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In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

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

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The expression \(a x^{2}+b x+c(a, b\) and \(c\) are real \()\) has the same sign as that of a for all \(x\) if

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

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The equation \(z \bar{z}+(2-3 i) z+(2+3 i) \bar{z}+4=0\) represents a circle of radius

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

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The number of complex numbers \(p\) such that \(|p|=1\) and imaginary part of \(p^{4}\) is 0 , is

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

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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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