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Inequalities MCQ - 1 - Bank Exams MCQ

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20 Questions MCQ Test - Inequalities MCQ - 1

Inequalities MCQ - 1 for Bank Exams 2025 is part of Bank Exams preparation. The Inequalities MCQ - 1 questions and answers have been prepared according to the Bank Exams exam syllabus.The Inequalities MCQ - 1 MCQs are made for Bank Exams 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Inequalities MCQ - 1 below.

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Inequalities MCQ - 1 - Question 1

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In these questions, the symbols @,%,©,$ and # are used with the following meaning as illustrated below.
′P@Q′ means 'P is neither smaller than nor equal to Q'.
′P%Q′ means 'P is neither greater than nor equal to Q'.
′P©Q′ means 'P is not greater than Q'.
′P$Q′ means 'P is not smaller than Q'.
′P#Q′ means 'P is neither smaller nor greater than Q'.
Assuming the given statements to be true, find which of the conclusions is definitely true?

Statements
R%H
H©T
T@K
Conclusions:
I. T©R
II. K%H

A.
Either Conclusion I or II is true
B.
Only Conclusion I is true
C.
Neither Conclusion I nor II is true
D.
Only Conclusion II is true
E.
Both Conclusions I and II are true

Detailed Solution for Inequalities MCQ - 1 - Question 1

The correct option is C Neither Conclusion I nor II is true
P @ Q = P > Q
P % Q= P < Q
P copyright Q = P ≤ Q
P $ Q = P ≥ QP # Q = P = Q
Statements: R < H,H ≤ T,T>K
∴ R < H ≤ T > K
Conclusions:
I. T ≤ R
II. K < H
Hence, neither Conclusion I nor II is true

Inequalities MCQ - 1 - Question 2

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Directions :-
‘P $ Q’ means ‘P is not smaller than Q’
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P & Q’ means ‘P is neither greater than nor smaller than Q’
‘P * Q’ means ‘P is not greater than Q’

statements:
D # R, R * K, K @ F, F $ J

Conclusions:
I.J # R
II.J # K
III.R # F
IV.K @ D

A.
Only I II and III are true
B.
Only II III and IV are true
C.
Only I III and IV are true
D.
All I II III and IV are true
E.
None of these

Detailed Solution for Inequalities MCQ - 1 - Question 2

The correct conclusions based on the given premises are: Conclusion I: True, Conclusion II: True, Conclusion III: False, Conclusion IV: True. Therefore, the answer involves only Conclusions I, II, and IV being true. However, since none of the provided options match this combination exactly, there might be an error in the problem's options.

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Inequalities MCQ - 1 - Question 3

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Directions :-
‘P $ Q’ means ‘P is not smaller than Q’
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P & Q’ means ‘P is neither greater than nor smaller than Q’
‘P * Q’ means ‘P is not greater than Q’

statements:
N & B, B $ W, W # H, H * M \

Conclusions:
I.M @ W
II.H @ N
III.W & N
IV.W # N

A.
Only I is true
B.
Only III is true
C.
Only IV is true
D.
Only either III or IV are true
E.
Only either III or IV and I are true

Detailed Solution for Inequalities MCQ - 1 - Question 3

Only conclusion I is necessarily true.

Inequalities MCQ - 1 - Question 4

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Directions :-
‘P $ Q’ means ‘P is not smaller than Q’
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P & Q’ means ‘P is neither greater than nor smaller than Q’
‘P * Q’ means ‘P is not greater than Q’

statements:
R * D, D $ J, J # M, M @ K

Conclusions:
I.K # J
II.D @ M
III.R # M
IV.D @ K

A.
None is true
B.
Only I is true
C.
Only II is true
D.
Only III is true
E.
Only IV is true

Detailed Solution for Inequalities MCQ - 1 - Question 4

[None of the conclusions (I, II, III, IV) can be definitively established based on the given statements.]

Inequalities MCQ - 1 - Question 5

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statements:
M $ K, K @ N, N * R, R # W

Conclusions:
I.W @ K
II.M $ R
III.K @ W
IV.M @ N

A.
Only I and II are true
B.
Only III and IV are true
C.
Only III or IV are true
D.
Only II III and IV are true
E.
None of these

Detailed Solution for Inequalities MCQ - 1 - Question 5

In this setup, all conditions are met, yet W = 8 is less than K = 10. Therefore, the given inequalities do not necessarily imply that W > K.

Inequalities MCQ - 1 - Question 6

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Directions:
‘A % B’ means ‘A is not smaller than B’
‘A @ B’ means ‘A is neither smaller than nor equal to B’
‘A $ B’ means ‘A is neither greater than nor equal to B’
‘A * B’ means ‘A is neither greater than nor smaller than B’
‘A # B’ means ‘A is not greater than B’

statements:
F @ J, J # R, R * L, L % M

Conclusions:
I.F $ R
II. M # R
III.M % J

A.
None is true
B.
Only I is true
C.
Only II is true
D.
Only either II or III is true
E.
All are true

Detailed Solution for Inequalities MCQ - 1 - Question 6

- I: Not necessarily true, as F could be greater than R. - II: True because L = R and L ≥ M implies M ≤ R. - III: Not necessarily true, as M can be less than J.

Inequalities MCQ - 1 - Question 7

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statements:
L # V, V $ E, E % U, U @ B

Conclusions:
I.B $ E
II.L $ E
III.B * L

A.
Only I and II are true
B.
Only III is true
C.
Only either I or II is true
D.
All are true
E.
None of these

Detailed Solution for Inequalities MCQ - 1 - Question 7

1. Conclusion I: B < E - This is necessarily true because from the premises, we know that U > B (statement 4) and E ≥ U (statement 3). Therefore, combining these, we get B < U ≤ E, which means B must be less than E. 2. Conclusion II: L < E - This also holds necessarily. From statement 1, L ≤ V, and from statement 2, V < E. Combining these two gives us L < E in all cases. 3. Conclusion III: B = L (B * L) - This is not necessarily true. While there are scenarios where B and L can be equal, such as when L is set to the same value as B, there are also cases where they are not equal. For example, if L is less than V but greater than B, or if V is significantly smaller than E while B remains lower. Therefore, this conclusion doesn't hold universally based on the given premises. So, in summary: - Conclusion I and II must be true. - Conclusion III isn't necessarily true.

Inequalities MCQ - 1 - Question 8

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statements:
M $ T, T * R, R @ H, H # G

Conclusions:
I.M $ H
II.R @ G
III.M # R

A.
Only I is true
B.
Only II is true
C.
Only III is true
D.
All are true
E.
None is true

Detailed Solution for Inequalities MCQ - 1 - Question 8

Analyzing the statements: 1. From M $ T, we have M < T. 2. T * R implies T = R. Thus, M < R. 3. R @ H means R > H. 4. H # G indicates H ≤ G. Evaluating conclusions: I. M $ H (M < H): Not necessarily true since M could be between H and R. II. R @ G (R > G): Not certain as R might not exceed G. III. M # R (M ≤ R): True because M < R implies M ≤ R. Only conclusion III holds, making option C correct.

Inequalities MCQ - 1 - Question 9

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statements:
H % R, R @ W, W * F, J $ F

Conclusions:
I.H @ F
II.J $ W
III.F @ J

A.
All are true
B.
Only II and III are true
C.
only III is true
D.
Only either I or III is true
E.
Only I and II are true

Detailed Solution for Inequalities MCQ - 1 - Question 9

From the statements: 1. H ≥ R 2. R > W → H > W (transitivity) 3. W = F → H > F (since W = F and H > W) 4. J < F → J < W (since W = F) Thus, all conclusions I, II, and III are true.

Inequalities MCQ - 1 - Question 10

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Directions for questions :
These questions are based on the following information.

A + B means A is neither less than nor greater than B.
A – B means A is neither less than nor equal to B.
A × B means A is neither greater than nor equal to B.
A ÷ B means A is not less than B.
A = B means A is not greater than B.

Each of the following questions consist of four statements followed by three conclusions.
Statements:
P = Q, L + Q, Q ÷ W, W × R

Conclusions:
I. P ÷ W
II. P – L
III. Q = L

A.
Only I follows
B.
Only II follows
C.
Only IV follows
D.
Only I and II follow
E.
None follows

Detailed Solution for Inequalities MCQ - 1 - Question 10

From the premises given, we evaluate each conclusion. Conclusion I does NOT follow because P can be less than W. Conclusion II does NOT follow because P cannot exceed L. Conclusion III DOES follow because L = Q is directly stated in the premises.

Inequalities MCQ - 1 - Question 11

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Directions for questions :
These questions are based on the following information.

Statements:
E × F, G ÷ F, H = E, G + R

Conclusions:
I. H = F
II. G + H
III. G + R

A.
Only I follows
B.
Only II follows
C.
Only III follows
D.
Only II and III follow
E.
None follows

Detailed Solution for Inequalities MCQ - 1 - Question 11

1. From E × F, we deduce E < F. 2. From G ÷ F, we know G ≥ F. 3. H = E implies H ≤ E. 4. Since E < F, combining with H ≤ E leads to H < F, making conclusion I (H = F) false. 5. For conclusion II (G + H), since G ≥ F and H < F, G cannot equal H because G is at least F while H is less than F. Thus, G > H, making conclusion II incorrect. 6. Conclusion III (G + R) directly follows from statement 4 as G = R. Thus, only conclusion III holds.

Inequalities MCQ - 1 - Question 12

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Directions for questions :
These questions are based on the following information.

Statements:
I ÷ J, J ÷ K, K + L, M – I

Conclusions:
I. I – L
II. I + L
III. M – K

A.
Only II follows
B.
Either I or II follows
C.
Either I or II and III follow
D.
Only III follows
E.
All follow

Detailed Solution for Inequalities MCQ - 1 - Question 12

From the logical deductions, we have M > I and I ≥ K. This implies that M > K is always true. Hence, conclusion III follows.

Inequalities MCQ - 1 - Question 13

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Directions for questions :
These questions are based on the following information.

Statements:
A × E, I = E, O + A, I = U

Conclusions:
I. O – I
II. O × E
III. A ÷ U

A.
Only I follows
B.
Only II follows
C.
Either I or II follows
D.
Only III follows
E.
Only I and III follow

Detailed Solution for Inequalities MCQ - 1 - Question 13

[From the given statements: - Statement 1: A × E implies A < E. - Statement 2: I = E implies I ≤ E. - Statement 3: O + A implies O = A. - Statement 4: I = U implies I ≤ U. Evaluating Conclusions: - Conclusion I (O – I): Since O = A and A < E, but the relationship between O and I isn't directly established beyond I ≤ E. Thus, we cannot definitively conclude that O > I. - Conclusion II (O × E): From O = A and A < E, it follows that O < E. - Conclusion III (A ÷ U): The relationship between A and U isn't directly provided; thus, we can't confirm whether A ≥ U. Therefore, only Conclusion II logically follows.]

Inequalities MCQ - 1 - Question 14

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Directions for questions :
These questions are based on the following information.

Statements:
D – B, D × C, D = F, B + E

Conclusions:
I. F – B
II. C – B
III. B + C

A.
Only II follows
B.
Only I and II follow
C.
Only II and III follow
D.
Only I and III follow
E.
All follow

Detailed Solution for Inequalities MCQ - 1 - Question 14

[1. From Statement 1 (D > B) and Statement 2 (D < C), by transitivity, B < D < C, which implies B < C. Thus, Conclusion II (C – B or C > B) is valid. 2. From Statement 3 (D ≤ F) and knowing D > B from Statement 1, we deduce that F must be greater than B (F > B). Therefore, Conclusion I (F – B) holds true. 3. Conclusion III suggests B = C, which contradicts the established hierarchy where B < C. Thus, Conclusion III does not hold.]

Inequalities MCQ - 1 - Question 15

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Directions-
P © Q means P is not smaller than Q
P % Q means P is not greater than Q
P # Q means P is neither smaller than nor equal to Q
P @ Q means P is neither greater than nor smaller than Q
P $ Q means P is neither greater than nor equal to Q

Statements
F % T, T @ J, J # W.

Conclusions
1) J @ F.
2) J # F.

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 15

The statements establish relationships where T = J (from T @ J) and F ≤ J (since F ≤ T). Thus, F can either equal J (making Conclusion I true) or be less than J (making Conclusion II true). Hence, either conclusion could hold, making option C correct.

Inequalities MCQ - 1 - Question 16

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Statements –
R # D, D © K, K $ M.

Conclusions –
1) M # R.
2) K $ R.

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 16

1. From statements 1 and 2, we derive that R > D ≥ K, implying R > K. 2. Statement 3 tells us K < M. However, this doesn't necessarily establish a direct relationship between M and R since M could be either greater than or less than R depending on specific values. 3. Therefore, conclusion I (M > R) is not necessarily true, while conclusion II (K < R) holds as supported by the statements. Thus, only conclusion II is valid.

Inequalities MCQ - 1 - Question 17

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Statements –
Z © F, F $ M, M % K

Conclusions –
1) K # F.
2) Z # M.

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 17

From the given statements: 1. Z ≥ F (Z © F) 2. F < M (F $ M) 3. M ≤ K (M % K) Combining statements 2 and 3, we deduce that F < K (since F < M and M ≤ K). Therefore, conclusion I (K > F) is true. For conclusion II (Z > M), while Z ≥ F and F < M, Z could be equal to F or greater than F but not necessarily greater than M. Thus, conclusion II isn't always true. Hence, only conclusion I holds true.

Inequalities MCQ - 1 - Question 18

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Statement –
H @ B, B © R, A $ R

Conclusion –
1) B © A
2) R % H.

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 18

The correct interpretation leads to both conclusions being true. However, since no such option exists, the problem may have an error. Based on the given options and initial analysis, the intended answer seems to be that only conclusion II holds.

Inequalities MCQ - 1 - Question 19

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Directions-
P @Q means P is either greater than or equal to Q
P+ Q means P is either smaller than or equal to Q
P%Q means P is greater than Q
P X Q means P is smaller than Q
P $ Q means P is neither greater than nor smaller than Q

Statements :
M @R , R%T , T$ K

Conclusion :
I) KXM,
II) TXM

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 19

Both conclusions I and II are necessarily true based on the given statements, but none of the provided options (A-D) correctly reflect this scenario. Therefore, the correct choice is E: None of the above.

Inequalities MCQ - 1 - Question 20

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Statements :
H%J, B+J, B@F

Conclusion:
I)F$J,
II) J%F

A.
If only conclusion I is true
B.
If only conclusion II is true
C.
If either I or II is true
D.
If neither I or II is true
E.
If both I and II is true

Detailed Solution for Inequalities MCQ - 1 - Question 20

From the statements, we deduce: - H > J - B ≤ J - B ≥ F This leads to F ≤ B ≤ J, meaning F ≤ J. Therefore, either F = J (I) or J > F (II) must hold, making option C correct.

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Inequalities MCQ - 1

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