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Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed) (32, 24, 8) (48, 42, 6)
Option 1: (64, 62, 8)
Option 2: (56, 50, 6)
Option 3: (16, 14, 4)
Option 4: (18, 12, 4)
Correct Answer: (56, 50, 6)
Solution : Given: (32, 24, 8); (48, 42, 6) The pattern is – (32, 24, 8)→32 – 24 = 8 (48, 42, 6)→48 – 42 = 6
Let's check each option – First option: (64, 62, 8) = 64 – 62 = 2 ≠ 8
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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