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

View Solution

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: