| 2023-06-09 | If there is an error of \( k \) in measuring the edge of a cube then the percent error in estima... | 2:58 | 0 | |
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| 2023-06-09 | The approximated value of \( f(3.02) \), where \( f\left(3 x^{2}+5 x+3\right) \)
(a) 45.46
(b) 4... | 4:23 | 0 | |
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| 2023-06-09 | The minimum distance between \( y=x^{4}+3 x^{2}+2 x \) and \( y=2 x-1 \),
(a) 1
(b) \( \sqrt{5} ... | 4:26 | 3 | |
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| 2023-06-09 | Tangent of an angle increases four times as the angle itself. At that angle, sine of the angle i... | 2:49 | 1 | |
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| 2023-06-09 | On dropping a stone in stationary water circular ripples are observed. Rate of flow of ripples i... | 2:28 | 0 | |
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| 2023-06-09 | The curves \( x^{2}-y^{2}=5 \) and \( \frac{x^{2}}{18}+\frac{y^{2}}{8}=1 \) cut each other at an... | 7:44 | 3 | |
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| 2023-06-09 | The radius of a sphere is changing at the rate of \( 0.1 \mathrm{~cm} / \mathrm{sec} \). The rat... | 2:07 | 0 | |
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| 2023-06-09 | A spherical balloon is being inflated at the rate of \( 35 \mathrm{~cm} / \) \( \min \). The rat... | 3:04 | 1 | |
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| 2023-06-09 | The approximated value of \( (26)^{1 / 3} \) (a) 2.963 (b) 2.763 (c) 3.245 | 2:45 | 1 | |
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| 2023-06-09 | The approximated change in the volume \( V \) of a cube of side \( x \) meters caused by increas... | 2:24 | 0 | |
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| 2023-06-09 | The minimum distance between \( y-x=1 \) and \( y^{2}=x \) is
(a) \( \frac{3}{4 \sqrt{2}} \)
(b)... | 3:22 | 0 | |
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| 2023-06-09 | The angle of intersection between two curves \( x y=6 \) and \( x^{2} y \) \( =12 \) is
(a) \( \... | 4:03 | 1 | |
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| 2023-06-09 | Consider the two graphs \( y=2 x \) and \( x^{2}-x y+2 y^{2}=28 \). The absolute value of the ta... | 4:43 | 4 | |
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| 2023-06-09 | The sub-tangent, ordinate and subnormal to the parabola \( y^{2}=4 a x \) at a point (different ... | 5:12 | 0 | |
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| 2023-06-09 | If \( \ell \) and \( m \) are lengths of the sub-tangent and sub-normal to the curve \( \beta y^... | 8:51 | 0 | |
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| 2023-06-09 | Angle of intersection of the curve \( x^{2}=32 y \) and \( y^{2}=4 x \) at the point \( (16,8) \... | 2:52 | 0 | |
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| 2023-06-09 | The length of the normal to the curve at \( (x, y) \) where \( y=a\left(\frac{e^{x / a}+e^{-x / ... | 3:58 | 0 | |
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| 2023-06-09 | For the curve \( y=b e^{x / a} \)
(a) Sub-tangent is constant
(b) Sub-normal to constant
(c) Len... | 6:20 | 0 | |
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| 2023-06-09 | The tangent to the curve \( 3 x y^{2}-2 x^{2} y=1 \) at \( (1,1) \) meets the curve again at the... | 8:52 | 0 | |
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| 2023-06-09 | At any point of a curve \( \sqrt{\frac{\text { Subnormal }}{\text { Subtangent }}}= \)
(a) The a... | 2:12 | 0 | |
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| 2023-06-09 | The slope of the tangent to the curve \( y=\cos ^{-1}(\cos x) \) at \( x=-\pi / 4 \) is
(a) 1
(b... | 1:20 | 1 | |
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| 2023-06-09 | If the tangent at \( t \) on the curve \( y=8 t^{3}-1, x=4 t^{2}+3 \) meets the curve again at... | 6:05 | 0 | |
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| 2023-06-09 | The tangent at \( \left(t, t^{2}-t^{3}\right) \) on the curve \( y=x^{2}-x^{3} \) meets the curv... | 5:19 | 0 | |
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| 2023-06-09 | The subtangent at any point of the curve \( x^{m} y^{n}=a^{m+n} \) varies as
(a) The ordinate
(b... | 3:17 | 0 | |
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| 2023-06-09 | Let \( C \) be the curve \( y=x^{3} \) (where \( \mathrm{x} \) takes all real values). The tange... | 5:09 | 0 | |
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| 2023-06-09 | The \( x \)-intercept of the tangent at any arbitrary point of the curve \( \frac{a}{x^{2}}+\fra... | 4:20 | 0 | |
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| 2023-06-09 | If the area of the triangle included between the axes and any tangent to the curve \( x y^{n}=a^... | 6:43 | 1 | |
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| 2023-06-09 | Curve is represented parametrically by the equations \( x=t+e^{a t} \) and \( y=-t+e^{a t} \) wh... | 4:10 | 0 | |
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| 2023-06-09 | The points on the curve \( y^{3}+3 x^{2}=12 y \) where the tangent is vertical, is (are)
(a) \( ... | 3:53 | 4 | |
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| 2023-06-09 | The line \( \frac{x}{a}+\frac{y}{b}=1 \) touches the curve \( y=b e^{-x / a} \) at the point:
\(... | 3:56 | 0 | |
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| 2023-06-09 | The angle made by the tangent of the curve \( x=a(t+t \sin t \) \( \operatorname{cost}), y=a(1+\... | 10:29 | 0 | |
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| 2023-06-09 | Equation of normal to the curve \( y=x+\sin x \cos x \) at \( x=\frac{\pi}{2} \) is
(a) \( x+\pi... | 2:52 | 0 | |
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| 2023-06-09 | Equation of tangent to cuve \( x=a \cos ^{3} t, y=a \sin ^{3} t \) at \( t \) is
(a) \( x \sec t... | 5:05 | 0 | |
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| 2023-06-09 | At what points on the curve \( x^{2}+y^{2}-2 x-4 y+1=0 \), the tangents are parallel to the y-ax... | 4:30 | 11 | |
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| 2023-06-09 | The curve \( y=a x^{3}+b x^{2}+c x+8 \) touches \( x \)-axis at \( P(-2,0) \) and cuts the \( y ... | 6:04 | 1 | |
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| 2023-06-09 | For the curve \( C:\left(x^{2}+y^{2}-3\right)+\left(x^{2}-y^{2}-1\right)^{5}=0 \), the value of ... | 9:10 | 2 | |
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| 2023-06-09 | Equation of tangent to curve \( y=\left|x^{2}-13 x+40\right| \) at point \( x= \) 6 is
(a) \( x+... | 2:27 | 1 | |
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| 2023-06-09 | On the curve \( y=\frac{1}{x^{2}+1} \) find a point at which the tangent is parallel to the axis... | 2:37 | 0 | |
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| 2023-06-09 | Let \( f: R \rightarrow R \), satisfy \( f(x+y)=2^{x} f(y)+4^{y} f(x), \forall x, y \in R \). If... | 8:10 | 3 | |
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| 2023-06-09 | Let \( f(x) \) be a polynomial function suchthat \( f(x)+f^{\prime}(x)+ \) \( f^{\prime \prime}(... | 9:39 | 0 | |
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| 2023-06-09 | Let \( f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\r... | 5:30 | 0 | |
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| 2023-06-09 | The slope of the normal to the curve \( x=a(\theta-\sin \theta) \), \( y=a(1-\cos \theta) \) at ... | 2:37 | 0 | |
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| 2023-06-09 | If \( y^{1 / 4}+y^{-1 / 4}=2 x \), and \( \left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+\alpha x ... | 8:26 | 8 | Let's Play |
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| 2023-06-09 | If \( \lim _{x \rightarrow 0} \frac{a e^{x}-b \cos x+c e^{-x}}{x \sin x}=2 \) then \( a+b+c \) i... | 6:16 | 0 | |
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| 2023-06-09 | If \( m \) is the slope of a tangents to the curve \( e^{y}=1+x^{2} \), then
(a) \( |m|1 \)
(b) ... | 3:01 | 0 | |
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| 2023-06-09 | If \( f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right) \) and its first... | 7:55 | 2 | |
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| 2023-06-09 | The value of \( \log _{e} 2 \frac{d}{d x}\left(\log _{\cos x} \operatorname{cosec} x\right) \) a... | 4:14 | 3 | Vlog |
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| 2023-06-09 | Let \( f(x)=\left\{\begin{array}{l}\left|4 x^{2}-8 x+5\right|, \text { if } 8 x^{2}-6 x+1 \geq 0... | 15:07 | 2 | |
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| 2023-06-09 | If \( y=y(x) \) is an implicit function of \( x \) such that \( \log _{\mathrm{e}}(x+y) \) \( =4... | 5:52 | 0 | Vlog |
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| 2023-06-09 | If \( [t] \) denotes the greatest integer \( \leq t \), then number of points, at which the func... | 12:01 | 1 | |
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| 2023-06-09 | Let \( a, b \in R, b \in 0 \), Define a function
\[
f(x)=\left\{\begin{array}{cc}
a \sin \frac{\... | 6:37 | 1 | |
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| 2023-06-09 | Let \( f: R \rightarrow R \) satisfy th equation \( f(x+y)=f(x) . f(y) \) for all \( x, y \in R ... | 4:30 | 0 | |
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| 2023-06-09 | Let \( f(x)=\cos \left(2 \tan ^{-1} \sin \left(\cot ^{-1} \sqrt{\frac{1-x}{x}}\right)\right), 0x... | 7:46 | 6 | |
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| 2023-06-09 | Let \( f: S \rightarrow S \) where \( S=(0, \infty) \) be a twice differentiable function such t... | 7:19 | 0 | |
|
| 2023-06-09 | The number of points where the function
\[
f(x)=\left\{\begin{array}{clc}
\left|2 x^{2}-3 x-7\ri... | 9:28 | 4 | |
|
| 2023-06-09 | The number of points, at which the function \( f(x)=|2 x+1| \) \( -3|x+2|+\left|x^{2}+x-2\right|... | 12:42 | 6 | |
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| 2023-06-09 | Let \( f \) be any function defined on \( R \) and let it satisfy the condition:
\[
|f(x)-f(y)| ... | 4:59 | 0 | |
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| 2023-06-09 | Let \( f: R \rightarrow R \) and \( g: R \rightarrow R \) be defined as
\[
f(x)=\left\{\begin{ar... | 8:48 | 1 | |
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| 2023-06-09 | Let \( [t] \) denote the greatest intetger \( \leq t \). The number of points where the function... | 9:35 | 1 | |
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| 2023-06-09 | Let \( f(x)=\left[2 x^{2}+1\right] \) and \( g(x)=\left\{\begin{array}{ll}2 x-3, & x0 \\ 2 x+3, ... | 6:31 | 2 | |
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| 2023-06-09 | Let \( f, g: R \rightarrow R \) be functions efined by
\[
\begin{array}{l}
f(x)=\left\{\begin{ar... | 11:43 | 0 | |
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| 2023-06-09 | The number of points, where the function \( f: R \rightarrow R, f(x)= \) \( |x-1| \cos |x-2| \si... | 11:28 | 2 | |
|
| 2023-06-09 | Let \( f, g: R \rightarrow R \) be two real valued functions defined as
\[
\begin{array}{l}
f(x)... | 11:50 | 4 | |
|
| 2023-06-09 | Let \( f: R \rightarrow \) be defined as
\[
f(x)=\left\{\begin{array}{cc}
\frac{\lambda \mid x^{... | 5:37 | 0 | |
|
| 2023-06-09 | Let a function \( f: R \rightarrow R \) be defined as
\[
f(x)=\left\{\begin{array}{ccc}
\sin x-e... | 6:06 | 0 | |
|
| 2023-06-09 | The function \( f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|} \) is not di... | 8:47 | 2 | |
|
| 2023-06-09 | Let \( f: R \rightarrow R \) be defined as
\[
f(x)=\left\{\begin{array}{cc}
\frac{x^{3}}{(1-\cos... | 7:51 | 2 | |
|
| 2023-06-09 | Let \( f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R \) be defined as
\[
f(x)=\left... | 7:47 | 6 | |
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| 2023-06-09 | If \( f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & ; \quad|x| \geq 1 \\ a x^{2}+b & ; \quad|x|1\... | 11:02 | 1 | |
|
| 2023-06-09 | Let \( \alpha \in R \) be such that the function
is continuous at \( x=0 \), where \( \{x\}=x-[x... | 9:21 | 1 | Let's Play |
|
| 2023-06-09 | Let \( f: R \rightarrow R \) be a function defined as
\[
f(x)=\left\{\begin{array}{cc}
\frac{\si... | 6:36 | 0 | |
|
| 2023-06-09 | If \( f(x)=\| \sin (|x|-1)-2 \mid \) then
(a) \( f(x) \) is continuous at \( x=2 \)
(b) \( f(x) ... | 17:00 | 12 | |
|
| 2023-06-09 | Let \( f: R \rightarrow R \) be defined as
\( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\... | 6:26 | 0 | |
|
| 2023-06-09 | \[
f(x)=\left\{\begin{array}{cc}
\frac{\tan 10 x-\sin x-\sin 3 x-\tan 2 x-\tan 4 x}{x^{3}}, & x ... | 12:37 | 0 | |
|
| 2023-06-09 | Let \( g(x) \) be a polynomial, of degree one \( \& f(x) \) be defined by \( f(x)=\left[\begin{a... | 10:02 | 1 | |
|
| 2023-06-09 | If \( f: R \rightarrow R \) is a function define by
\[
f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\rig... | 6:43 | 1 | |
|
| 2023-06-09 | Let \( f(x) \) be a differentiable and \( \mathrm{g}(\mathrm{x}) \) be a twice differentiable fu... | 12:03 | 2 | |
|
| 2023-06-09 | Let \( f(n)=1-4 \sin ^{2} \frac{\pi}{3 \cdot 2^{n}} \) be a function and \( T_{k}=\prod_{n=2}^{k... | 3:50 | 3 | |
|
| 2023-06-09 | Find number of points of non-differentiability of \( f(x)=\lim _{n \rightarrow \infty} \frac{\le... | 7:29 | 7 | |
|
| 2023-06-09 | If \( y=\cos ^{-1} \frac{a+b \cos x}{b+a \cos x}, ba \) then \( \frac{d y}{d x}= \)
(a) \( \frac... | 8:37 | 0 | |
|
| 2023-06-09 | Let \( f(x) \) be a real valued function such that \( f(x)=\frac{2 x-1}{x-2} \forall x \in \) \(... | 17:07 | 4 | |
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| 2023-06-09 | \( y=\sqrt[3]{\frac{x-5}{\sqrt[5]{x^{2}+4}}} \) find \( 60 \sqrt[3]{25 \sqrt[5]{4}} f^{\prime}(0) \) | 4:42 | 1 | |
|
| 2023-06-09 | Let \( f(x) \) be a function which is differentiable everywhere any number of times and \( f\lef... | 4:30 | 1 | |
|
| 2023-06-09 | If \( f(x)=[\ln x] \operatorname{sgn}\left(\{x\}-\frac{1}{2}\right) \) where \( 1 \leq x \leq 4 ... | 7:31 | 2 | |
|
| 2023-06-09 | Let \( f(x) \) be a non-constant thrice differential function defined on \( (-\infty, \infty) \)... | 15:36 | 3 | |
|
| 2023-06-09 | If \( f(x)=2 x^{3}-3 x^{2}+1 \) then number of distinct real solutions of the equation \( f(f(x)... | 8:35 | 0 | |
|
| 2023-06-09 | Number of points of inflexion on the curve \( f(x)=(x-1)^{7} \) \( (x+2)^{8} \) is equal to \( \... | 10:20 | 2 | |
|
| 2023-06-09 | \( \mathrm{f}(\mathrm{x})=[\sqrt{x}] \) for \( \mathrm{x} \in[1,50] \) where \( [\cdot] \) is th... | 3:09 | 0 | |
|
| 2023-06-09 | The complete set of non-zero values of \( k \) such that the equation \( \left|x^{2}-7 x+6\rig... | 8:35 | 0 | |
|
| 2023-06-09 | The function \( f(x)=2 x^{3}+\alpha x^{2}+\beta x+r \) where \( \alpha, \beta, r \in R \) has lo... | 8:28 | 0 | Let's Play |
|
| 2023-06-09 | For \( x \) to be real, maximum value of \( y=4(\sin x-x) \) \( \left(x+\sqrt{x^{2}+\cos ^{2} x}... | 12:38 | 0 | |
|
| 2023-06-09 | Match the columns:
(a) \( \mathrm{A}-(\mathrm{p}), \mathrm{B}-(\mathrm{r}), \mathrm{C}-(\mathrm{... | 18:09 | 0 | |
|
| 2023-06-09 | \( f(x)=x^{5}-5 x^{4}+5 x^{3}-10 \) has local maxima and minima at \( x \) \( =l \) and \( x=m \... | 7:17 | 0 | |
|
| 2023-06-09 | If \( f(x) \) is a twice differentiable function such that \( f(a)=0 . f(b) \) \( =2 . f(c)=-1, ... | 7:15 | 2 | |
|
| 2023-06-09 | For the cubic \( f(x)=\frac{x^{3}}{3}-(m-3) \frac{x^{2}}{2}+m x+3=0 \); find the value of \( m ... | 15:55 | 0 | |
|
| 2023-06-09 | Match the columns:
\begin{tabular}{|l|l|c|c|}
\hline \multicolumn{2}{|c|}{ Column - I } & \multi... | 17:07 | 2 | |
|
| 2023-06-09 | If \( l x+m y=1 \) touches the curve \( (a x)^{n}+(b y)^{n}=1 \). If \( \left(\frac{l}{a}\right)... | 7:21 | 0 | |
|
| 2023-06-09 | If \( f(x)=x-2 \sin x, 0 \leq x \leq 2 \pi \) is increasing in the interval \( [a \pi, b \pi] \)... | 3:41 | 0 | |
|
| 2023-06-09 | From a given solid cone of height \( H \) , another inverted cone is carved such that its volum... | 10:49 | 5 | |
|
| 2023-06-09 | Match the columns:
(a) \( \mathrm{A}-(\mathrm{p}), \mathrm{B}-(\mathrm{r}), \mathrm{C}-(\mathrm{... | 14:09 | 2 | |
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