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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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The greatest and least values of \(f(x)=\tan ^{-1} x-\frac{1}{2} \ln x\) on \(\left[\frac{1}{\sqrt{3}}, \sqrt{3}\right]\) are

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

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Whichever of the following is/are correct?

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

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\(\lim _{n \rightarrow \infty} \frac{\sqrt{n}}{\sqrt{\left(n^{3}\right)}}+\frac{\sqrt{n}}{\sqrt{(n+4)^{3}}}+\frac{\sqrt{n}}{\sqrt{(n+8)^{3}}}+\cdots \cdots+\frac{\sqrt{n}}{\sqrt{[n+4(n-1)]^{3}}}\) is

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

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Let \(P\) be a variable point on a circle \(C\) and \(Q\) be a fixed point outside \(C\). If \(R\) is the midpoint of the line segment \(P Q\), then locus of \(R\) is

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

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A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centroid of \(\triangle A B C\) is \(\left(1, r, r^{2}\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(r=\)

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

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Let \(f(x)\) be a continuous periodic function with period \(T\). Let \(I=\int_{a}^{a+T} f(x) d x\). Then

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

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The differential of \(f(x)=\log _{e}\left(1+e^{10 x}\right)-\tan ^{-1}\left(e^{5 x}\right)\) at \(x=0\) and for \(d x=0.2\) is

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

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If \(b=\int_{0}^{1} \frac{e^{t}}{t+1} d t\), then \(\int_{a-1}^{a} \frac{e^{-1}}{t-a-1}\) is

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

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3 answers

The plane \(\ell x+m y=0\) is rotated about its line of intersection with the plane \(z=0\) through an angle \(\alpha\). The equation changes to

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

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1 answer

Let \(I=\int_{\pi / 4}^{\pi / 3} \frac{\sin x}{x} d x\). Then

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

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The points of intersection of two ellipses \(x^{2}+2 y^{2}-6 x-12 y+20=0\) and \(2 x^{2}+y^{2}-10 x-6 y+15=0\) lie on a circle. The centre of the circle is

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

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1 answer

The determinant \(\left|\begin{array}{ccc}a^{2}+10 & a b & a c \\ a b & b^{2}+10 & b c \\ a c & b c & c^{2}+10\end{array}\right|\) is

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

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2 answers

Let \(R\) be the real line. Let the relations \(S\) and \(T\) on \(R\) be defined by \(S=\{(x, y): y=x+1,0<x<2\}, T=\{(x, y):(x-y)\) is an integer \(\}\). Then

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

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The co-efficient of \(a^{3} b^{4} c^{5}\) in the expansion of \((b c+c a+a b)^{6}\) is

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

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Three unequal positive numbers \(a, b, c\) are such that \(a, b, c\) are in G.P. while \(\log \left(\frac{5 c}{2 a}\right), \log \left(\frac{7 b}{5 c}\right), \log \left(\frac{2 a}{7 b}\right)\) are in A.P. Then \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are the lengths of the sides of

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

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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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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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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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