Symmetric Angles

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The correct answer is: 0.5 AExplanation: Electric power (P) can be calculated using the formula, P = VI. Rearranging for current (I), we get $ \displaystyle I=\frac{P}{V}=\frac{{60W}}{{120V}}=0.5A.$

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The correct answer is: $ \displaystyle x$ = 1, 2, –3 Explanation: We are asked to solve the equation x³ – 7x + 6 = 0, which is a cubic equation. We will find the roots using the trial-and-error method followed by factorization. 1. Check for a Root via Substitution: We can start by trying

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If $ \displaystyle x$³ – 6$ \displaystyle x$² + 11$ \displaystyle x$ – 6 is factorized as ($ \displaystyle x-a$)($ \displaystyle x-b$) ($ \displaystyle x-c$), what are the values of $ \displaystyle a$, $ \displaystyle b$, and $ \displaystyle c$?

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± 4 Explanation: According to the question, the distance between the points (4, p) and (1, 0) = 5 i.e., $ \displaystyle \sqrt{{{{{(1-4)}}^{2}}+{{{(0-p)}}^{2}}}}=5$ [∵ distance between the points $ \displaystyle {{x}_{1}},{{y}_{1}}$ and $ \displaystyle {{x}_{2}},{{y}_{2}}$, d= $ \displaystyle \sqrt{{{{{\left( {{{x}_{2}}-{{x}_{1}}} \right)}}^{2}}+{{{\left( {{{y}_{2}}-{{y}_{1}}} \right)}}^{2}}}}$​] $ \displaystyle \begin{array}{l}\Rightarrow \sqrt{{{{{(-3)}}^{2}}+{{p}^{2}}}}=5\\\Rightarrow \sqrt{{9+{{p}^{2}}}}=5\end{array}$​ On squaring both the sides, we get

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The correct answer is: 24 sq. units Explanation: The area of the triangle formed by the vertices A(1,−1),B(−4,6) and C(−3,−5), by using the formula above, is given by $\displaystyle \dfrac{1}{2}$ ​[1(6 + 5) + ( − 4)( − 5 + 1) + ( − 3)( − 1 − 6)] =$\displaystyle \dfrac{1}{2}$ (11 + 16 +

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sec²θ(1 + sinθ)(1 − sinθ) = sec²θ(1 − sin²θ) = sec²θ × cos²θ = $ \displaystyle \left( {\dfrac{1}{{{{{\cos }}^{2}}\theta }}} \right)\times {{\cos }^{2}}\theta $ = 1

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The correct answer is: 180 cm Explanation: In rt. angled △ABP, $ \displaystyle \dfrac{{AB }}{{AP}}$ ​= sin30° ⇒ $ \displaystyle \dfrac{{60}}{{AP}}$​= $\displaystyle \dfrac{1}{2}$  ⇒ AP = 60 × 2 ⇒AP = 120 cm.  In rt. angled ΔADQ, $\displaystyle \dfrac{{AD}}{{AQ}}$ = sin30° ⇒$\displaystyle \dfrac{{30}}{{AQ}}$ =$\displaystyle \dfrac{1}{2}$​ ⇒ AQ= 30 × 2 ⇒AQ = 60 cm. Hence, AP + AQ = 120 +

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The correct answer is: $\displaystyle \dfrac{{a\sin \left( {\alpha +\beta } \right)}}{{\sin \left( {\beta -\alpha } \right)}}m$ Explanation: Let BD be horizontal position of the lake and A be the given point at height h above it. If position of the cloud and its reflection be P and Q respectively, then from diagram ∠PAC = a

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The correct answer is: 20√3 Explanation: In Figure , AB is the tower and BC is the length of the shadow when the Sun’s altitude is 60°, i.e., the angle of elevation of the top of the tower from the tip of the shadow is 60° and DB is the length of the shadow, when

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