Inequality MCQ Quiz - Objective Question with Answer for Inequality - Download Free PDF

According to the question:

Given statements: 

PAQ ⇒ P\(\ {<}\llap{/\,}\) Q

QFR ⇒ Q = R

SER ⇒ S < R

Combining the statements: P\(\ {<}\llap{/\,}\) Q = R > S

So, checking each option one by one:

Option 1) PDS, RCP

PDS → P > S → True, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' thus we get P > S. Therefore, it is true)  

RCP → R \({>}\llap{/\,}\) P → True, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' thus we get P > R. Therefore, it is false)  

Option 2) PES, RBF

PES → P < S → False, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' thus we get P > S. Therefore, it is false)  

RBF → R ≠ F → False, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, no relation can be determined between R and F. Therefore, it is false) 

Option 3) RBQ, PFS

RBQ → R ≠ Q → False, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, we get Q = R. Therefore, it is false)

PFS → P = S → False, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' therefore we get P > S. Thus, it is false)

Option 4) PAS, PCR

PAS → P \(\ {<}\llap{/\,}\) S → True, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' thus we get P > S. Therefore, it is true)  

PCR → P \({>}\llap{/\,}\) R → False, (As P\(\ {<}\llap{/\,}\) Q = R > S. So, here '\(\ {<}\llap{/\,}\)' can also be written as '>' thus we get P > R. Therefore, it is false)

Hence, "Option 1" is the correct answer.

Statement : B > R ≥ A = M < F ≤ S

Conclusions :

I B > M - True( As, B > R ≥ A = M is given)

II S ≥ A - False(As, A = M< F ≤ S is given, so S > A).

Thus, Only conclusion I is true.

Hence, the correct answer is "Option 1".

Given statements: C < H ≤ A = M > P ≥ I > O ≥ N

Conclusions:

I) H < M → True (As C < H ≤ A = M > P ≥ I > O ≥ N. Here, we get H ≤ M, therefore it is false)

II) I ≥ N → False (As C < H ≤ A = M > P ≥ I > O ≥ N. Here, we get I ≥ N, therefore it is false)

Thus, (B) Only conclusion II follows.

Hence, the correct answer is "Option 1".

Given statement: S < A ≤ N < D = W > I ≥ C > H

Conclusions:

I) N > I → False (As S < A ≤ N < D = W > I ≥ C > H. So, no relation between N and I can be determined, therefore it is false.)

II) C < A → False (As S < A ≤ N < D = W > I ≥ C > H. So, no relation between A and C can be determined, therefore it is false.)

Thus, (D) Neither I nor II follows.

Hence, the correct answer is "Option 2".

Given statement: 

H < I ≤ S = T

Y < R ≤ O < T

Combining the statements: H < I ≤ S = T > O ≥ R > Y

Conclusions:

I) H < O → Does not follow (As H < I ≤ S = T > O ≥ R > Y. So, no relation can be determined between H and O, therefore it is false.)

II) I < R → Does not follow (As H < I ≤ S = T > O ≥ R > Y. So, So, no relation can be determined between H and O, therefore it is false.)

Thus, (D) Neither I nor II follows.

Hence, the correct answer is "Option 1".

The given statement is: C < L > I = E ≥ N > T

Conclusion i) I > T

From the statement, we can see that I = E, and E ≥ N > T. Therefore, I > T is logically correct. Hence, conclusion i) is logical.

Conclusion ii) T < C

From the statement, we can see that C < L > I. However, there is no direct relation between C and T. Therefore, we cannot conclude that T < C. Hence, conclusion ii) is not logical.

Therefore, the only conclusion that is logical is i), 

Hence, the correct answer is option A.

Given Statements:  C = U < F ≤ H > G = I > R

Conclusions:

I. H > R → True (as H > G = I > R → as H is greater than G,I and I is greater than R.)

II. H > C → True (as in  C = U < F ≤ H → as C is equal to U and less than F . F is less than H. hence, H is greater than C. )

Hence, 'Both conclusions I and II are true'.

Given:

J > K = L, M \( \ge \) N < K, O < J < P, N > Q > R

Conclusions:

I. P > M → False

We have P > J and J > K which means P > K

also M \( \ge \) N < K so relation between P and M cannot be determined.

II. N < P → True

We have P > J and J > K which means P > K also N < K (given)

when we combine both the relations we get, P > K > N so P > N.

So only conclusion II is true.

Hence, the correct answer is Option 4.

Given statement: S = Q > R ≤  U = M > B

According to the given information:

​S is equal to Q, Q is greater than R, R is less than or equal to U, U is equal to M, and M is greater than B.

Conclusions:

I. Q > U → False( Q > R ≤ U; A definite relation cannot be established between Q and U)

.II. R < S → True ( S = Q > R; S > R → R < S)

​Hence, the correct answer is "Only II is true".

Given Statement: C ≤ U < E; C = O > M ≥ T; M = A > L

Now,

Combined Statement: C ≤ U < E; C = O > M ≥ T; M = A > L

Conclusions:

i): E > M → True (From C ≤ U < E and C = O > M, it implies E > M)

ii): C ≥ T → False (From C = O > M ≥ T, it implies C > T or C = T)

iii): L > T → False (From M = A > L and M ≥ T, no direct relation can be established between L and T)

So, only conclusions (i) follow,

Hence the correct answer is 'Option (3)'.

Given inequality is: P ≤ Q ≥ R; E ≥ Q; L < Q = D

1. L < P → P ≤ Q, L < Q, data is not sufficient to determine the relation → False

2. E ≥ R → E ≥ Q ≥ R, E ≥ R → True.

3. E < D → E ≥ Q, L < Q = D, E ≥ D → False.

4. Q < R → Q ≥ R → False.

Given inequality is, P > Q ≤ R = S ≥ T

1. Q > S → Q ≤ R = S, Q < S → False.

2. Q = T → Q ≤ R = S ≥ T, data is not sufficient to determine the relation → False.

3. R < T → R = S ≥ T, R ≥ T → False.

Given statements: Q > J ≥ M > L = K < S

I. Q > L → True (as Q > J ≥ M > L)

II. J > K → True (as J ≥ M > L = K)

III. L < S → True (as L = K < S)

Given Statement: P ≤ T < K = Y ≥ S ≥ E < L

Now,

Conclusions:

1) K > E → False (K = Y ≥ S ≥ E, this gives K ≥ E).

2) E = K → False (K = Y ≥ S ≥ E, this gives K ≥ E).

Here, both the conclusions are false but it forms the complementary pair for Either Or.

So, Either conclusion 1 or 2 is true.

Hence, the correct answer is 'Option 2'.

Additional Information Conditions of Either-or case:

1. The elements should be the same in both the statements.

2. Both the conclusions should be false individually.

3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1) All + Some not

2) No + Some

Note: Some + Some not is not considered under Either - or case.

Statements:

U > H = G ≥ N; E < N > W ≥ O

Conclusion:

I. G > E → True → According to the statement G ≥ N > E

II. H > N → False → According to the statement U > H = G ≥ N

Hence, Option (2) is correct.

Mistake Points

As from the equation H = G ≥ N.

Mistake points:

There is a difference in (≥, >) both the sign.

When H ≥ N means H is greater or equal to N.

When H > N means H is greater than N.

As in conclusion 2, it is said H = G ≥ N from this we cannot say H is greater than N.

Thus conclusion 2 is false.