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\(y=\int \cos \left\{2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right\} d x\) is an equation of a family of

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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If \(\int \cos x \log \left(\tan \frac{x}{2}\right) d x=\sin x \log \left(\tan \frac{x}{2}\right)+f(x)\) then \(f(x)\) is equal to, (assuming \(c\) is a arbitrary real constant)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(\lim _{x \rightarrow 0+}\left(x^{n} \ln x\right), n>0\)

asked Dec 11, 2021 in Sets, relations and functions by kritika (90.1k points)

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Tangent is drawn at any point \(P(x, y)\) on a curve, which passes through \((1,1)\). The tangent cuts \(X\)-axis and \(Y\)-axis at \(A\) and \(B\) respectively. If \(A P: B P=3: 1\), then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(f(x)=\frac{1}{3} x \sin x-(1-\cos x)\). The smallest positive interger \(k\) such that \(\lim _{x \rightarrow 0} \frac{f(x)}{x^{k}} \neq 0\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(y=\frac{x^{2}}{(x+1)^{2}(x+2)}\). Then \(\frac{d^{2} y}{d x^{2}}\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Consider a tangent to the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{1}=1\) at any point. The locus of the midpoint of the portion intercepted between the axes is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The equation of the straight line passing through the point \((4,3)\) and making intercepts on the co-ordinate axes whose sum is \(-1\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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A and B are independent events. The probability that both A and B occur is \(\frac{1}{20}\) and the probability that neither of them occurs is \(\frac{3}{5}\). The probability of occurrence of \(A\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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In a certain test, there are \(n\) questions. In this test \(2^{n-i}\) students gave wrong answers to at least i questions, where i \(=1,2, \ldots \ldots \mathrm{n}\). If the total number of wrong answers given is 2047 , then \(\mathrm{n}\) is equal to

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The equation \(x^{\left(\log _{3} x\right)^{2}-\frac{9}{2} \log _{3} x+5}=3 \sqrt{3}\) has

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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A particle is projected vertically upwards. If it has to stay above the ground for 12 seconds, then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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The area of the figure bounded by the parabola \(x=-2 y^{2}, x=1-3 y^{2}\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Consider the curve \(y=\) be \(^{-x / a}\) where a and \(b\) are non-zero real numbers. Then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(y=\frac{1}{1+x+\ln x}\), Then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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\(\lim _{x \rightarrow 1}\left(\frac{1}{\ln x}-\frac{1}{(x-1)}\right)\)

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(0<\alpha<\beta<1\). Then \(\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \int_{1 /(k+\beta)}^{1 /(k+\alpha)} \frac{d x}{1+x}\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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A line cuts the \(x\)-axis at \(A(7,0)\) and the \(y\)-axis at \(B(0,-5)\). A variable line \(P Q\) is drawn perpendicular to \(A B\) cutting the \(x\)-axis at \(P(a, 0)\) and the \(y\)-axis at \(Q(0, b)\). If \(A Q\) and \(B P\) intersect at \(R\), the locus of \(R\) is

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Consider the curve \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\). The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(\rho_{1}\) and \(\rho_{2}\) be two equivalence relations defined on a non-void set \(S\). Then

asked Dec 10, 2021 in Sets, relations and functions by kritika (90.1k points)

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