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Let \(f: R \rightarrow R\) be given by \(f(x)=\left|x^{2}-1\right|, x \in R\). then

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

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A bulb is placed at the centre of a circular track of radius \(10 \mathrm{~m}\). A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of \(10 \mathrm{~m} / \mathrm{sec}\). Starting from P the speed with which his shadow is running along the wall when he is at an angular distance of \(60^{\circ}\) from \(\mathrm{P}\) is

asked Dec 9, 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 f' respectively. If \(A\) takes \(\mathrm{m}\) sec. more than that of \(\mathrm{B}\) and describes \(\mathrm{n}\) units more than that of \(\mathrm{B}\) in acquiring the same velocity, then

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

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If \(x \frac{d y}{d x}+y=\frac{x f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal to

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

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The value of \(\int_{0}^{5} \max \left\{x^{2}, 6 x-8\right\} d x\) is

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

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The straight line through the origin which divides the area formed by the curves \(y=2 x-x^{2}, y=0\) and \(x=1\) into two equal halves is

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

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If \(A, B\) are two events such that \(P(A \cup B) \geq \frac{3}{4}\) and \(\frac{1}{8} \leq P(A \cap B) \leq \frac{3}{8}\) then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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Let \(f: X \rightarrow X\) be such that \(f(f(x))=x\) for all \(x \in X\) and \(X \subseteq R\), then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \(z=\sin \theta-i \cos \theta\) then for any integer \(n\),

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If the equation \(x^{2}+y^{2}-10 x+21=0\) has real roots \(x=a\) and \(y=\beta\) then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \(\varphi(t)=\left\{\begin{array}{l}1, \text { for } 0 \leq t+1 \\ 0 \text { othenwe then }\end{array} \int_{-3000}^{3000}\left(\sum_{r=2014}^{2016} \varphi\left(t-r^{\prime}\right) \varphi(t-2016)\right) d t=\right.\)

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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On the ellipse \(4 x^{2}+9 y^{2}=1\), the points at which the tangents are parallel to the line \(8 x=9 y\) are

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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if \(f(x)\) is a function such that \(f^{\prime}(x)=(x-1)^{2}(4-x)\), then

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If the parabola \(x^{2}=\) ay makes an intercept of length \(\sqrt{40}\) unit on the line \(y-2 x=1\) then a is equal to

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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The coordinates of a point on the line \(x+y+1=0\) which is at a distance \(\frac{1}{5}\) unit from the line \(3 x+4 y+2=0\) are

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If the first and the \((2 n+1)^{\text {th }} t\) erms of an AP, GP and HP are equal and their \(n^{\text {th }}\) terms are respectively \(a, b, c\) then always

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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The equation \(x^{3}-y x^{2}+x-y=0\) represents

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the selected person is female, is

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \({ }^{n} C_{r-1}=36,{ }^{n} C_{r}=84\) and \({ }^{n} C_{r+1}=126\) then the value of \({ }^{n} C_{8}\) is

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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If \(\omega\) is an imaginary cube root of unity, then the value of \((2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3-\omega^{2}\right)+\ldots . .+(n-1)(n-\omega)\left(n-\omega^{2}\right)\) is

asked Dec 8, 2021 in Sets, relations and functions by deepak01 (12.2k points)

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