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

Given Statements: M > K, R > P, F ≤ G, H = R, K ≤ P, G = H

Conclusions:

I. G > P → True (As G = H = R > P → its clear  G > P).

II. K → its clear K

Hence, both conclusion I and II follow.

Given statements:
H L ≥ M; N

On combining:
H L ≥ M

Conclusions:

1. N L ≥ M à N

2. L = H → False (As H L ≥ M, there is no relation between L and H because of the opposite sign between L and H)

Hence, only I follow.

Given statements:
T G ≥ D = S

Conclusions:

1. G > T → False (There is no relation between G and T because of the opposite sign between G and T)

2. U ≤ S → False (There is no relation between U and S because of the opposite sign between U and S)

Hence, neither I nor II follow.

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

After decoding we get

P F > G = H ≤ O

Conclusions:

I. Y > P → true (as P P)

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

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

Hence, the correct answer is all follow.

Given Statements: L ≥ M = N

On combining: P

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 ≥ F > Y

Conclusions:

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

II. Y > H → False (as H ≥ X ≥ 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 Q ≥ U

Conclusions:

I. M

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)

Hence, conclusion I and III are complementary pairs. So, either conclusion I or III is true.

I. D

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

As T ≥ D, either T = D or T > D.

Hence, either Conclusion I or II follow.

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

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

Conclusions:

I. Q

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
• A = B

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

I. N W ≥ G ≤ M)

II. M T = N ≥ D > W ≥ G ≤ M gives either M

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.

Note: We can say only that option as definitely false if we get definite result of getting false, if relation does not set up then that inequality will not be called as definitely false

Let us check each option:

1) W >T → As W T → No relation can be determined between W and T, so option W > T is not definitely false.

2) N

3) S = N → As S ≥ W

4) T = D → As T 5) C ≤ I → As C > R = S ≥ W T

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.