trigonometric ratios and identities mcq Model Questions & Answers, Practice Test for ibps clerk prelims 2024
ibps clerk prelims 2024 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentage
Time & Work
Time & Distance
Mensuration
Trigonometric Ratios & Identities
If cos θ = $1/{√5}$, where 0 < θ < ${π}/2$ , then ${2 tan θ}/{1 - tan^2 θ}$ is equal to
Answer: (a)
cos θ = $1/{√5}$
from ΔABC
AB = $√{(AB)^2 + (BC)^2}$
= $√{(√5)^2 - (1)^2} = √{5 - 1} = √4 = 2$
∴ tan θ = ${AB}/{BC} = 2/1 = 2$
Now, ${2 tan θ}/{1 - tan^2 θ} = {2 × 2}/{1 - (2)^2} = - 4/3$
What is cot 1° cot 23° cot 45° cot 67° cot 89° equal to?
Answer: (a)
cot 1° cot 23° cot 45° cot 67° cot 89°
= cot 1° × cot 23° × cot 45° × cot (90 - 23)° × cot (90 - 1)°
= cot 1° × cot 23° × cot 45° × tan 23° × tan 1° cot 1° × tan 1° × cot 23° × tan 23° × cot 45°
= 1 × 1 × 1 = 1
Consider the following :
1. sin 1° > sin $1^c$
2. cos 1° < cos $1^c$
3. tan 1° > tan $1^c$ .
Which of the above are not correct?
Answer: (c)
1 and 3 only
sin $1^c$ = sin 57° (approx)
$cos 1^c$ = cos 57°
$tan 1^c = tan 57°$
∴ 180° = ${22^c}/7$
cos 0° = 1, cos 1° = 0.99
cos 57° = 0.54
What is the angle (in radian) included between the hands of a clock, when the time is 10 min past 5?
Answer: (a)
In 60 min h hand gains = 5 min
In 1 min h hand gains = $5/{60}$ min
In 10 min h hand gains = $5/{60} × 10 = 5/6$ min
There is 15 min gap between hours and minutes
hand but in 10 min h hand gains $5/6$ min more.
So, the actual gap = 15 + $5/6 = {95}/6$ min
In 1 min, there are 6°,
In ${95}/6$ min, there are
${95}/6 × 6° = {95}/6 × 6 × {π}/{180} = {19 π}/{36}$ radian
If x + y = 90° and sin x : sin y = $√3$ : 1, then what is x : y equal to?
Answer: (c)
sin x : sin y = $√3 : 1 = {√3}/2 : 1/2$
= sin 60° : sin 30°
∴ x : y = 60 : 30
⇒ x : y = 2 : 1.
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