Recent questions in Maths

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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 \((5,2)\)

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

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The graphs of the polynomial \(x^{2}-1\) and \(\cos x\) intersect

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

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Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in \mathbb{R}\). Then

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

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The value of \(\lim _{x \rightarrow 0+} \frac{x}{p}\left[\frac{q}{x}\right]\) is

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

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65.5k answers

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then the eccentricity e is,

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

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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

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

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3 answers

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

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

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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)

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

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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,

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

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For any non-zero complex number \(z\), the minimum value of \(|z|+|z-1|\) is

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

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The position vectors of the points \(A, B, C\) and \(D\) are \(3 \hat{i}-2 \hat{j}-\hat{k}, 2 \hat{i}-3 \hat{j}+2 \hat{k}, 5 \hat{i}-\hat{j}+2 \hat{k}\) and \(4 \hat{i}-\hat{j}+\lambda \hat{k}\) respectively. If the points \(A, B, C\) and \(D\) lie on a plane, the value of \(\lambda\) is

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

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Let \(\hat{\alpha}, \hat{\beta}, \hat{\gamma}\) be three unit vectors such that \(\hat{\alpha} \times(\hat{\beta} \times \hat{\gamma})=\frac{1}{2}(\hat{\beta}+\hat{\gamma})\) where \(\hat{\alpha} \times(\hat{\beta} \times \hat{\gamma})=(\hat{\alpha} \cdot \hat{\gamma}) \hat{\beta}-(\hat{\alpha} . \hat{\beta}) \hat{\gamma}\). If \(\hat{\beta}\) is not paralle to \(\hat{\gamma}\), then the angle between \(\hat{\alpha}\) and \(\hat{\beta}\) is

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

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Let \(a>b>0\) and \(I(n)=a^{\gamma}-b^{\gamma}, J(n)=(a-b)^{\gamma}\) for all \(n \geq 2\). Then

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

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Let \(a=\min \left\{x^{2}+2 x+3: x \in R\right\}\) and \(b=\lim _{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta^{2}}\). Then \(\sum_{r=0}^{n} a^{r} b^{n-r}\) is

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

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Let \(f:[1,3] \rightarrow R\) be a continuous function that is differentiable in \((1,3)\) an \(f^{\prime}(x)=|f(x)|^{2}+4\) for all \(x \in(1,3)\). Then,

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

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Let \(f(x)\) be a derivable function, \(f^{\prime}(x)>f(x)\) and \(f(0)=0\). Then

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

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$$ \lim _{x \rightarrow 0+}\left(e^{x}+x\right)^{y / x} $$

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

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Consider the function \(f(x)=\cos x^{2}\). Then

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

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3 answers

Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} .\) Then \(f^{\prime}(x)\) will be

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

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The limit of the interior angle of a regular polygon of \(n\) sides as \(n \rightarrow \infty\) is

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

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Recent questions in Maths

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