Q321. If \(log_{10}\: 8 = t\), then find the value of \(log_{10} (\frac{1}{80}) =\) _____

Q322. Choose the sentence with the correct placement of commas.

Q323. A vector, 14 units from the origin, along the X axis, is added to vector 16 units from the origin along the Y axis and is added to vector 12 units from the origin along the Z axis. What is the resultant vector?

Q324. \(\mathbf{Passage:}\)

Dark matter, although invisible and undetectable directly, plays a crucial role in shaping the universe. It is believed to constitute about 27% of the universe's mass-energy content. The presence of dark matter is inferred through its gravitational effects on visible matter, such as galaxies and galaxy clusters. Understanding the nature of dark matter remains one of the greatest mysteries in astrophysics.

Q.1: How is the presence of dark matter inferred?
Q.2: What fraction of the universe's mass-energy content is believed to be dark matter?

Q325. If a line has slope 3 and pass through point (1, 2) then the equation of line is \(_{------}\)

Q326. She likes to swim, to hike, and ________ to read.

Q327. What is the derivative of the function \(f(x) = x^3+4^x+2^3\) with respect to \(x\)?

Q328. What is the product rule for logarithms?

Q329. \(cot(A + B) = _{------------}\)

Q330. \(cos 3x = _{-------------}\).