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 2×2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2=I.Statement 1: If A=Iand A=−I, then det A=−1.Statement 2: If A=Iand A=−I, then tr(A)=0.
It is given that the events A and B are such that P(A)=41,P(BA)=21andp(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
The vapour pressure of water at 202C is 17.5 mm Hf. If 18 g of glucose (C6H12O6) is added to 178.2 g of water at 20∘C, the vapour pressure of the resulting solution will be
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 1.0×103ms−1 (Mass of proton =1.67×10−27kgandh=6.63×10−34Js)
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 4πwith 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