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Let \(f(x)=3 x^{10}-7 x^{8}+5 x^{6}-21 x^{3}+3 x^{2}-7\). Then \(\lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}\)

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(f:[a, b] \rightarrow \mathbb{R}\) be differentiable on \([a, b] \& k \in \mathbb{R} .\) Let \(f(a)=0=f(b)\) Also let \(J(x)=f^{\prime}(x)+k f(x)\). Then

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The domain of definition of \(f(x)=\sqrt{\frac{1-|x|}{2-|x|}}\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let \(f_{1}(s)=e^{x}, f_{2}(x)=e^{f(x)}, \ldots \ldots . f_{n+1}(x)=e^{f(x)}\) for all \(n \geq 1\). The for any fixed \(n, \frac{d}{d x} f_{n}(x)\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The approximate value of \(\sin 31^{\circ}\) is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Consider the function \(f(x)=\frac{x^{3}}{4}-\sin \pi x+3\)

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

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Let \(f\) and \(g\) be differentiable on the interval \(I\) and let \(a, b \in I, a<b\). Then

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

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Equation of a tangent to the hyperbola \(5 x^{2}-y^{2}=5\) and which passes through an external point \((2,8)\) is

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

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Straight lines \(x-y=7\) and \(x+4 y=2\) intersect at \(B\). Points \(A\) and \(C\) are so chosen on these two lines such that \(A B\) \(=A C\). The equation of line AC passing through \((2,-7)\) is

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

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Let \(A=\left(\begin{array}{lll}3 & 0 & 3 \\ 0 & 3 & 0 \\ 3 & 0 & 3\end{array}\right) .\) Then the roots of the equation \(\operatorname{det}\left(A-\lambda I_{3}\right)=0\) (where \(I_{3}\) is the identity matrix of order 3 ) are

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

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If \(\theta \in \mathbb{R}\) and \(\frac{1-i \cos \theta}{1+2 i \cos \theta}\) is real number, then \(\theta\) will be (when I: Set of integers)

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

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Let \(x_{1}, x_{2}\) be the roots of \(x^{2}-3 x+a=0\) and \(x_{3}, x_{4}\) be the roots of \(x^{2}-12 x+b=0\). If \(x_{1}<x_{2}<x_{3}<x_{4}\) and \(x_{1}\), \(x_{2}, x_{3}, x_{4}\) are in G.P. then \(a b\) equals

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

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The area bounded by \(y=x+1\) and \(y=\cos x\) and the \(x\)-axis, is

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

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Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and \(h\) respectively. If \(A\) takes \(m\) seconds more than \(B\) and describes \(n\) units more than that of \(B\) acquiring the same speed, then

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

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Let \(I_{n}=\int_{0}^{1} x^{n} \tan ^{-1} x d x\). If \(a_{n} I_{n+2}+b_{n} I_{n}=c_{n}\) for all \(n \geq 1\), then

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

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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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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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