Ten eggs are drawn successively will replacement from a lot containing 10 % defective eggs. Find the probability that there is at least one defective egg.

Ten eggs are drawn successively will replacement from a lot conta…

If $\begin{bmatrix}\text{x}+3&\text{z}+4&2\text{y}-7\\4\text{x}+6&\text{a}-1&0\\\text{b}-3&3\text{b}&\text{z}+2\text{c}\end{bmatrix}=\begin{bmatrix}0&6&3\text{y}-2\\2\text{x}&-3&2\text{c}-2\\2\text{b}+4&-21&0\end{bmatrix}$ Obtain the values of a, b, c, x, y and z.

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Write the identity element for the binary operation * on the set R₀ of all non-zero real numbers by the rule $\text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all a, b ∈ R₀.

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Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^3\text{x}}{\text{dt}^3}+\frac{\text{d}^3\text{x}}{\text{dt}^2}+\Big(\frac{\text{ dx}}{\text{dt}}\Big)^2=\text{e}^\text{t}$

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Let D be the domain of the real valued function f defined by $\text{f}(\text{x})=\sqrt{25-\text{x}^2}.$ Then, write D.

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Express $\tan ^{-1}( \frac{\cos x}{1-\sin x}),-\frac{3 \pi}{2}<x<\frac{\pi}{2}$ in the simplest form.

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Find the position vector of the min-point of the line segment AB, where A is the point (3, 4, -2) and B is the point (1, 2, 4).

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Evaluate the following:
$\sec^{-1}\Big\{\sec\Big(-\frac{7\pi}{3}\Big)\Big\}$

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Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\frac{1}{\frac{\text{dy}}{\text{dx}}}=2$

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If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors, then write the value of $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2.$

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Write the principal value of $\sin^{-1}\Big\{\cos\Big(\sin^{-1}\frac{1}{2}\Big)\Big\}$

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Model Paper 2 — Maths STD 12 Science — Question

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