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Tan 30 = \(\frac{h}{40}\) \(\frac{1}{\sqrt{3}}=\frac{h}{40}\) h\(\sqrt{3}\) = 40 h = \(\frac{40}{\sqrt{3}}\) h = \(\frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\) h = \(\frac{40\sqrt{3}}{3}\)

Locus of point P equidistant from y - 5 = 0 and y - 3 = 0 is y = 4 i.e y - 4 = 0

(1-k+2) / 2 = - k and -4 + k + 1 = k 3-k = -2k and -3 + k = 2k K = -3 and k = -3

Each Exterior ∠ = 360/n = 360/8 = 45o

\(\frac{tan 60^o - tan 30^o}{tan 60^o + tan 30^o}= \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{\sqrt{3}+\frac{1}{\sqrt{3}}}\\ =\left(\frac{\sqrt{3}\sqrt{3}-1}{\sqrt{3}}\right)\div \left(\frac{\sqrt{3}\sqrt{3}+1}{\sqrt{3}}\right)\\ =\frac{(3-1)}{(3+1)}\\ =\frac{2}{4}=\frac{1}{2}\)

Area of a square = x * x 144 = x2 \sqrt144 = x 12 = x But d2 = 122 + 122 = 144 + 144 = 288 d = \sqrt288 = \sqrt144 x 2 = 12\sqrt2

If the linear expansivity = ∝ => area expansivity \beta = 2∝. And cubic expansivity δ = 3∝. => 6.3 x 10\(^{-6}\) = 3∝ ∴ ∝ = \(\frac{6.3 \times 10^{-11}}{3}\) = 2.1 x 10\(^{-6}\) ∴ Area = 2∝ = 2 x 2.1x10\(^{-6}\) = 4.2 x 10\(^{-6}\)K\(^{-1}\)

Sodium chloride, which is obtained by neutralization of hydrochloric acid and sodium hydroxide, is a neutral salt. A neutral salt is formed when a strong acid reacts with a strong base. This is because the strong acid is completely neutralized by the strong base. When a strong acid and a strong base are combined in the right amounts, the result is a neutral solution with a pH of 7. The acid and base have neutralized each other, and the acidic and basic properties are no longer present. The salt formed from a strong acid and a strong base is neutral because the anion and cation are both weak. They are stable in water and do not react with water to form the original acid or base.

Elements in period 3 have 3 shells in their atomic structure. These include elements from sodium to argon.

If y = (1 + x)2, find \(\frac{dy}{dx}\) y = (1 + x)2 \(\frac{dy}{dx}\) = 2(1 + x) = 2 + 2x

M + L = 28, M : L = 600 : 800 = 3 : 4 \(\frac{M}{L}\) = \(\frac{3}{4}\) \(\to\) M = \(\frac{3}{4}\)L \(\frac{3}{4}\)L + L = 28 \(\frac{7L}{4}\) = 28 L = \(\frac{4 \times 28}{7}\) = 16

Deprecated; to express disapproval of something Condemn is to express complete disapproval of something.

“Reversed” means the decision must be withdrawn or cancelled officially. "Resciended" means officially cancelled or withdrawn, which is the closest in meaning to “reversed” in this context.

Depraved implies morally corrupt; wicked

'Made in ignorance' implies made without information or knowledge. The most appropriate answer is option A as other options can be considered as antonyms