandh=6.63×10_{−34}Js$)

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

If a line makes an angle of $4π $with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is