Simplification Model Questions & Answers, Practice Test for ssc steno grade c d 2024
ssc steno grade c d 2024 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Power, Indices And Surds
Ratio & Proportion
Percentage
Time & Work
Time & Distance
Mensuration
One of the factors of the polynomial $x^4 – 7x^3 + 5x^2$ – 6x + 81 is:
Answer: (d)
Let f(x) = $x^4 – 7x^3 + 5x^2$ – 6x + 81
By hit and trial method,
$x^4 – 7x^3 + 5x^2$ – 6x + 81
= $x^3 (x – 3) – 4x^2(x – 3)$ – 7x(x – 3) – 27(x – 3)
= (x – 3) ($x^3 – 4x^2$ – 7x – 27)
(x – 3) is one of the factor of the given polynomial.
If , $a/b = b/c = c/d$ then which of the following is/are correct?
1. ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$
2.${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$
Select the correct answer using the code given below.
Answer: (c)
Let $a/b = b/c = c/d$ = k
⇒a = bk, c = ck, c = dk
⇒abc = $bcdk^3$
⇒a = $dk^3$
(1) ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$
(2) ${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$
⇒${b^3 + c^3 + d^3}/{b^3k^3 + c^3k^3 + d^3k^3} = d/a$
⇒${b^2k^2 + c^2k^2 + d^2k^2}/{b^2 + c^2 + d^2} = a/d$
⇒${b^3 + c^3 + d^3}/{(b^3 + c^3 + d^3)k^3} = d/a$
⇒${(b^2 + c^2 + d^2)k^2}/{b^2 + c^2 + a^2} = a/d$
⇒$1/{k^3} = d/a$
⇒$k^2 = a/d$
⇒$k^2 – k^3$
⇒$1/{a/d} = d/a$
which is not possible
⇒$d/a = d/a$
⇒only (1) is true.
∴ Option (a) is correct.
If ab + bc + ca = 0, then the value of ${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$
Answer: (a)
ab + bc + ca = 0
– ab = c(b + a).........(i)
– bc = a(b + c) .........(i)
– ca = b(a + c) .........(i)
ATQ,
${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$
$1/{a^2 - bc} + 1/{b^2 - ca} + 1/{c^2 - ab}$
$1/{a(a + b + c)} + 1/{b(a + b + c)} + 1/{c(a + b + c)}$
From (i)
${bc + ac + ab}/{(a + b + c) abc}$ = 0
ssc steno grade c d 2024 IMPORTANT QUESTION AND ANSWERS
-
Number System Questions Test PDF For SSC STENO C & D 2024 »
-
Simplification Questions Test PDF For SSC STENO C, D 2024 »
-
Free Surds and Indices MCQ Test PDF | SSC Steno 2024 Exam »
-
Free Ratio & Proportion MCQ Test for SSC STENO 2024 Exam »
-
Free Percentage Questions Answers for SSC STENO 2024 Exam »
-
SSC STENO: Time & Work Questions Solved Problems with PDF »
-
SSC STENO: Speed Time and Distance MCQ Questions Test PDF »
-
SSC STENO: Mensuration Area & Volume Questions Test PDF »
ssc steno grade c d 2024TOPICS
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
Direction and Distance Sense Test Model Exercises, PDF
Direction and Distance Sense Test model exercises with solutions, PDF for SSC. Aptitude objective questions answer for Banks, Govt, Competitive exa
Continue Reading »
SSC Blood Relations Aptitude Practice MCQ Exercises, PDF
Practice Blood Relations model exercises with detailed solutions, PDF for SSC. Aptitude multiple choice questions answers for Banks, Govt, Competitive exams
Continue Reading »
Simple Interest Practice Exercise, Solutions Pdf for SSC
Practice Simple Interest 100+ questions and answers with solutions, PDF for SSC. Aptitude MCQ model exercise for Banks, Govt, and Competitive exams
Continue Reading »
Top Profit Loss Aptitude Practice Exercises, PDF for SSC
Practice Profit and Loss objective questions and answers with solutions, download PDF for SSC. Aptitude MCQ exercise for Banks, Govt, and Competitive exams
Continue Reading »