Preparing for competitive exams like those conducted by the Odisha Sub-ordinate Staff Selection Commission (OSSSC) for roles such as Revenue Inspector (RI), Assistant Revenue Inspector (ARI), Amin, SFS, and ICDS requires rigorous practice and a solid grasp of arithmetic and reasoning concepts. Multiple Choice Questions (MCQs) serve as an effective tool for assessing candidates’ understanding and proficiency in these subjects. In this article, we’ll delve into some important arithmetic and reasoning MCQs tailored specifically for aspirants of OSSSC exams.
- 1, 6, 11,____ what will be its 15th term?
(A) 41
(B) 61
(C) 71
(D) 56
ANS:- (C) 71
Sol:- To find the pattern and subsequently the 15th term, let’s analyze the differences between consecutive terms:
The difference between 6 and 1 is 5.
The difference between 11 and 6 is also 5.
It appears that the series is increasing by 5 each time. So, to find the 15th term, we can continue this pattern:
1 = 1st term
1 + 5 = 6; 2nd term
6 + 5 = 11; 3rd term
Continuing this pattern:
11 + 5 = 16; 4th term
16 + 5 = 21; 5th term
21 + 5 = 26; 6th term
26 + 5 = 31; 7th term
31 + 5 = 36; 8th term
36 + 5 = 41; 9th term
41 + 5 = 46; 10th term
46 + 5 = 51; 11th term
51 + 5 = 56; 12th term
56 + 5 = 61; 13th term
61 + 5 = 66; 14th term
66 + 5 = 71; 15th term
So, the 15th term in the series is 71. - What is the missing number in the series: 3, 7, 12, 18, ?, 33?
A) 22
B) 23
C) 24
D) 25
ANS:- D) 25
Sol:- To find the missing number in the series, let’s analyze the pattern:
The differences between consecutive numbers in the series are increasing by 1 each time:
7 – 3 = 4
12 – 7 = 5
18 – 12 = 6
So, following this pattern, the next difference should be 7:
The next number should be 18 + 7 = 25.
Next number is 33 – 25 = 8
Therefore, the missing number in the series is 25. - Complete the analogy:
Water : Wet:: Fire:?
Options:
a) Hot
b) Cold
c) Burning
d) Dry
d) Dry
Sol:- Water is wet, and fire is dry. Options (a), (b), and (c) are related to properties or states of fire, but only option (d) represents the opposite property to “wet.” - Complete the analogy:
Plane: Pilot:: Ship:?
Options:
a) Driver
b) Sailor
c) Captain
d) Navigator
ANS:- c) Captain
Sol:- A pilot flies a plane, and a captain commands a ship. Options (a), (b), and (d) are roles associated with transportation, but only option (c) corresponds to the person in charge of a ship. - Solve the equation for x: 3x + 6 = 21
a) x = 3
b) x = 5
c) x = 6
d) x = 7
NS:- b) x=5
Sol:- To solve the equation 3x + 6 = 21 for x, you first isolate x by subtracting 6 from both sides of the equation:
3x + 6 − 6 = 21 − 6
3x + 0 = 15
Then, divide both sides by 3 to solve for
3x/3 = 15/3
X = 5
So, the correct answer is b) x = 5 - Balance the equation: 25 ÷ 5 + 3 = 4 × 2 – ?
a) 2
b) 4
c) 6
d) 8
ANS:- d) 0
Sol:- To balance the equation 25 ÷ 5 + 3 = 4 × 2 − ?, let’s solve each side separately:
Left side:
25 ÷ 5 + 3
=5 + 3
=8
Right side:
4 × 2 − ?
= 8 −?
To balance the equation, we need to find the value of? such that both sides are equal.
From the left side, 25÷5+3=8, so we need the right side to also equal 8. Therefore, 8−?=8.
To solve for ? we subtract 8 from both sides:
8 − ? = 8
8 − 8
? = 0
? must be 0 to balance the equation.
Therefore, the correct answer is d) 0 - If ‘V’ represents addition, ‘^’ represents subtraction, ‘X’ represents multiplication, and ‘@’ represents division, what does the expression ’12 V 3 ^ 4 X 2 @ 2′ equal to?
(A) 11
(B) 54
(C) 36
(D) 30
ANS:- (A) 11
Sol:- o solve the expression using the BODMAS (Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication, Addition and Subtraction) theory:
12 V 3 ^ 4 X 2 @ 2
Given:
V represents addition (+)
^ represents subtraction (-)
X represents multiplication (*)
@ represents division (/)
So the expression becomes: 12 + 3 – 4 * 2 / 2
Let’s break down the expression step by step:
First, we perform the multiplication and division operations:
2 / 2 = 1
Now, the expression becomes: 12 + 3 – 4 * 1 = 12 + 3 – 4
Next, we perform the addition operation (V):
12 + 3 = 15
Now, the expression becomes:
15 – 4
Next, we perform the subtraction (-) operation:
15 – 4 = 11
So, the expression ’12 V 3 ^ 4 X 2 @ 2′ equals 11. - If 5 workers can complete a task in 12 days, how many days would it take for 8 workers to complete the same task?
(A) 5
(B) 8
(C) 7.5
(D) 9
ANS:- (C) 7.5
Sol:- To solve this problem, we can use the concept of man-days, which is the amount of work done by one person in one day.
Given:
5 workers can complete the task in 12 days.
So, the total man-days required to complete the task are:
5 workers * 12 days = 60 man-days
Now, if 8 workers are to complete the same task, you can find out how many days it would take by dividing the total man-days required by the number of workers:
Number of days = Total man-days / Number of workers
Number of days = 60 man-days / 8 workers
Number of days = 7.5 days
So, it would take approximately 7.5 days for 8 workers to complete the same task. - Which of the following is a valid conclusion from the statements:
Statements:
(A) All cats are mammals.
(B) Some mammals are dogs.
Conclusion:
I. Some cats are dogs.
II. Some dogs are cats.
III. All dogs are mammals.
IV. Some mammals are cats.
Options:-
(a) None follows
(b) Only IV follows
(c) Only I follow
(d) Both I and IV follow
ANS:- (c) Only I follow.
Sol:- Let’s analyze each conclusion:
Conclusion I: Some cats are dogs.
This conclusion logically follows from the given statements. If all cats are mammals (statement A) and some mammals are dogs (statement B), then it’s logical to conclude that some cats are dogs.
Conclusion II: Some dogs are cats.
This conclusion cannot be logically derived from the given statements. While some mammals are dogs and all cats are mammals, it doesn’t necessarily mean that some dogs are cats.
Conclusion III: All dogs are mammals.
This conclusion cannot be derived from the given statements. While all cats are mammals and some mammals are dogs, it doesn’t mean that all dogs are mammals. Statement A explicitly states that all cats are mammals, but it doesn’t extend to all dogs. Conclusion IV: Some mammals are cats.
This conclusion cannot be logically inferred from the given statements. Although all cats are mammals and some mammals are dogs, it doesn’t imply that some mammals are cats.
Based on the analysis:
Conclusion I “Some cats are dogs” is valid.
Conclusion IV “Some mammals are cats” cannot be logically inferred from the given statements.
The other conclusions (II and III) are not valid.
So, the correct answer is (c) Only I follow. - If “All fish are aquatic” and “Some aquatic are mammals” are true, which of the following conclusions follows logically?
Conclusion:
I. Some mammals are fish.
II. All mammals are fish.
III. Some fish are aquatic.
IV. All aquatic are fish.
Options:-
(a) None follows
(b) Only IV follows
(c) Only I follow
(d) Both I and IV follow
ANS:- (c) Only I follow.
Sol:- Let’s analyze each conclusion:
Conclusion I: Some mammals are fish.
This conclusion logically follows from the given statements. If all fish are aquatic and some aquatic beings are mammals, then it’s logical to conclude that some mammals are fish.
Conclusion II: All mammals are fish.
This conclusion cannot be logically inferred from the given statements. While some aquatic beings are mammals and all fish are aquatic, it doesn’t necessarily mean that all mammals are fish. There may be other types of mammals that are not fish.
Conclusion III: Some fish are aquatic.
This conclusion is redundant and doesn’t add any new information. It is already given in the statements that all fish are aquatic, so this conclusion is not necessary.
Conclusion IV: All aquatic are fish.
This conclusion cannot be logically inferred from the given statements. While all fish are aquatic, it doesn’t imply that all aquatic beings are fish. Some aquatic beings may be mammals, as stated in the premises.
Based on the analysis:
Conclusion I “Some mammals are fish” is valid.
Conclusion IV “All aquatic are fish” is not valid.
The other conclusions (II and III) are not necessary or valid.
So, the correct answer is (c) Only I follow. - Shanu is facing south, She turns 90 degrees left, then she turns 90 degrees right, then she turns 180 degrees left. Now in which direction is she facing?
A) North
B) East
C) South
D) West
ANS:- A) North
Sol:- Let’s analyze Shanu’s movements:
Shanu starts facing South.
She turns 90 degrees left, which means she is now facing East.
Then she turns 90 degrees right from East, which means she is now facing South again.
Next, she turns 180 degrees left from South, which means she makes a complete turn and ends up facing North.
So, after all the movements, Shanu is facing North.
Therefore, Shanu is facing A) North - Which of the following statements is true about acceleration?
(A) Acceleration is always positive.
(B) Acceleration is the rate of change of speed.
(C) Acceleration can be positive, negative, or zero.
(D) Acceleration is a scalar quantity.
ANS:- The correct answer is (C) Acceleration can be positive, negative, or zero.
Sol:- Acceleration is defined as the rate of change of velocity concerning time. It can be positive if an object is speeding up, negative if it’s slowing down, or zero if it’s moving at a constant velocity.
It’s essential to understand that acceleration is a vector quantity because it has both magnitude and direction, unlike a scalar quantity which only has magnitude.
While option (B) mentions the rate of change of speed, acceleration is the rate of change of velocity, which includes both speed and direction.
Option (A) is incorrect because acceleration can be negative if the object is decelerating or slowing down.
Option (D) is incorrect because acceleration is a vector quantity, not a scalar quantity.
The correct answer is (C) Acceleration can be positive, negative, or zero. - What does a negative velocity indicate?
(A) Acceleration
(B) Deceleration
(C) Motion in the opposite direction
(D) No motion
ANS:- (C) Motion in the opposite direction
Sol:- Velocity is a vector quantity that describes the rate of change of an object’s position concerning time, including both speed and direction.
A negative velocity indicates that the object is moving in the opposite direction to the positive direction defined in the coordinate system.
Option (A) Acceleration refers to the rate of change of velocity, not velocity itself.
Option (B) Deceleration refers to a decrease in velocity, but it does not specify the direction of motion.
Option (D) No motion would be indicated by a velocity of zero, not a negative velocity.
The correct answer is (C) Motion in the opposite direction - Gita said to Mamta, “The girl I met yesterday at the beach was the youngest daughter of my friend’s mother’s brother-in-law.” How is the girl related to Gita’s friend?
(A) Cousin
(B) Daughter
(C) Friend
(D) Aunt
ANS:- (A) Cousin
Sol:- Let’s restructure the statement to make it clearer:
Gita said to Mamta, “The girl I met yesterday at the beach was the youngest daughter of my friend’s mother’s brother-in-law.”
Now, let’s break it down:
Gita’s friend’s mother’s brother-in-law is Gita’s friend’s uncle.
The youngest daughter of Gita’s friend’s uncle is Gita’s friend’s cousin.
So, the girl is related to Gita’s friend as her cousin. - Manisha said, “This girl is the wife of the grandson of my mother.” How is Manisha related to the girl?
(A) Brother
(B) Grandfather
(C) Husband
(D) Father-in-law
ANS:- (D) Father-in-law
Sol:- Manisha said, “This girl is the wife of the grandson of my mother.”
Let’s break this down:
Manishas mother’s grandson is Manisha’s nephew.
The wife of Manisha’s nephew is Manisha’s nephew’s wife.
Manisha’s nephew’s wife is Manisha’s nephew’s daughter-in-law.
So, Manisha is related to the girl as her father-in-law, which corresponds to option (D). - Which of the following is the correct representation of the number five in binary?
A) 101
B) 100
C) 110
D) 111
ANS:- B) 101
Sol:- In binary, the number 5 is represented as 101, which corresponds to
= 1 x 22 + 0 x 21 + 1 x 20
= [1 x (2 x 2)] + [0 x (2 x 1)] + [1 x 20]
= (1 x 4) + (0 x 2) + (1)
= 4 + 0 + 1
= 5 - Which of the following is a prime number?
A) 20
B) 17
C) 16
D) 15
ANS:- B) 17
Sol:- A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself.
Let’s check each option:
A) 20 – This is not a prime number because it has divisors other than 1 and itself (2, 4, 5, 10).
B) 17 – This is a prime number because its only divisors are 1 and 17.
C) 16 – This is not a prime number because it has divisors other than 1 and itself (2, 4, 8).
D) 15 – This is not a prime number because it has divisors other than 1 and itself (3, 5).
So, the correct answer is B) 17. - Find the domain of the function f(x) = √(x+1).
A) {x ∈ ℝ : x ≥ -1}
B) {x ∈ ℝ : x ≤ -1}
C) {x ∈ ℝ : x > -1}
D) {x ∈ ℝ : x < -1}
S2. ANS:- A) {x ∈ ℝ : x ≥ -1}
Sol:- The domain of a square root function includes all real numbers that make the expression under the square root non-negative.
For the function f(x) = √x+1, the expression under the square root, x + 1, must be greater than or equal to zero for the function to be defined.
So, we solve the inequality x + 1 ≥ 0 for X
x + 1 ≥ 0
x ≥ −1
So, the domain of the function is all real numbers greater than or equal to -1.
The correct answer is A) {x ∈ ℝ : x ≥ -1} - Determine if the function f(x) = x22 is one-to-one.
A) Yes
B) No
S3. ANS:- B) No
Sol:-The function f(x)=x2 is not one-to-one.
A function is one-to-one (or injective) if each element of the function’s codomain is mapped to by at most one element of its domain.
However, in the case of f(x) = x2, multiple inputs can result in the same output. For example, both f(2) = 4 and f(−2) = 4, indicating that the function fails the horizontal line test.
So, the correct answer is B) No - What is the solution to the equation 5x + 3 = 28?
A) x = 5
B) x = 6
C) x = 7
D) x = 8
ANS:- A) x=5
Sol:- To solve the equation 5x + 3 = 28, we need to isolate x on one side of the equation.
First, subtract 3 from both sides:5x+3−3=28−3
5x = 25
Then, divide both sides by 5 to solve for
5x/5 = 25/5
x=5
So, the correct answer is A) x=5 - Which of the following is an example of a linear equation in three variables?
A) x+2y=3z
B) x2+y2 =9
C) 2x+3y−z=7
D) x+y+z=1
ANS:- A) x+2y=3z
Sol:- Option A) x+2y=3z is indeed an example of a linear equation in three variables. It includes all three variables (x, y, z) raised to the first power, satisfying the definition of a linear equation in three variables. - What does the “±” sign represent in the quadratic formula?
A) The discriminant
B) The coefficient of x
C) The presence of two solutions
D) The constant term
ANS:- C) The presence of two solutions
Sol:- In the quadratic formula
, the “±” sign indicates that there are two possible solutions for the quadratic equation. This is because the quadratic formula considers both the positive and negative roots of the discriminant, resulting in two solutions. Therefore, option C) The presence of two solutions
is the correct choice. - Calculate log10 (85) using antilogarithm.
A) 1.928
B) 1.894
C) 1.956
D) 1.863
ANS:- A) 1.928
Sol:- To calculate log10(85) using antilogarithm, you’ll want to find the number that 10 needs to be raised to equal 85.
So, using the antilogarithm:
log10(85) = x
10^x = 85
Now, solving for x:
x ≈ log10(85) = 1.929
The closest option is A) 1.928. - If antilog(2.876)=768, what is log10 (768)?
A) 2.876
B) 3.876
C) 4.876
D) 5.876
ANS:- A) 2.876.
Sol:- To find log10 (768), we can use the fact that antilog(2.876) = 768.
Antilog(2.876) = 768 means 10^2.876 = 768.
So, log10 (768) = 2.876.
Therefore, the correct answer is A) 2.876. - How many doublings are required to reach a value of 32 with a base 2 logarithm?
A) 2
B) 3
C) 4
D) 5
ANS:- D) 5.
Sol:- To find out how many doublings are required to reach a value of 32 with a base 2 logarithm, we need to determine the exponent to which 2 must be raised to get 32.
In other words, we need to solve the equation
2x =32
x = log2 (32)
x = log2 (25)
x = 5
So, 5 doublings are required to reach a value of 32 with a base 2 logarithm.
Therefore, the correct answer is D) 5. - What is the approximate value of the base e?
A) 3.14159
B) 2.7183
C) 10
D) 1.4142
NS:- B) 2.7183
Sol:- The base e, also known as Euler’s number, is approximately equal to 2.7183. So the correct answer is B) 2.7183 - What is the value of secant θ if cosine θ = 0.6?
A) 0.6
B) 1.67
C) 1.25
D) 1.67
ANS:- D) 1.67.
Sol:- To find the value of secant θ, we can use the identity:
sec(θ) = 1 / cos(θ)
Given that cos(θ) = 0.6, we can plug this value into the formula:
sec(θ) = 1/ 0.6
= 5 / 3
= 1.67.
So, the value of secant θ is option D) 1.67. - If cotθ= 4 / 3, what is the value of tanθ?
A) 3 / 4
B) 4 / 3
C) 9 / 16
D) 16 / 9
ANS:- A) 3/4
Sol:- To find the value of tanθ when cotθ = 4 / 3, we can use the relationship between cotangent and tangent:
Cotθ = 1 / tanθ
Given that cotθ = 4/3, we can rewrite this equation as:
4/3 = 1/tanθ - A flagpole casts a shadow of 10 meters when the angle of elevation of the sun is 45°. What is the height of the flagpole?
a) 5 √2 meters
b) 10 meters
c) 10 √2 meters
d) 20 meters
ANS:- 10 meters
Sol:- To find the height of the flagpole, we can use the trigonometric relationship between the height of the flagpole, the length of its shadow, and the angle of elevation of the sun.
Let h be the height of the flagpole, and s be the length of its shadow.
Given that the angle of elevation of the sun is 45∘, we can use the tangent function:
tan(45∘) = h/ s
Since tan(45∘) = 1, we have:
1 = h/ 10
Multiplying both sides by 10, we get:
h = 10
So, the height of the flagpole is 10 meters, which matches option b) 10 meters - A kite is flying at an angle of elevation of 45°. If the length of the kite string is 50 meters, how high is the kite above the ground?
a) 25 √2 meters
b) 50 meters
c) 50 √2 meters
d) 100 meters
ANS:- a) 25 √2 meters,
Sol:- We can use trigonometry to find the height of the kite above the ground.
Let h be the height of the kite above the ground.
Given that the angle of elevation of the kite is 45∘, and the length of the kite string (hypotenuse) is 50 meters, we can use the sine function:
sin(45∘) = h/ 50
Since sin(45∘) = √2 /2, we have:
√2 /2 = h/ 50
Multiplying both sides by 50, we get:
h = √2/ 2 × 50
h = 25√2
So, the height of the kite above the ground is 25 √2 meters,
