Question for IOCL Junior Engineer (Computer Science and IT) 2026 - Quiz / Questions / MCQ

Objective Questions

Latest IOCL JE Computer Science and IT Exam Question (Objective Questions), MCQ in English

Subjects : Domain Knowledge, Quantitative Aptitude, Logical Reasoning, English Language

Question Bank IOCL Junior Engineer (Computer Science and IT) Exam - English

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Domain Knowledge

Question 1Single Answer

The determinant of an upper triangular matrix is equal to:

A
Product of diagonal elements
B
Sum of diagonal elements
C
Product of non-diagonal elements
D
Zero

Question 2Single Answer

The sum of the eigenvalues of a square matrix is equal to its:

A
Rank
B
Determinant
C
Trace
D
Nullity

Question 3Single Answer

A square matrix \(A\) is invertible when:

A
\(\det(A)=0\)
B
Its rank is zero
C
Its trace is zero
D
\(\det(A)\neq 0\)

Question 4Single Answer

For an \(m \times n\) matrix \(A\), the rank-nullity theorem states:

A
Rank + Nullity = \(n\)
B
Rank × Nullity = \(n\)
C
Rank + Nullity = \(m\)
D
Rank − Nullity = \(n\)

Question 5Single Answer

All eigenvalues of a real symmetric matrix are:

A
Purely imaginary
B
Positive
C
Zero
D
Real

Question 6Single Answer

If \(Q\) is an orthogonal matrix, then:

A
\(Q^{-1}=Q\)
B
\(Q^{-1}=-Q\)
C
\(Q^{-1}=Q^T\)
D
\(Q^T=0\)

Question 7Single Answer

Two nonzero vectors are orthogonal when their dot product is:

A
1
B
Zero
C
−1
D
Infinity

Question 8Single Answer

Interchanging two rows of a determinant:

A
Leaves it unchanged
B
Changes its sign
C
Doubles its value
D
Makes it zero

Question 9Single Answer

The possible eigenvalues of an idempotent matrix are:

A
0 and −1
B
−1 and 1
C
0 and 1
D
Any real numbers

Question 10Single Answer

The rank of an \(n \times n\) identity matrix is:

A
0
B
1
C
\(n\)
D
\(n-1\)

Question 11Single Answer

The derivative of \(\ln x\) is:

A
\(1/x\)
B
\(x\)
C
\(e^x\)
D
\(\ln x/x\)

Question 12Single Answer

The indefinite integral of \(e^x\) is:

A
\(xe^x+C\)
B
\(e^{x+1}+C\)
C
\(e^x+C\)
D
\(1/e^x+C\)

Question 13Single Answer

The value of \(\lim_{x\to 0}\frac{\sin x}{x}\) is:

A
1
B
0
C
Infinity
D
−1

Question 14Single Answer

If \(f(x,y)=x^2y\), then \(\partial f/\partial x\) is:

A
\(x^2\)
B
\(xy^2\)
C
\(2x^2y\)
D
\(2xy\)

Question 15Single Answer

The second derivative of \(x^3\) is:

A
\(3x^2\)
B
6
C
\(6x\)
D
\(x\)

Question 16Single Answer

At an interior local maximum of a differentiable single-variable function:

A
\(f''(x)=0\) is always necessary
B
\(f'(x)=1\)
C
\(f'(x)=0\) is a necessary condition
D
The function must be discontinuous

Question 17Single Answer

The gradient vector points in the direction of:

A
Maximum decrease
B
Maximum increase
C
Zero curvature
D
Constant function value

Question 18Single Answer

The divergence of a constant vector field is:

A
1
B
Zero
C
−1
D
Infinity

Question 19Single Answer

The value of \(\int_0^1x^2dx\) is:

A
\(1/2\)
B
1
C
\(1/3\)
D
2

Question 20Single Answer

An infinite geometric series with common ratio \(r\) converges when:

A
\(r>1\)
B
\(r=1\)
C
\(|r|<1\)
D
\(|r|>1\)

Question 21Single Answer

The sequence \(1/n\) converges to:

A
Zero
B
Infinity
C
1
D
−1

Question 22Single Answer

The general solution of \(\frac{dy}{dx}=ky\) is:

A
\(y=C+kx\)
B
\(y=Ce^{kx}\)
C
\(y=Cx^k\)
D
\(y=C/kx\)

Question 23Single Answer

The Laplace transform of the constant function 1 is:

A
\(s\)
B
\(1/s^2\)
C
\(1/s\)
D
\(e^{-s}\)

Question 24Single Answer

The Newton–Raphson iteration formula is:

A
\(x_{n+1}=x_n+f(x_n)\)
B
\(x_{n+1}=f'(x_n)\)
C
\(x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}\)
D
\(x_{n+1}=x_n/2\)

Question 25Single Answer

According to De Morgan’s law, \(\neg(P\land Q)\) is equivalent to:

A
\(\neg P\land\neg Q\)
B
\(P\land\neg Q\)
C
\(P\lor Q\)
D
\(\neg P\lor\neg Q\)

Question 26Single Answer

The implication \(P\rightarrow Q\) is logically equivalent to:

A
\(P\land Q\)
B
\(P\lor\neg Q\)
C
\(\neg P\lor Q\)
D
\(\neg P\land Q\)

Question 27Single Answer

Which of the following is a tautology?

A
\(P\lor\neg P\)
B
\(P\land\neg P\)
C
\(P\land Q\)
D
\(\neg(P\lor\neg P)\)

Question 28Single Answer

The contrapositive of \(P\rightarrow Q\) is:

A
\(Q\rightarrow P\)
B
\(\neg Q\rightarrow\neg P\)
C
\(\neg P\rightarrow\neg Q\)
D
\(P\rightarrow\neg Q\)

Question 29Single Answer

A set containing \(n\) elements has how many subsets?

A
\(2^n\)
B
\(2n\)
C
\(n^2\)
D
\(n!\)

Question 30Single Answer

An equivalence relation is:

A
Irreflexive and transitive
B
Reflexive, antisymmetric and transitive
C
Symmetric and antisymmetric only
D
Reflexive, symmetric and transitive

Question 31Single Answer

A partial-order relation is:

A
Reflexive, antisymmetric and transitive
B
Reflexive, symmetric and transitive
C
Irreflexive, symmetric and transitive
D
Symmetric and total

Question 32Single Answer

If 11 objects are placed in 10 boxes, then at least one box contains:

A
At least two objects
B
Exactly one object
C
No object
D
All 11 objects

Question 33Single Answer

The number of edges in a complete graph \(K_n\) is:

A
\(n(n-1)/2\)
B
\(n(n-1)\)
C
\(n^2\)
D
\(n+1\)

Question 34Single Answer

A tree with \(n\) vertices contains:

A
\(n\) edges
B
\(n+1\) edges
C
\(n-1\) edges
D
\(2n\) edges

Question 35Single Answer

A connected undirected graph has an Euler circuit if:

A
Every vertex has odd degree
B
Exactly two vertices have odd degree
C
Every vertex has even degree
D
It is complete

Question 36Single Answer

An undirected graph is bipartite if and only if it contains:

A
No odd cycle
B
No even cycle
C
No vertices of odd degree
D
Exactly one cycle

Question 37Single Answer

The shortest paths from a source in an unweighted graph can be found using:

A
DFS
B
Kruskal’s algorithm
C
Prim’s algorithm
D
BFS

Question 38Single Answer

A simple planar graph with \(n\geq 3\) vertices has at most:

A
\(3n-6\) edges
B
\(2n\) edges
C
\(n-1\) edges
D
\(n^2\) edges

Question 39Single Answer

The chromatic number of a nonempty bipartite graph containing at least one edge is:

Question 40Single Answer

The number of ways to select \(r\) objects from \(n\) distinct objects is:

A
\(\binom{n}{r}\)
B
\(n^r\)
C
\(n!\)
D
\(r!\)

Question 41Single Answer

The number of permutations of \(n\) distinct objects is:

A
\(n!\)
B
\(2^n\)
C
\(n^2\)
D
\(n(n-1)/2\)

Question 42Single Answer

For two finite sets \(A\) and \(B\):

A
\(|A\cup B|=|A|+|B|\) always
B
\(|A\cup B|=|A|+|B|-|A\cap B|\)
C
\(|A\cup B|=|A\cap B|\)
D
\(|A\cup B|=|A|-|B|\)

Question 43Single Answer

The Fibonacci recurrence is:

A
\(F_n=F_{n-1}-F_{n-2}\)
B
\(F_n=2F_{n-1}\)
C
\(F_n=F_{n-1}+F_{n-2}\)
D
\(F_n=nF_{n-1}\)

Question 44Single Answer

The ordinary generating function for the sequence \(1,1,1,\ldots\) is:

A
\(1+x\)
B
\(1/(1-x)\)
C
\(1/(1+x)\)
D
\(e^x\)

Question 45Single Answer

For any event \(A\), \(P(A^c)\) equals:

A
\(1-P(A)\)
B
\(1+P(A)\)
C
\(P(A)\)
D
\(1/P(A)\)

Question 46Single Answer

Events \(A\) and \(B\) are independent if:

A
\(P(A\cap B)=0\)
B
\(P(A\cup B)=1\)
C
\(P(A)=P(B)\)
D
\(P(A\cap B)=P(A)P(B)\)

Question 47Single Answer

Conditional probability \(P(A\mid B)\), where \(P(B)>0\), is:

A
\(P(A)/P(B)\)
B
\(P(A\cup B)/P(B)\)
C
\(P(A\cap B)/P(B)\)
D
\(P(B)/P(A)\)

Question 48Single Answer

Bayes’ theorem is primarily used to:

A
Calculate derivatives
B
Reverse conditional probabilities
C
Find graph connectivity
D
Solve matrix equations

Question 49Single Answer

The expected value of a Bernoulli random variable with success probability \(p\) is:

A
\(1-p\)
B
\(p^2\)
C
\(p\)
D
\(1/p\)

Question 50Single Answer

The variance of a Bernoulli random variable is:

A
\(p^2\)
B
\(p/(1-p)\)
C
\(1-p\)
D
\(p(1-p)\)

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Quantitative Aptitude

Question 51Single Answer

The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:__________ ?

A
51:52
B
52:53
C
51:53
D
52:55

Question 52Single Answer

Which of the following numbers is irrational ?

A
√49
B
0.125
C
√2
D
22/7

Question 53Single Answer

356 x 936 – 356 x 836 = ?

A
35600
B
34500
C
9630
D
93600

Question 54Single Answer

Arrange in descending order: 5/8, 7/10, 3/4

A
3/4 > 7/10 > 5/8
B
7/10 > 3/4 > 5/8
C
3/4 > 5/8 > 7/10
D
5/8 > 7/10 > 3/4

Question 55Single Answer

What is (3^{^}{4} times 9^{^}{2}) ?

A
3⁶
B
3⁸
C
3¹⁰
D
9⁶

Question 56Single Answer

If 3⁴X^-2 = 729, then find the value of X.

Question 57Single Answer

Convert 0.6 into fraction ?

A
3/5
B
2/3
C
4/5

Question 58Single Answer

The no. plate of a bus had peculiarity. The bus number was a perfect square. It was also a perfect square when the plate numbers were reversed. The bus company had only five hundred buses numbered from 1 to 500. What was the number ?

A
169
B
36
C
196
D
Can not say

Question 59Single Answer

If a and b are positive integers, such that ab = 125, then (a-b)^a+b-4= ?

A
16
B
25
C
28
D
30

Question 60Single Answer

If x^*y = x² + y² – xy, then value of 9^*11 is

A
93
B
103
C
60.5
D
121

Question 61Single Answer

Passage :

Direction : Each of the questions below consists of a question and two statements numbered (I) and (II) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer :

How many employees of bank ‘X’ opted for VRS ?
(I) 18% of the 950 officer cadre employees and 6% of the 1100 of all other cadre employees opted for VRS.
(II) 28% of the employees in the age group of 51 to 56 and 17% of the employees in all other age groups opted for VRS.

A
Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B
Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
EACH statement ALONE is sufficient

Question 62Single Answer

Passage :

The area of a playground is 1600 square meters. What is its perimeter ?
(I) It is a perfect square playground
(II) It costs Rs.3200 to put a fence around the playground at the rate of Rs.20 per meter.

A
Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B
Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
EACH statement ALONE is sufficient

Question 63Single Answer

Passage :

What is the value of m – n ÷ 37 ?
(I) m is the largest possible six-digit number and n is the smallest possible six-digit number.
(II) The difference between m and n is known.

A
Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B
Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
EACH statement ALONE is sufficient

Question 64Single Answer

Passage :

What is the value of x ?
(I) If 10 is added to x, the result is 34.
(II) If x is multiplied by y, the result is 38.

A
Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B
Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
EACH statement ALONE is sufficient

Question 65Single Answer

Passage :

What was the total compound interest on a sum after three years ?
(I) The interest after one year was Rs. 100 and the sum after was Rs.1000.
(II) The difference between simple and compound interest on a sum of Rs.1000 at the end of two years was Rs.10.

A
Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B
Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
EACH statement ALONE is sufficient

Question 66Single Answer

Passage :

Each of the questions below consists of a question and two statements numbered (1) and (2) given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.

Among Japanese Yen, Australian Dollar, Hong Kong Dollar and Singapore Dollar, which currency has the lowest value in terms of Indian rupees ?
(1) One rupee is equal to 2.56 Japanese Yen, 0.338 Australian Dollar, and 0.465 Hong Kong Dollar.
(2) Value of Australian Dollar is equal to Singapore Dollar.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
Statements (1) and (2) TOGETHER are NOT sufficient

Question 67Single Answer

Passage :

What is the value of a two-digit number ?
(1) The sum of the two digits is 4.
(2) The difference between the two digits is 2.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
Statements (1) and (2) TOGETHER are NOT sufficient

Question 68Single Answer

Passage :

What was the population of State ‘A’ in 1999 ?
(1) Population of the State increases every year by 20% and its population in 1997 was 1,20,000.
(2) Population of State A in 1997 was twice that of State B in the same year.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
Statements (1) and (2) TOGETHER are NOT sufficient

Question 69Single Answer

Passage :

What is the speed of the boat in still water ?
(1) It takes 2 hours to cover the distance between A and B downstream.
(2) It takes 4 hours to cover the distance between A and B upstream.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
Statements (1) and (2) TOGETHER are NOT sufficient

Question 70Single Answer

Passage :

How many vinyl squares with sides 5 inches long will be needed to cover the rectangular floor of a room ?
(1) The floor is 5ft long.
(2) The floor is 3 ft wide.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (I) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D
Statements (1) and (2) TOGETHER are NOT sufficient

Logical Reasoning

Question 71Single Answer

How many such pairs of letters are there in the word ‘CLEANLINESS’ each of the which has as many letters between them in the word as they have in the English alphabet, in the same sequence?

A
Two
B
Three
C
Five
D
Four
E
None of these

Question 72Single Answer

Team A has scored more goals than Team B
Team C has scored fewer goals than Team B
Team A has scored fewer goals than Team C .
If the first two statements are true, the third statement is

A
True
B
False
C
Uncertain
D
None

Question 73Single Answer

If it is possible to make only one meaningful word with the second, the third, the sixth and the eight letters of the word FRAGMENT using each only once, which of the following will be the third letter of that word ? If no such word can be formed, give ‘X’ as the answer and if more than one such word can be formed, give ‘Y’ as the answer.

Question 74Single Answer

How many such letters are there in the word ORIENTAL each of which is as far away from the beginning of the word as when they are arranged alphabetically?

A
None
B
One
C
Two
D
Three
E
More than three

Question 75Single Answer

How many such pairs of letters in the word CREDIT each of which has as many letters between them in the word as in the English alphabet?

A
None
B
One
C
Two
D
Three
E
More than three

Question 76Single Answer

How many meaningful words can be made from the letters ‘LMEA’ using each letter only once in each word?

A
None
B
One
C
Two
D
Three
E
More than three

Question 77Single Answer

If it is possible to make only one meaningful word with the first, the second, the seventh and the eighth letters of the word TEMPORAL, which of the following will be the first letter of that word? If more than one such word can be made, give ‘Y’ as the answer and if no such word can be made, give ‘X’ as the answer.

Question 78Single Answer

If the letters of the word HANDOVER are arranged alphabetically from left to right how many letters will remain at the same position?

A
None
B
One
C
Two
D
Three
E
More than three

Question 79Single Answer

How many such pairs of letters are there in the word EXCURSION, each of which has as many letters between them in the word as they have in the English alphabet?

A
None
B
One
C
Two
D
Three
E
More than three

Question 80Single Answer

If it is possible to make only one meaningful word with the first, the second, the third, the sixth and the eighth letters of the word DEVIATION first letter of that word is your answer? If more than one such word can be made formed your answer is ‘A’ and if no such word can be formed your answer is ‘B’.

Question 81Single Answer

Passage :

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z .

Which letter in this alphabet is the eighth letter to the right of the letter and which is tenth letter to the left of the last but one letter of the alphabet ?

Question 82Single Answer

Passage :

Direction : The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)

If the third alphabet of each of the words is changed to the next alphabet in the English alphabetical series, which of the following will form a meaningful English word?

A
SUM
B
BIG
C
Both BIG and THE
D
FOR
E
Both FOR and BIG

Question 83Single Answer

Passage :

Direction : The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)

If the given words are arranged in the order as they would appear in a dictionary from left to right, which of the following will be second from the right ?

A
AND
B
FOR
C
THE
D
BIG
E
SUM

Question 84Single Answer

Passage :

Direction: The following question is based on the five words given below:
AND FOR THE BIG SUM (The new words formed after performing the mentioned operations may or may not necessarily the meaningful English words.)

If second alphabet in each of the words is changed to next alphabet in the English alphabetical order, how many words having two vowels (same or different vowels) will be formed ?

A
None
B
One
C
Two
D
Three
E
Four

Question 85Single Answer

Passage :

How many letters are there in the English alphabetical series between the second letter of the word which is second from the right and the second letter of the word which is second from the left of the given words?

A
Two
B
Five
C
Six
D
Nine
E
Three

English Language

Question 86Single Answer

I go to Madurai by —– Vaigai Express

A
a
B
an
C
some
D
the

Question 87Single Answer

Have the car stolen!

A
Steal the car
B
You should have the stolen car
C
Get someone to steal the car
D
They have stolen the car

Question 88Single Answer

The payment was collected by the hardworking salesman.

A
The hardworking salesman collected the payment.
B
the salesman who worked heard was able to collect the payment.
C
to collect the payment the salesman had to work hard.
D
The hardworking salesman was able to collect the payment.

Question 89Single Answer

I had to stop all my work to complete this project.

A
All other work had to be stopped to complete this project by me
B
For completing this project all other work must be stopped
C
For completing this project I had to stop all my work
D
To complete this project all other work had been stopped by me

Question 90Single Answer

They have published the names of all the successful candidates.

A
The candidates who have succeeded their names they had published.
B
The names of all the successful candidates have been published by them
C
The candidates who have succeeded their names have been published by them.
D
The names of all the successful candidate were published by them.

Question 91Single Answer

The online shopping site lowered the prices.

A
Lowering of the prices was done by the online shopping site
B
The prices were lowered by the online shopping site
C
The prices had been lowered by the online shopping site
D
The prices have been lowered by the online shopping site

Question 92Single Answer

Who taught you to drive a truck ?

A
To drive a truck by whom were you taught?
B
Driving a truck by who were you taught?
C
Driving a truck by who were you being taught?
D
By whom were you taught to drive a truck?

Question 93Single Answer

We shall invite Suresh.

A
Suresh would be invited by us
B
Suresh would have been invited by us
C
Suresh will be invited by us
D
Suresh will have been invited by us

Question 94Single Answer

Dark clouds have overcast the evening sky.

A
By the dark clouds the evening sky was overcast.
B
The evening sky has been overcast by the dark clouds.
C
Dark clouds overcastted the evening sky.
D
The sky of the evening was overcasted by dark clouds.

Question 95Single Answer

The partners will celebrate their triumph tomorrow.

A
The triumph would be celebrated by the partners a day before
B
The triumph would be celebrated by the partners a day after
C
The triumph would have been celebrated by the partners a day after
D
The triumph will have been celebrated by the partners tomorrow

Question 96Single Answer

Passage :

Direction : Question below has two blanks, each blank indicting that some thing has been omitted. Choose the word for each blank which best fits the meaning of the sentence as a whole.

The Finance Department has ……………a centralized online databank system for all statutory government bodies to …………an eye on their assets and liabilities.

A
presented , stay
B
introduced , keep
C
announce , make
D
created , let
E
proclaimed , hold

Question 97Single Answer

Passage :

Direction : The five items in this section consists of a word or group of words followed by four words as (a), (b), (c) and (d). Select the word which is nearly opposite to the meaning of the original word or group of words and mark your response as (a), (b), (c) and (d), as the case may be, in your Answer Sheet.

Assets

A
liabilities
B
responsibilities
C
estates
D
profits

Question 98Single Answer

Passage :

Direction : In the question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Affidavit

A
Affirmation
B
Slander
C
Oath
D
Testimony

Question 99Single Answer

Passage :

Direction: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Hollow

A
Alveolate
B
Cleft
C
Cavernous
D
Solid

Question 100Single Answer

Passage :

Directions: In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it

Cosset

A
Ignoreb
B
Close
C
Caress
D
Fondle

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