Mathematical Inequalities MCQ Quiz - Objective Question with Answer for Mathematical Inequalities - Download Free PDF

Given statements: 

On combining: 

Conclusions:

I. A = T → False (Since, A is less than T).

II. O > M → False (Since, no direct relation between O and M can be determined).

III. A > T → False (Since, A is less than T).

IV. E < N  → False (Since, no direct relation between E and N can be determined).

Hence, none of the conclusions follow.

Given Statements: 

On combining: 

Conclusions:

I. K > W  → True (It is clear from the above combination K is greater than W).

II. W < S → False (Since, S is greater than W not less than).

III. M = G → False (Since M is less than G).

IV. T > R → True (It is clear from the above combination that T is greater than R).

Hence, both conclusion I and IV follows.

Given Statements: 

On combining: 

Conclusions:

 → True (From the above combination it is clear K is greater than O)

 → False (Since, I is greater than M is correct but not equal to M)

 → False (Since, K is greater than O not less than)

 → False (Clear relation between S and M can not be determined).

Hence, only conclusion I follows.

Given Statement: V < C ≤ L > Y ≥ R = I < W ≥ M

Let's analyze each conclusion:

1) I < L

From the statement: L > Y ≥ R = I

This implies L > I. So, I < L is True.

2) L ≥ R

From the statement: L > Y ≥ R

This implies L > R is true

While L ≥ R is not true.

3) L > V

From the statement: V < C ≤ L

This clearly implies V < L, or L > V. So, L > V is True.

Hence, the correct answer is "Option 2".

Given Statement: B > O ≥ T = Q < C ≤ W > U

Let's analyze each conclusion:

1) B > T

From the statement: B > O ≥ T.

Since there is a strict inequality ('>') in the path between B and T, B is definitely greater than T (B > T). So, B > T is Definitely True.

2) W > T

From the statement: T = Q < C ≤ W.

Combining these, we get T < W. So, W > T is Definitely True.

3) Q ≤ O

From the statement: O ≥ T = Q.

This directly implies O ≥ Q, or Q ≤ O. So, Q ≤ O is Definitely True.

4) Q < U

From the statement: Q < C ≤ W > U.

Therefore, no definite relation can be established between Q and U. Q < U is not True.

Hence, the correct answer is "Option 4".

The given statement is: P ≱ S ≱ T = Y > F ≰ G = H ≤ O < A

After decoding we get

P < S < T = Y > F > G = H ≤ O < A

Conclusions:

I. Y > P → true (as P < S < T = Y given so Y > P)

II. A > G → true (as G = H ≤ O < A given as A > H and H = G so A > G true)

III. O ≥ G → true (as G = H ≤ O given)

Given Statements: L ≥ M = N < O, P < Q ≥ R = S ≥ L

On combining: P < Q ≥ R = S ≥ L≥ M = N < O

Conclusions: I. Q > M → False (as Q ≥ R = S ≥ L ≥ M → Q ≥ M)

II. N = Q → False (as Q ≥ R = S ≥ L ≥ M = N → Q ≥ N)

In statement ‘N = M’

Hence, either I or II is true.

Mistake Points From the Given statement we have N = M.

Therefore,

Conclusion I : I. Q > M 

conclusion II: N = Q → M = Q (Q ≥ R = S ≥ L ≥ M → Q ≥ M)

Hence, It makes either I or II conclusions is true.

Given statements: D > F ≥ G ≥ H; H ≥ I = J

On combining: D > F ≥ G ≥ H ≥ I = J

Conclusions:

I. J = F → False (as F ≥ G ≥ H ≥ I = J → J ≤ F)

II. F > J → False (as F ≥ G ≥ H ≥ I = J → F ≥ J)

Therefore, conclusion I and II forms a complementary pair.

Hence, Either I or II is True.

Given statements: H ≥ X < R < D ≥ F > Y

Conclusions:

I. H ≥ Y → False (as H ≥ X < R < D ≥ F > Y, thus clear relation cannot be determined)

II. Y > H → False (as H ≥ X < R < D ≥ F > Y, thus clear relation cannot be determined)

Therefore, Conclusion I and Conclusion II forms complementary pair

Hence, Either I or II is true

NOTE:

If all three possible conditions (<, >, =) between any two entities are included in conclusions, and both the conclusion are individually false then it would be a case of ‘either-or’.

Given statement: P ≤ M < C ≥ $ > Q ≥ U

Conclusions:

I. M < $ → False (no definite relation shows between $ and M, hence the conclusion is false)

II. C ≥ U → False(as C > U, hence C is not equal to U, so conclusion if definitely false)

III. $ ≤ M → False (no definite relation shows between $ and M, hence conclusion is false)

I. D < T → False (As, T ≥ O = I ≥ L = D → T ≥ D)

II. D = T → False (As, T ≥ O = I ≥ L = D → T ≥ D)

As T ≥ D, either T = D or T > D.

Given statements: A > B ≥ C; D > E ≥ F; P = Q = F; D < C

On combining: A > B ≥ C > D > E ≥ F = Q = P

Conclusions:

I. Q < E → False (as E ≥ F = Q → Q ≤ E)

II. P = E → False (as E ≥ F = Q = P →P = Q ≤ E)

As P = Q

Therefore, conclusion I and II forms a complementary pair.

Hence, either I or II is true.

Important Points 

Conditions for Either - or

I. Subject and predicate should be same

II. Both the individual conclusions must be false

III. Both the subject should have all the three possibilities i.e. >, <, =

There can be only three possibilities between two subjects

• A > B
• A < B
• A = B

Given statement: F > T = N ≥ D > W ≥ G ≤ M < L

I. N < M → False (as N ≥ D > W ≥ G ≤ M)

II. M < F → False (as F > T = N ≥ D > W ≥ G ≤ M gives either M < F or M ≥ F)

III. T ≥ G → False (as T = N ≥ D > W ≥ G)

IV. F ≤ M → False (as F > T = N ≥ D > W ≥ G ≤ M)

F > T = N ≥ D > W ≥ G ≤ M is given in the statement. Therefore conclusion II and IV makes a complementary pair. 

Hence, the correct answer either conclusion II or IV follow.

Given statements: H ≤ X ≤ R = O > T; Y = F ≥ R > D 

Conclusions:

I. H > Y → False (as H ≤ X ≤ R ≤ F = Y, thus H ≤ Y)

II. Y > H → False (as H ≤ X ≤ R ≤ F = Y, thus H ≤ Y)

After combining the statement we are getting 

H ≤ X ≤ R≤ F = Y

H≤Y

that is why either or case is not possible because it leads to a common conclusion.

Hence, Neither I nor II is true.

Statement:

P ≤ Q < S = T ≥ U ≥ W < Z

Conclusion:

I. S > W: False: As, P ≤ Q < S = T ≥ U ≥ W < Z. so, the relation between S and W is S ≥ W.

II. W = T: False: As, P ≤ Q < S = T ≥ U ≥ W < Z. so, the relation between T and W is T ≥ W.

As S = T, Both form complementary pairs.

Therefore, either I or II follows.