Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

The correct answer is(B): \((grad f)\times\overrightarrow V + fcurl(\overrightarrow V)\)

\((grad f) \cdot\overrightarrow V + fdiv(\overrightarrow V)\)

\((grad f)\times\overrightarrow V + fcurl(\overrightarrow V)\)

\((grad f)\cdot(div\overrightarrow V) + curl(curl\overrightarrow V)\)

\(grad [div\overrightarrow V] - fcurl(\overrightarrow V)\)

Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

\((grad f)\times\overrightarrow V + fcurl(\overrightarrow V)\)

\((grad f) \cdot\overrightarrow V + fdiv(\overrightarrow V)\)

\((grad f)\times\overrightarrow V + fcurl(\overrightarrow V)\)

\((grad f)\cdot(div\overrightarrow V) + curl(curl\overrightarrow V)\)

\(grad [div\overrightarrow V] - fcurl(\overrightarrow V)\)

Let V be a vector field and f be a scalar point function, then curl (fV) is equivalent to_______

If \( X \) is a random variable such that \( P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6} \), and \( P(X = 0) = \frac{1}{3} \), then the mean of \( X \) is

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Match List-I with List-II:

List-I	List-II
(A) 4î − 2ĵ − 4k̂	(I) A vector perpendicular to both î + 2ĵ + k̂ and 2î + 2ĵ + 3k̂
(B) 4î − 4ĵ + 2k̂	(II) Direction ratios are −2, 1, 2
(C) 2î − 4ĵ + 4k̂	(III) Angle with the vector î − 2ĵ − k̂ is cos⁻¹(1/√6)
(D) 4î − ĵ − 2k̂	(IV) Dot product with −2î + ĵ + 3k̂ is 10

Choose the correct answer from the options given below:

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If \( \theta \) is the angle between \( \vec{f} = i + 2j - 3k \) and \( \vec{g} = 2i - 3j + ak \) and \( \sin \theta = \frac{\sqrt{24}}{28} \), then \( 7a^2 + 24a = \) ?

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Let \( \overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w} \) be three unit vectors. Let \( \overrightarrow{p} = \overrightarrow{u} + \overrightarrow{v} + \overrightarrow{w} \), \( \overrightarrow{q} = \overrightarrow{u} \times (\overrightarrow{p} \times \overrightarrow{w}) \). If \( \overrightarrow{p} \cdot \overrightarrow{u} = \frac{3}{2} \), \( \overrightarrow{p} \cdot \overrightarrow{v} = \frac{7}{4} \), \( |\overrightarrow{p}| = 2 \), and \( \overrightarrow{v} = K \overrightarrow{q} \), then \( K = ? \)

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Let \( \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} \) be non-coplanar vectors. If \( \alpha \overrightarrow{d} = \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} \), \( \beta \overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} \), then \( | \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} | = ? \)

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Let \(\overrightarrow V\) be a vector field and f be a scalar point function, then curl \((f\overrightarrow V)\) is equivalent to________.

The Correct Option is B

Solution and Explanation

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