In each of the following examples verify that the given function is a solution of the differential equation. x^2+y^2=r^2 ; x d y d x +r 1+ (d y d x )^2 =y

In each of the following examples verify that the given function …

If polar co$-$ordinates of point $P$ are $\left(\sqrt{2}, \frac{7 \pi}{4}\right)$, then Cartestan co$-$ordinates of point $P$ are $.......$

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The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
more than one.

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Evaluate the following integrals:$\int\frac{\sec^2\text{x}}{\sqrt{4+\tan^2\text{x}}}\text{ dx}$

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Suppose that a radio tube inserted into a certain type of set has probability $0.2$ of functioning more than $500$ hours. If we test $4$ tubes at random what is the probability that exactly three of these tubes function for more than $500$ hours?

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Let A be a $3 × 3$ square matrix, such that A (adj A) = 2I, where I is the identity matrix. Write the value of |adj A|.

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Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=4$ and $\vec{\text{a}}.\vec{\text{b}}=1$

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Let $'o'$ be a binary operation on the set $Q_0$ of all non-zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2}$ for all $\text{a},\text{b}\in\text{Q}_0.$
Show that $'o'$ is both commutative and associate.

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For each of the following p.d.f. of r.v. $X$, find (a) $P(X<1)$ and (b) $P(|X|<1)$ : $f(x)=\frac{x^2}{18}, \quad$ for $-3<x<3$ and $=0$, otherwise.

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Find the Cartesian equation of the plane passing through A(1, -2, 3) and the direction ratios of whose normal are 0, 2, 0.

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Evaluate:
$\int\Big(\frac{2\cos^2\text{x}-\cos2\text{x}}{\cos^2\text{x}}\Big)\text{dx}$

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Differential Equations — Maths STD 12 Science — Question

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