Q531. Find the \(\frac{d}{dx} (3 \sin(x) - 4 \sin^3 (x))\).

Q532. What is the value of \(\frac{d(\sin⁡ x^3 \: \cos⁡ x^2)}{dx} ?\)

Q533. By this time next year, I __________ my degree.

Q534. Which of the below condition is incorrect for the inverse of a matrix \(A\)?

Q535. \(\mathbf{Passage:}\) The concept of black holes, predicted by Einstein's theory of general relativity, describes regions in spacetime where gravity is so intense that nothing, not even light, can escape. These celestial objects are formed by the gravitational collapse of massive stars. Despite their mysterious nature, black holes play a crucial role in shaping the structure of the universe. Q.1: According to general relativity, what defines a black hole? Q.2: How are black holes formed?

Q536. What does the acronym "FAQ" stand for in written communication?

Q537. Choose the sentence with the appropriate use of "their," "there," or "they're":

Q538. When two vectors in the same direction are added, the magnitude of resulting vector is equal to \(_{--------} \)

Q539. What is the derivative of the constant function \(f(x) = 5\) with respect to \(x\)?

Q540. Choose the sentence with the accurate use of the modal verb.