Sail E0 Webinar

Quantitative Aptitude

SURDS AND INDICES MCQs

Surds & Indices, Indices And Surds, Power

Total Questions : 753 | Page 24 of 76 pages
Question 231.

`(2^(n + 4) - 2 xx 2^n)/(2 xx 2^((n + 3))) + 2^ -3 ` is equal to :


  1.    `2^(n + 1)`
  2.    `((9)/(8) - 2^n)`
  3.    `(- 2^(n + 1) + 1/8)`
  4.    1
 Discuss Question
Answer: Option D. -> 1

`(2^(n + 4) - 2 xx 2^n)/(2 xx 2^((n + 3))) + 2^ -3 `  =  `(2^(n + 4) - 2^(n + 1))/(2^(n + 4)) + 1/2^3`

                        =    `(2^(n + 1)  (2^3 - 1))/(2^(n + 4))  + 1/2^3`

                         = `(2^(n + 1) xx 7)/(2^(n + 1) xx 2^3) + 1/2^3 `  = `(7/8 + 1/8)`   = `8/8` = 1.  


Question 232.

If `3^x - 3^(x - 1)   = 18`, then the value  of  ` x^x` is :


  1.    3
  2.    8
  3.    27
  4.    216
 Discuss Question
Answer: Option C. -> 27

`3^x - 3^(x - 1)   = 18 `   `hArr 3^(x - 1) (3 - 1) = 18   hArr  3^(x - 1) =  9 = 3^2  hArr  x - 1 = 2 hArr  x = 3`

`:.`  ` x^x =  3^3 = 27`


Question 233.

If `2^(n - 1) + 2^(n + 1) `= 320, then n is equal to :


  1.    6
  2.    8
  3.    5
  4.    7
 Discuss Question
Answer: Option D. -> 7

`2^(n - 1) + 2^(n + 1) =  320    hArr  2^(n - 1) (1 + 2^2) = 320    hArr  5 xx 2^(n - 1)  = 320`

`hArr   2^(n - 1) = 320/5= 64 =  2^6   hArr n- 1 = 6   hArr  n= 7`



Question 234.

If  `2^(n + 4) - 2^(n +2)` = 3, then  n is equal to :


  1.    0
  2.    2
  3.    - 1
  4.    - 2
 Discuss Question
Answer: Option D. -> - 2

`2^(n + 4) - 2^(n + 2) =  3    hArr  2^(n + 2)  (2^2  - 1) = 3     hArr  2^(n + 2)   = 1   = 2^0   hArr n + 2 = 0 hArr  n = - 2.`



Question 235.

If `(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)` = 27,  then the value of n is :


  1.    0
  2.    2
  3.    3
  4.    4
 Discuss Question
Answer: Option C. -> 3

`(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)` = 27       `hArr   ((3^2)^n xx 3^5 xx (3^3)^3)/(3 xx (3^4)^4) = 3^3`

`hArr     (3^(2n) xx 3^5 xx 3^((3xx3)))/(3 xx 3^(4 xx 4))  = 3^3      hArr (3^(2n + 5 + 9))/(3 xx 3^16)  = 3^3`

`hArr (3^(2n + 14))/(3^17)  = 3^3           hArr   3^(2n + 14 - 17)  = 3^3`

`hArr  3^(2n - 3) = 3^3   hArr  2n - 3 = 3      hArr  2n = 6      hArr  n` =  3.



Question 236.

IIf `(sqrt(3))^5 xx 9^2 = 3^n xx 3sqrt(3)`, then the value of  n is :


  1.    2
  2.    3
  3.    4
  4.    5
 Discuss Question
Answer: Option D. -> 5

`(sqrt(3))^5 xx 9^2 = 3^n xx 3sqrt(3)`    `hArr      (3^(1/2))^5 xx  (3^3)^3  = 3^n xx 3 xx 3^(1/2)`

                                                

     `hArr    3^((1/2 xx 5)) xx 3^(2 xx 2) =   3^((n + 1 + 1/2))      hArr   3^((5/2+ 4))  = 3^((n + 3/2))`


`hArr   n + 3/2 = 13/2     hArr  n = (13/2  - 3/2)       = 10/2     = 5.`                          



Question 237.

If `sqrt(2^n)`  = 64, then the value of n is :


  1.    2
  2.    4
  3.    6
  4.    12
 Discuss Question
Answer: Option D. -> 12

`sqrt(2^n) = 64      hArr   (2^n)^(1/2) = 2^6   hArr  2^(n/2) = 2^6     hArr   n/2  = 6    hArr   n = 12`.


Question 238.

If `5sqrt(5) xx 5^3 -: 5^(-3/2)` =  `5^(a + 2)`,  then the value of a is :


  1.    4
  2.    5
  3.    6
  4.    8
 Discuss Question
Answer: Option A. -> 4

`5sqrt(5) xx 5^3 -: 5^(-3/2)` =  `5^(a + 2)`  `hArr`    `(5 xx 5^(1/2) xx 5^3)/(5^(- 3/2))` = `5^(a + 2)`             
`hArr    5^((1 + 1/2 + 3 + 3/2))      =  5^(a + 2)       hArr     5^6  =   5^(a + 2)      hArr   a + 2  = 6    hArr   a = 4`.


Question 239.

If `5^a` = 3125, then the value of `5^((a - 3))`  is:


  1.    25
  2.    125
  3.    625
  4.    1625
 Discuss Question
Answer: Option A. -> 25

`5^a` = 3125   `hArr    5^a     =   5^5     hArr    a = 5`

`:.`   `5^(a -3) = 5^(5 - 3)=  5^2 `= 25.



Question 240.

If `2^(2n - 1) = 1/8^(n - 3)`, then the value of n is :


  1.    3
  2.    2
  3.    0
  4.    - 2
 Discuss Question
Answer: Option B. -> 2

`2^(2n - 1) = 1/8^(n - 3)`  `hArr`   `2^(2n - 1)` = `1/(2^3)^(n - 3)` = `(1)/2^(3(n - 3))`  =  `1/2^(3n - 9)`=  `2^(9 - 3n)`

                                         `hArr     2n - 1 =  9 - 3n       hArr      5n    =10        hArr      n = 2`



Latest Videos
Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)
Direction Sense Test Part 1 Reasoning (Hindi)
Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE
Cube & Cuboid Part 1 Reasoning (Hindi)
Data Interpretation (DI) Basic Concept Reasoning (Hindi)
Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)
Sail E0 free webinar Webinars
Real Numbers Part 7 Class 10 Maths
Real Numbers Part 1 Class 10 Maths
Polynomials Part 1 Class 10 Maths

Latest Test Papers

DSP Combined 1 Free Revision Test SAIL JO E-0
GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0
BSP Plant Specific Review Test SAIL JO E-0
BSL Combined 1 Free Revision Test SAIL JO E-0
GFM Combined 1 Free Revision Test SAIL JO E-0