trigonometric ratios and identity Model Questions & Answers, Practice Test for ibps clerk prelims 2023
ibps clerk prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Ratio & Proportion
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Trigonometric Ratios & Identity
Linear Equations
Quadratic Equations
Logarithm
For what value of θ is (sin θ + cosec θ) = 2.5, where 0 < θ < 90°?
Answer: (b)
Here, $(\text"sin θ + cosec θ")$ = 2.5
⇒ $(sin θ + 1/{\text"sin θ"}) = 5/2$
⇒ $2 sin^2 θ - 5 sin θ + 2 = 0$
⇒ $2 sin^2 θ$ - 4 sin θ - sin θ + 2 = 0
⇒ 2 sin θ (sin θ - 2) - 1 (sin θ - 2) = 0
⇒ (2 sin θ - 1) (sin θ - 2) = 0
⇒ sin θ = $1/2$ (∵ sin θ ≠ 2)
∴ θ = 30°
Assume the Earth to be a sphere of radius R. What is the radius of the circle of latitude 40° S?
Answer: (b)
In ΔOAB,
cos 40° = ${AB}/{OB} ⇒ cos 40° = r/R$
⇒ r = R cos 40°
So, the radius of the circle of latitude 40° S is R cos 40°
Consider the following statements :
1. $cos^2 θ = 1 - {p^2 + q^2}/{2pq}$ , where p, q are non-zero real numbers, is possible only when p = q.
2. $tan^2 θ = {4pq}/{(p + q)^2}$ - 1 , where p, q are non-zero real numbers, is possible only when p = q.
Which of the statements given above is/are correct?
Answer: (c)
We know that $cos^2$ θ is defined in [0, 1]
so $cos^2 θ = 1 - {p^2 + q^2}/{2pq},$ where p, q are non zero real number, is possible only when p = q.
2. We know that $tan^2$ θ is defined in [0, ∞]. So $tan^2$ θ
= ${4pq}/{(p + q)^2} -1$ where p, q are non zero numbers, is possible only when p = q.
Two sides of an acute angle triangle are 6 cm and 2 cm, respectively. Which one of the following represents the correct range of the third side in cm?
Answer: (a)
∵ cos θ = ${a^2 + b^2 - c^2}/{2ab}$ By cosine rule
= ${6^2 + 2^2 - c^2}/{2 × 6 × 2} = {40 - c^2}/{24}$
For acute angle,
cos θ > 0 ⇒ ${40 - c^2}/{24} > 0 ⇒ c^2 < 40$
⇒ 0 < c < 2 $√{10}$ (since, c cannot be negative) ....(i)
Also, b + c > a
c > 6 - 2 ⇒ c > 4
From equations (i) and (ii),
c ε (4, 2 $√{10}$)
Consider the following statements :
1. $(sec^2 θ – 1) (1 – cosec^2 θ)$ = 1
2. sin θ $(1 + cos θ)^{–1} + (1 + cos θ) (sin θ)^{–1}$ = 2 cosec θ
Which of the above is/are correct?
Answer: (a)
Checking statement 1
$(sec^2 θ - 1) (1 - cosec^2 θ) = 1$
L.H.S
$(sec^2 θ - 1) × (- 1) (cosec^2 θ - 1)$
$tan^2 θ × (- 1) × cot^2$ θ = -1
Here L.H.S ≠ R.H.S
Hence, statement 1 is incorrect.
check in statement 2.
sin θ $(1 + cos θ)^{-1} + (1 + cos θ)(sin θ)^{-1}$ = 2 cosec θ
L.H.S
${\text"sin θ"}/{\text"1 + cos θ"} + {\text"1 + cos θ"}/{\text"sin θ"} = {sin^2 θ + (\text"1 + cos θ")^2}/{(\text"1 + cos θ") sin θ}$
= ${sin^2 θ + 1 + cos^2 θ \text"+ 2 cos θ"}/{(\text"1 + cos θ) sin θ"}$
= ${\text"1 + 1 + 2 cos θ"}/{\text"sin θ (1 + cos θ")} = {2 (\text"1 + cos θ")}/{\text"sin θ (1 + cos θ")} = 2/{\text"sin θ"}$
= 2 cosec θ = R.H.S
Hence, only statement 2 is correct.
ibps clerk prelims 2023 IMPORTANT QUESTION AND ANSWERS
-
Ratio and Proportion MCQ Test For IBPS Clerk Prelims 2023 »
-
New 150+ Quadratic Equation Questions For IBPS Clerk 2023 »
-
Logarithm Questions and Answers PDF For IBPS CLERK 2023 »
-
Top Linear Equations Aptitude MCQ PDF For IBPS CLERK 2023 »
-
Algebra Aptitude MCQ Mock Test PDF For IBPS CLERK 2023 »
-
Top Percentage Questions & Answers For IBPS Clerk Prelims »
-
Simple & Compound Interest MCQ Test For IBPS CLERK 2023 »
-
Time and Work Problems with Solutions for IBPS Clerk Exam »
-
New Profit and Loss Aptitude Questions PDF For IBPS Clerk »
-
Time and Distance Aptitude Questions For IBPS CLERK 2023 »
-
Trigonometric Ratios & Identities MCQ For IBPS CLERK 2023 »
-
Free 50 Mensuration MCQ Mock Test PDF For IBPS CLERK 2023 »
ibps clerk prelims 2023TOPICS
Read More
All Exams
-
SSC
»
Model MCQ Test [Syllabus Wise], Syllabus, Notification -
BANKING
»
Model MCQ Test [Syllabus Wise], Syllabus, Notification -
TNPSC
»
Model MCQ Test [Syllabus Wise], Syllabus, Notification
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
100+ Quadratic Equation Questions Answers PDF for Bank
Quadratic Equation multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
IBPS Aptitude Linear Equations MCQ Questions Answers PDF
Linear equations multiple choice questions with detailed answers for IBPS RRB SO. more than 250 Attitude practice test exercises for all competitive exams
Continue Reading »
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »