Recent questions in Maths

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If \(a(\vec{\alpha} \times \vec{\beta})+b(\vec{\beta} \times \vec{\gamma})+c(\vec{\gamma} \times \vec{\alpha})=\overrightarrow{0}\), where \(a, b, c\) are non-zero scalars, then the vectors \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) are

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

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2 answers

If the tangent at the point \(P\) with co-ordinates \((h, k)\) on the curve \(y^{2}=2 x^{3}\) is perpendicular to the straight line \(4 x=3 y\), then

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

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2 answers

Given that \(f: S \rightarrow R\) is said to have a fixed point at \(c\) of \(S\) if \(f(c)=c\). Let \(f:[1, \infty) \rightarrow R\) be defined by \(f(x)=1+\sqrt{x}\). Then

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

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1 answer

The area bounded by the parabolas \(y=4 x^{2}, y=\frac{x^{2}}{9}\) and the straight line \(y=2\) is

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

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The \(\lim _{x \rightarrow \infty}\left(\frac{3 x-1}{3 x+1}\right)^{4 x}\) equals

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

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If \(\int_{\log _{e} 2}^{x}\left(e^{x}-1\right)^{-1} d x=\log _{e} \frac{3}{2}\) then the value of \(x\) is

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

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The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is

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

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102 answers

The normal to a curve at \(P(x, y)\) meets the \(x\)-axis at \(G\). If the distance of \(G\) from the origin is twice the abscissa of \(P\) then the curve is

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

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3 answers

Let \(g(x)=\int_{x}^{2 x} \frac{f(t)}{t} d t\) where \(x>0\) and \(f\) be continuous function and \(f(2 x)=f(x)\), then

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

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2 answers

The value of the integral \(\int_{-1 / 2}^{1 / 2}\left\{\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2\right\}^{1 / 2} d x\) is equal to

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

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1 answer

$$ \int_{1}^{3} \frac{|x-1|}{|x-2|+|x-3|} d x= $$

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

If \(\mathrm{I}=\lim _{x \rightarrow 0} \sin \left(\frac{e^{x}-x-1-\frac{x^{2}}{2}}{x^{2}}\right)\), then limit

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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2 answers

If \(\int \frac{\sin 2 x}{(a+b \cos x)^{2}} d x=\alpha\left[\log _{e}|a+b \cos x|+\frac{a}{a+b \cos x}\right]+c\), then \(\alpha=\)

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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2 answers

Let \(f: R \rightarrow R\) be such that \(f(0)=0\) and \(\left|f^{\prime}(x)\right| \leq 5\) for all \(x\). Then \(f(1)\) is in

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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1 answer

The equation \(6^{x}+8^{x}=10^{x}\) has

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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1 answer

Let \(f: D \rightarrow R\) where \(D=[0,1] \cup[2,4]\) be defined by \(f(x)=\left\{\begin{array}{l}x, \quad \text { if } x \in[0,1] \\ 4-x, \text { if } x \in[2,4]\end{array}\right.\). Then,

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

For \(y=\sin ^{-1}\left\{\frac{5 x+12 \sqrt{1-x^{2}}}{13}\right\} ;|x| \leq 1\), if \(a\left(1-x^{2}\right) y_{2}+b x y_{1}=0\) then \((a, b)=\)

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

Consider the functions \(f_{1}(x)=x, f_{2}(x)=2+\log _{e} x, x>0\). The graphs of the functions intersect.

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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3 answers

\(f(x)\) is real valued function such that \(2 f(x)+3 f(-x)=15-4 x\) for all \(x \in R\). Then \(f(2)=\)

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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If from a point \(P(a, b, c)\), perpendiculars \(P A\) and \(P B\) are drawn to \(Y Z\) and \(Z X\) planes respectively, then the equation of the plane \(\mathrm{OAB}\) is

asked Dec 9, 2021 in Sets, relations and functions by kritika (90.1k points)

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Recent questions in Maths

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