trigonometric ratios and identity Model Questions & Answers, Practice Test for ssc mts paper 1 2023
ssc mts paper 1 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
LCM & HCF
Ratio Proportion & Partnership
Percentages
Profit & Loss
Time & Work
Time & Distance
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Algebraic Expressions
Trigonometric Ratios & Identity
A wheel makes 12 revolutions per min. The angle in radian described by a spoke of the wheel in 1 s is
Answer: (a)
In 1 min = 60s, distance travelled by the wheel
= 12 × Its circumference
= 12 × 2 π r
∴ In 1 s distance travelled by the wheel
= ${12 × 2 π r}/{60} = 2/5$ π r
∵ Angle = ${Ram}/{Radius} = {2/5 π r}/r = 2/5 π$
Which is the required angle.
If tan 8θ = cot 2θ, where 0 < 8θ < , ${π}/2$ then what is the value of tan 5θ?
Answer: (a)
tan 8 θ = cot 2 θ ⇒ tan 8 θ = tan (90 - 2 θ)
⇒ 8 θ = 90 - 2 θ ⇒ θ = 9°
∴ tan 5 θ ⇒ tan 45° = 1
If ΔABC is right angled at C, then what is cos (A + B) + sin (A + B) equal to?
Answer: (c)
In ΔABC, if ∠ C is 90°, then
∠A + ∠B = 180° - 90° = 90°
then, cos(A + B) + sin (A + B)
= cos 90° + sin 90°
= 0 + 1 = 1
If sin x cos x = $1/2$, then what is the value of sin (x – cos x)?
Answer: (c)
Now, $(sin x - cos x)^2 = (sin^2 x + cos^2 x)$ - 2 sin x cos x
= 1 - 2 $(1/2)$ (∵ sin x cos x = $1/2$, given)
If cos x + sec x = 2, then what $cos^n x + sec^n$ x equal to, where n is a positive integer?
Answer: (b)
cos x + sec x = 2 ......(i)
On squaring both sides, we get
$cos^2 x + sec^2 x$ + 2 = 4
⇒ $cos^2 x + sec^2 x$ = 2 ......(ii)
On cubing equation (i), we get
$cos^3 x + sec^3 x$ + 3 (cos x + sec x) = 8
⇒ $cos^3 x + sec^3 x +$ (3 × 2) = 8
⇒ $cos^3 x + sec^3$ x = 2 .....(iii)
Similarly, when we multiply n in power both sides,
$cos^n x + sec^n x = 2$
Alternate Method
of we put x = 90°
then cos 90° + sec 90° = 1 + 1 =2
Similarly $cosec^h x + sec^h x$
= $cosec^h 90° + sec^h 90°$
= 1 + 1 = 2
ssc mts paper 1 2023 IMPORTANT QUESTION AND ANSWERS
-
Top 199+ Number System MCQ Quiz & Mock Test For SSC MTS 2023 »
-
Top 150+ Trigonometry MCQ Mock Test PDF For SSC MTS 2023 »
-
New 100+ Ratio and Proportion MCQ Test PDF For SSC MTS 2023 »
-
100+ Time and Work Aptitude MCQ Mock Test For SSC MTS 2023 »
-
New 200+ Area and Volume Mensuration MCQ For SSC MTS 2023 »
-
Top 200+ Percentage Questions Aptitude Test For SSC MTS 2023 »
-
Top 300+ Simple & Compound Interest MCQ PDF For SSC MTS 2023 »
-
New 299+ LCM & HCF Aptitude Questions For SSC MTS 2023 Exam »
-
Time Speed and Distance Aptitude Mock Test For SSC MTS 2023 »
-
New 199+ Profit and Loss Aptitude MCQ Test For SSC MTS 2023 »
-
200+ Algebra Questions Solved Answer PDF For SSC MTS 2023 »
ssc mts paper 1 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 »