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A nucleus \(X\) emits a beta particle to produce a nucleus \(Y\). If their atomic masses are \(M_{x}\) and \(M_{y}\) respectively, the maximum energy of the beta particle emitted is (where \(m_{e}\) is the mass of an electron and \(c\) is the velocity of light)
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If \(R\) is the Rydberg Constant in \(\mathrm{cm}^{-1}\), then hydrogen atom does not emit any radiation of wave-length in the range of
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In a Frounhofer diffraction experiment, a single slit of width \(0.5 \mathrm{~mm}\) is illuminated by a monochromatic light of wavelength \(600 \mathrm{~nm}\). The diffraction pattern is observed on a screen at a distance of \(50 \mathrm{~cm}\) from the slit. What will be the linear separation of the first order minima?
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The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be \(1.5\) limes the intensity of light emerging from the other slit. What will be the approximate ratio of intensity of an interference maximum to that of an interference
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Dec 11, 2021
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Properties of solids and liquids
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Consider the function \(f(x)=\frac{x^{3}}{4}-\sin \pi x+3\)
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Let \(f\) and \(g\) be differentiable on the interval \(I\) and let \(a, b \in I, a<b\). Then
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Equation of a tangent to the hyperbola \(5 x^{2}-y^{2}=5\) and which passes through an external point \((2,8)\) is
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Dec 11, 2021
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Straight lines \(x-y=7\) and \(x+4 y=2\) intersect at \(B\). Points \(A\) and \(C\) are so chosen on these two lines such that \(A B\) \(=A C\). The equation of line AC passing through \((2,-7)\) is
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Let \(A=\left(\begin{array}{lll}3 & 0 & 3 \\ 0 & 3 & 0 \\ 3 & 0 & 3\end{array}\right) .\) Then the roots of the equation \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\) (where \(I_{3}\) is the identity matrix of order 3 ) are
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If \(\theta \in \mathbb{R}\) and \(\frac{1-i \cos \theta}{1+2 i \cos \theta}\) is real number, then \(\theta\) will be (when I: Set of integers)
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Dec 11, 2021
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Let \(x_{1}, x_{2}\) be the roots of \(x^{2}-3 x+a=0\) and \(x_{3}, x_{4}\) be the roots of \(x^{2}-12 x+b=0\). If \(x_{1}<x_{2}<x_{3}<x_{4}\) and \(x_{1}\), \(x_{2}, x_{3}, x_{4}\) are in G.P. then \(a b\) equals
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The area bounded by \(y=x+1\) and \(y=\cos x\) and the \(x\)-axis, is
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Dec 11, 2021
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Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and \(h\) respectively. If \(A\) takes \(m\) seconds more than \(B\) and describes \(n\) units more than that of \(B\) acquiring the same speed, then
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Let \(I_{n}=\int_{0}^{1} x^{n} \tan ^{-1} x d x\). If \(a_{n} I_{n+2}+b_{n} I_{n}=c_{n}\) for all \(n \geq 1\), then
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Dec 11, 2021
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A point is in motion along a hyperbola \(y=\frac{10}{x}\) so that its abscissa \(x\) increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate, when the point passes through \((5,2)\)
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Dec 11, 2021
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The graphs of the polynomial \(x^{2}-1\) and \(\cos x\) intersect
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Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in \mathbb{R}\). Then
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The value of \(\lim _{x \rightarrow 0+} \frac{x}{p}\left[\frac{q}{x}\right]\) is
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The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity e is,
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The polar coordinate of a point \(\mathrm{P}\) is \(\left(2,-\frac{\pi}{4}\right)\). The polar coordinate of the point \(\mathrm{Q}\), which is such that the line join \(\mathrm{PQ}\) is bisected perpendicularly by the initial line, is
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