Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Four angles $a, b, c, d$ lie sequentially on a straight line. What is the average of $a, b, c,$ and $d$?
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Step-by-Step Explanation & Concept Rationale
Since the angles lie on a straight line, their total sum is $a + b + c + d = 180^\circ$. Their average is: \[\text{Average} = \frac{a + b + c + d}{4} = \frac{180^\circ}{4} = 45^\circ\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Angles around a point are $85^\circ, 105^\circ, 60^\circ,$ and $a$. Find the value of angle $a$.
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Step-by-Step Explanation & Concept Rationale
The sum of all angles around a point is $360^\circ$: \[85^\circ + 105^\circ + 60^\circ + a = 360^\circ \implies 250^\circ + a = 360^\circ \implies a = 110^\circ\] Thus, the correct option is (C).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Angles on a straight line are given as $30^\circ, 60^\circ,$ and $a$. Find the value of angle $a$.
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Step-by-Step Explanation & Concept Rationale
Angles on a straight line sum to $180^\circ$: \[30^\circ + 60^\circ + a = 180^\circ \implies 90^\circ + a = 180^\circ \implies a = 90^\circ\] Thus, the correct option is (D).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If the circumference of a circle is $3\pi$, find its area.
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Step-by-Step Explanation & Concept Rationale
The circumference is $C = 2\pi r = 3\pi \implies r = \frac{3}{2}$. The area of the circle is: \[A = \pi r^2 = \pi \left(\frac{3}{2}\right)^2 = \frac{9\pi}{4}\] Thus, the correct option is (B).
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