Recent questions in Sets, relations and functions

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If \(2 \log (x+1)-\log \left(x^{2}-1\right)=\log 2\), then \(x=\)

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

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If \(a\) and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

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

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If the function \(f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1[a>0]\) attains its maximum and minimum at \(p\) and \(q\) respectively such that \(p^{2}=q\), then \(a\) is equal to

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

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Let \(f(x)=1-\sqrt{\left(x^{2}\right)}\) where the square root is to be taken positive, then

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

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If \(x \sin \left(\frac{y}{x}\right) d y=\left[y \sin \left(\frac{y}{x}\right)-x\right] d x, x>0\) and \(y(1)=\frac{\pi}{2}\) then the value of \(\cos \left(\frac{y}{x}\right)\) is

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

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Let \(f\) be a differentiable function with \(\lim _{x \rightarrow \infty} f(x)=0\). If \(y^{\prime}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0, \lim _{x \rightarrow \infty} y(x)=0\), then \(\left(\right.\) where \(\left.y^{\prime}=\frac{d y}{d x}\right)\)

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

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Let \(f\) be a differentiable function with \(\lim _{x \rightarrow \infty} f(x)=0\). If \(y^{\prime}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0, \lim _{x \rightarrow \infty} y(x)=0\), then \(\left(\right.\) where \(\left.y^{\prime}=\frac{d y}{d x}\right)\)

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

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Let \(f\), be a continuous function in \([0,1]\), then \(\lim _{n \rightarrow \infty} \sum_{j=0}^{n} \frac{1}{n} f\left(\frac{j}{n}\right)\) is

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

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If \(x^{2}+y^{2}=a^{2}\), then \(\int_{0}^{a} \sqrt{1+\left(\frac{d y}{d x}\right)^{2}} d x=\)

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

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If the tangent to the curve \(y^{2}=x^{3}\) at \(\left(m^{2}, m^{3}\right)\) is also a normal to the curve at \(\left(M^{2}, M^{3}\right)\), then the value of \(m M\) is

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

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\(\int_{0}^{2}\left[x^{2}\right] d x\) is equal to

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

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The value of \(\sum_{n=1}^{10} \int_{-2 n-1}^{-2 n} \sin ^{27} x d x+\sum_{n=1}^{10} \int_{2 n}^{2 n+1} \sin ^{27} x d x\) is equal to

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

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$$ \int \frac{f(x) \varphi^{\prime}(x)+\varphi(x) f^{\prime}(x)}{(f(x) \varphi(x)+1) \sqrt{f(x) \varphi(x)-1}} d x= $$

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

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Let \(\varphi(x)=f(x)+f(1-x)\) and \(f^{\prime \prime}(x)<0\) in \([0,1]\), then

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

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Let \(\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}\). Then

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

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If \(|z+i|-|z-1|=|z|-2=0\) for a complex number \(z\), then \(z=\)

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

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The remainder when \(7^{7^{7^{-7}}}(22\) times 7\()\) is divided by 48 is

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

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\(\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0\) is true for

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

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Let \(f(x)=\left\{\begin{array}{l}0, \text { if }-1 \leq x<0 \\ 1, \text { if } x=0 \\ 2, \text { if } 0<x \leq 1\end{array}\right.\) and let \(F(x)=\int_{-1}^{x} f(t) d t,-1 \leq x \leq 1\), then

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

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Let \(f\) and \(g\) be periodic functions with the periods \(T_{1}\) and \(T_{2}\) respectively. Then \(f+g\) is

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

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