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Mathematics
Find A−1, if \[A = \begin{bmatrix}1 & 2 & 5 \\ 1 & - 1 & - 1 \\ 2 & 3 & - 1\end{bmatrix}\] . Hence solve the following system of linear equations:x + 2y + 5z = 10, x − y − z = −2, 2x + 3y − z = −11
Chapter: [4] Determinants
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An amount of Rs 10,000 is put into three investments at the rate of 10, 12 and 15% per annum. The combined income is Rs 1310 and the combined income of first and second investment is Rs 190 short of the income from the third. Find the investment in each using matrix method.
Chapter: [4] Determinants
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\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{x^2 + x + 1} \text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]
Chapter: [7] Integrals
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\[\int\cos x \sqrt{4 - \sin^2 x}\text{ dx}\]
Chapter: [7] Integrals
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\[\int e^x \sqrt{e^{2x} + 1} \text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{9 - x^2}\text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{16 x^2 + 25} \text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{4 x^2 - 5}\text{ dx}\]
Chapter: [7] Integrals
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\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]
Chapter: [7] Integrals
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\[\frac{dy}{dx} + y \tan x = x^2 \cos^2 x\]
Chapter: [9] Differential Equations
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\[\left( 1 + x^2 \right)\frac{dy}{dx} + y = e^{tan^{- 1} x}\]
Chapter: [9] Differential Equations
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x dy = (2y + 2x4 + x2) dx
Chapter: [9] Differential Equations
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\[y^2 \frac{dx}{dy} + x - \frac{1}{y} = 0\]
Chapter: [9] Differential Equations
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\[\left( 2x - 10 y^3 \right)\frac{dy}{dx} + y = 0\]
Chapter: [9] Differential Equations
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(x + tan y) dy = sin 2y dx
Chapter: [9] Differential Equations
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dx + xdy = e−y sec2 y dy
Chapter: [9] Differential Equations
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\[\frac{dy}{dx}\] = y tan x − 2 sin x
Chapter: [9] Differential Equations
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