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Question : If $\sin 3x=\cos(3x-45^{\circ}), 0^{\circ}<3x<90^{\circ}$, then $x$ is equal to:
Option 1: $45^\circ$
Option 2: $22.5^\circ$
Option 3: $35^\circ$
Option 4: $27.5^\circ$
Correct Answer: $22.5^\circ$
Solution : Given: $\sin 3x = \cos(3x - 45^\circ)$ We know that, $\sin \theta = \cos(90^\circ - \theta)$ ⇒ $\sin 3x = \sin(90^\circ - (3x- 45^\circ))$ ⇒ $3x = 90^\circ - 3x+45^\circ$ ⇒ $6x = 135^\circ$ ⇒ $x = 22.5^\circ$ Hence, the correct answer is $22.5^\circ$.
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Question : Assertion: An increase in the exchange rate leads to a decrease in exports.
Reason: A higher exchange rate makes exports relatively more expensive, reducing their competitiveness.
Option 1: Both Assertion and Reason are true and correct explanation
Option 2: Both Assertion and Reason are true and incorrect explanation
Option 3: Assertion is true but Reason is false
Option 4: Assertion is false but Reason is true
Correct Answer: Both Assertion and Reason are true and correct explanation
Solution : The correct answer is (a) Both the Assertion and the Reason are true and provide a correct explanation.
The Assertion states that an increase in the exchange rate leads to a decrease in exports, which is true.
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