If matrix A= [ lll 2 & 4 & 6 1 & 2 & 1 ], and 2 A+B= [ lll 3 & 4 & 2 4 & 1 & 2 ] then find matrix B.

If matrix A= [ lll 2 & 4 & 6 1 & 2 & 1 ], and 2 A+B= [ lll 3 & 4 …

Discuss the continuity of the function: $f(x) = \sin x.\cos x$

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Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is

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Write the equation of a plane which is at a distance of $5\sqrt{3}$ units from origin and the normal to which is equally inclined to coordinate axes.

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$\text{Find} \lambda, \text{if the vectors} \overrightarrow{\text{a}} = \hat{\text{i}} + 3\hat{\text{j}} + \hat{\text{k}}, \overrightarrow{\text{b}} = 2\hat{\text{i}} - \hat{\text{j}} - \hat{\text{k}}$ $\text{and} \overrightarrow{\text{c}} = \lambda \hat{\text{j}} + 3\hat{\text{k}} $ $\text{are coplanar}.$

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If vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}}$ are such that, $|\vec{\text{a}}|=3,\ |\vec{\text{b}}|=\frac{2}{3}\ \text{and}\ \vec{\text{a}}\times\vec{\text{b}}$ is a unit vector, then write the angle between $\vec{\text{a}}\ \text{and}\ \vec{\text{b}}$.

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Evaluate, $\int\limits_0^3\frac{\text{dx}}{9 + \text{x}^{2}}.$

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Write the value of the expression $\tan\Big(\frac{\sin^{-1}\text{x}+\cos^{-1}\text{x}}{2}\Big),$ when $\text{x}=\frac{\sqrt3}{2}$

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Find the sum of the vectors $\overrightarrow{a}=\hat{\text{i}}-\hat{\text{2j}}+\hat{\text{k}},\text{ }\overrightarrow{b}=-\hat{\text{2i}}+\hat{\text{4j}}+\hat{\text{5k}}\text{ and }\overrightarrow{c}=\hat{\text{i}}-\hat{\text{6j}}-\hat{\text{7k}}.$

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$\text{If}\ \text{P}(\text{A})=0.8,\ \text{P}(\text{B})=0.5\ \text{and}\ \text{P}(\text{B}|\text{A})=0.4,\ \text{find}:$
$\text{P}(\text{A}\cap\text{B})$

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$\sin^{-1}\left(1-x\right)-2\sin^{-1}x=\frac{\pi}{2}$, then x is equal to:

$0,\frac{1}{2}$
$1,\frac{1}{2}$
0
$\frac{1}{2}$

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