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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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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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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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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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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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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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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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Let \(S, T, U\) be three non-void sets and \(f: S \rightarrow T, g: T \rightarrow U\) be so that \(g \circ f: S \rightarrow U\) is surjective. Then
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Lef \(f: X \rightarrow Y\) and \(A, B\) are non-void subsets of \(Y\), then (where the symbols have their usual interpretation)
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The system of equations $$ \begin{aligned} &\lambda x+y+3 z=0 \\ &2 x+\mu y-z=0 \\ &5 x+7 y+z=0 \end{aligned} $$ has infinitely many solutions in \(\mathbb{R}\). Then,
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