Sail E0 Webinar

MCQs

Total Questions : 65 | Page 7 of 7 pages
Question 61.

Which one of the following expressions does NOT represent exclusive NOR of x and y? 


  1.    xy + x'y'
  2.    x `oplus` y'
  3.    x' `oplus` y
  4.    x' `oplus` y'
 Discuss Question
Answer: Option D. -> x' `oplus` y'

(A)  x `oplus`  y =  xy + `overline(x)` `overline(y)`

(B )  x `oplus`  y  = x`overline(y)` + `overline(x)` `overline(y)` = x `oplus` y 

(C)  `overline(x)` `oplus`   y = (`overline(x)`) `overline(y)` + `overline(x)` `overline(y)` + xy = x `oplus` y

(D)  `overline(x)` `oplus`  `overline(y)` = (`overline (x)`) y + x `overline(y)`  = x `oplus` y



Question 62.

Function f is known at the following points: 

x      0         0.3           0.6          0.9         1.2            1.5            1.8           2.1         2.4           2.7             3.0 

f(x)   0        0.09        0.36        0.81       1.44          2.25           3.24        4.41        5.76         7.29           9.00 

The value of `int_0^3` f ( x ) dx computed using the trapezoidal rule is 


  1.    8.983
  2.    9.003
  3.    9.017
  4.    9.045
 Discuss Question
Answer: Option D. -> 9.045

`int_0^3` f ( x )dx = `h/2`[ f (` x_0` ) + f ( `x_10` ) + 2 (f (`x_1` ) + f (`x_2`) + ....+ f ( `x_9`))]

= `(0.03)/2`[9.00 + 2(25.65)] = 9.045


Question 63.

Consider an  undirected  random graph of eight vertices. The  probability that there is an 

edge
between a pair of vertices is `1/2` . What is the expected number of unordered cycles

 of length
three?


  1.    1/8
  2.    1
  3.    7
  4.    8
 Discuss Question
Answer: Option C. -> 7

P(edge)
= `1/2`

Number of ways we can choose the vertices out of 8 is `8_(c3)`

(Three edges in each cycle)

Expected number of unordered cycles of length 3 =  `8_(c3)` x `(1/2)^3` = 7


Question 64.

Which one of the following functions is continuous at x = 3 ?  


  1.    f(`x`) ={2,if x = 3; x - 1, if x > 3; `(x + 3)/3`, if x < 3
  2.    f (`x`) = {4, if `x` = 3; 8 - `x` if `x` = 3
  3.    f (`x`) = {`x` + 3, if `x` `le`3 `x` - 4 if `x` > 3
  4.    f (`x`) = `1/(x^3 - 27), if `x` = 3
 Discuss Question
Answer: Option A. -> f(`x`) ={2,if x = 3; x - 1, if x > 3; `(x + 3)/3`, if x < 3

lim f (`x`) = lim (`x` - 1)  = 2 = f (3)

x`rightarrow` 3 +    x`rightarrow` 3 +

lim f (`x`) = lim `((x + 3)/3)`  = 2 = f (3)

x`rightarrow` 3 -     x`rightarrow` 3 -

`:.`   f (`x`) is continious at `x` = 3



Question 65.

Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree 

vertices is even.
Q: Sum of degrees of all vertices is even.  


  1.    P only
  2.    Q only
  3.    Both P and Q
  4.    Neither P nor Q
 Discuss Question
Answer: Option C. -> Both P and Q

Q: Sum of degrees of all vertices = 2 x ( number of edges )


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

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI
Tabulation - Test Paper 2 Data Interpretation Reasoning & DI
Test Paper 1 Direction Sense Test Reasoning & DI
ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0
GFM Combined 1 Free Revision Test SAIL JO E-0