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Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\] interms of A.
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If A and B are square matrices such that B = − A−1 BA, then (A + B)2 = ________ .
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If \[A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix},\text{ then }A^5 =\] ____________ .
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If A is a square matrix such that A2 = I, then A−1 is equal to _______ .
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Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.
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Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
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Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
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If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
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A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
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Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?
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If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere ?
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The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .
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The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that k is small ?
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Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?
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1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
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Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
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Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
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Using differential, find the approximate value of the \[\sqrt{401}\] ?
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