model 3 based on positive and negative exponent Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on power, indices and surds topic of quantitative aptitude
(a) $√3$ i
(b) - $√3$
(c) - $√3$ i
(d) + $√3$
The correct answers to the above question in:
Answer:(b)
$x^2 - √3$ = 0
$x^2-(3)^{1/2}=0$
$x^2-(3^{1/4})^2=0$
$(x+3^{1/4})(x-3^{1/4})=0$
$x=3^{1/4} or {-3}^{1/4}$
Product of roots
$=3^{1/4}×-3^{1/4}=-√3$
Note : Product of the roots of $ax^2+bx+c=0 is c/a$
Product of the roots of $x^2-b. 0-√3=0 is -√3$
Discuss Form
Read more positive and negative exponent Based Quantitative Aptitude Questions and Answers
Question : 1
If $(3/4)^3(4/3)^{-7}= (3/4)^{2x}$, then x is :
a) 2
b) 2$1/2$
c) 5
d) - 2
Answer »Answer:(c)
$(3/4)^×3(4/3)^{-7}= (3/4)^{2x}$
$(3/4)^3×(3/4)^{7}= (3/4)^{2x}$
$(3/4)^10=(3/4)^{2x}$
2x=10⇒ x=5
Question : 2
The quotient when $10^100$ is divided by $5^75$ is :
a) $10^25$
b) $2^75 × 10^25$
c) $2^75$
d) $2^25 × 10^75$
Answer »Answer:(b)
Expression = $(10)^100/(5)^75$
= $(2×5)^100/(5)^75$
= ${(2)^100 × (5)^100}/(5)^75$
= $2^100× 5^25$
= $2^25× 5^25× 2^75$
= $(10)^25 ×2^75$
Question : 3
The value of $[(0.87)^2+(0.13)^2 + (0.87) × (0.26)]^2013$ is
a) 2013
b) - 1
c) 1
d) 0
Answer »Answer:(c)
Expression
= $[(0.87)^2 + (0.13)^2 + 0.87 × 0.26]^2013$
= $(0.87 + 0.13)^{2013} = 1^{2013}$ = 1
[Since, $(a + b)^2 = a^2 + b^2$ + 2ab]
Question : 4
If $2^{x - 1} + 2^{x + 1}$ = 320, then the value of x is
a) 8
b) 7
c) 5
d) 6
Answer »Answer:(b)
$2^{x - 1} + 2^{x + 1}$ = 320
$2^{x-1}(1+ 2^2) = 320$
$2^{x-1} ×5 =320$
$2^{x-1}= 320/5 =64 ⇒2^{x -1} = 2^{6}$
$x - 1 = 6 ⇒ x = 7$
Question : 5
Solve for x : $3^x - 3^{x - 1}$ = 486.
a) 9
b) 6
c) 5
d) 7
Answer »Answer:(b)
$3^x - 3^{x - 1} = 486$
$3^{x - 1}$(3 - 1) = 486
$3^{x - 1}$ × 2 = 486
$3^{x - 1} = 486/2$ = 243
$3^{x - 1} = 3^5$ ⇒ x - 1 = 5
x = 5 + 1 = 6
Question : 6
Simplify : $[√^3{√^6{√{5^9}}}]^4[√^3{√^6{√{5^9}}}]^4$
a) $5^4$
b) $5^12$
c) $5^8$
d) $5^2$
Answer »Answer:(a)
$[√^3{√^6{√{5^9}}}]^4[√^3{√^6{√{5^9}}}]^4$
=$[5^{9×1/6×1/3}]^4[5^{9×1/6×1/3}]^4$
=$[5^{1/2×4}][5^{1/2×4}]=5^2×5^2=5^4$
GET power, indices and surds PRACTICE TEST EXERCISES
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
power, indices and surds Shortcuts and Techniques with Examples
-
model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
Verbal Reasoning
Question & Answer Quiz
Non Verbal Reasoning
Question & Answer Quiz
Quantitative Aptitude
Question & Answer Quiz
Computer MCQ
Question & Answer Quiz
General English
Question & Answer Quiz
History GK
Question & Answer Quiz
Polity GK
Question & Answer Quiz
Geography GK
Question & Answer Quiz
Economy GK
Question & Answer Quiz
General Awareness GK
Question & Answer Quiz
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 »