# Inequalities - 1

1. Which of the following expressions is true, if the given expression is true? P > A ≤ S < U = M ≥ B

A) A = B    B) P > U    C) M > A   D) S < B   E) None of these]

2. Statements: A ≤ M ≤ B = Q > E > S; M > U

Conclusions: I. Q ≥ A II. B > S

A) Only conclusion I is true    B) Either conclusion I or II is true   C) Only conclusion II is true    D) Both conclusions I and II are true    E) Neither conclusion I nor II are true

Explanation:

Statements: A ≤ M ≤ B = Q > E > S ...(i) M > U ...(ii)

From (i), we get

A ≤ Q or Q ≥ A.

Thus, conclusion I is true.

Again, B > S is true.

Hence both conclusions I and II are true.

Ans: D

3. Statements: I > S ≥ G = A ≤ U ≤ W; E ≤ A ≤ K

Conclusions: I. U ≥ E II. S > W

A) Only conclusion I is true     B) Either conclusion I or II is true    C) Only conclusion II is true    D) Both conclusions I and II are true    E) Neither conclusion I nor II are true

Explanation:

Statements: I > S ≥ G = A ≤ U ≤ W ...(i)

E ≤ A ≤ K ...(ii)

Combinng (i) and (ii), we get

E ≤ A ≤ U

Thus, E ≤ U or U ≥ E. Hence I is true.

Again we can't compare S and W.

Hence II (S > W) is not true.

Ans: A

4. Statements: C ≥ D > E ≤ F ≤ G < H

Conclusions: I. C ≥ G II. E < H

A) Only conclusion I is true     B) Either conclusion I or II is true    C) Only conclusion II is true   D) Both conclusions I and II are true    E) Neither conclusion I nor II are true

Explanation:

Statement: C ≥ D > E ≤ F ≤ G < H

Thus, we can't compare C and G. Hence I (C ≥ G) is not true.

Again, E < H is true.

Hence II is true.

Ans: C

5. Statements: i) I = J < K ii) J = L > M ≥ N iii) M > G ≤ T < U

Conclusions: I. I > N II. L > T

A) Only conclusion I follows.       B) Only conclusion II follows.   C) Both conclusions I and II follow.    D) Either conclusion I or conclusion II follows.   E) Neither of the conclusions follows.

Explanation:

For conclusion I: I > N

Combining statements i and ii: I = J = L > M ≥ N

As, “>”, is the highest priority sign in the combination so, “I > N”, is the true relation between I and N.

Hence, conclusion I follows.

For conclusion II: L > T

Combining statements II and III:

L > M > G ≤ T

As, sign between “L” and “T” are in different direction so, this conclusion does not follow.

Ans: A

6. Statements: i) B > C ≥ D = E ii) D < F = G > H ≥ I iii) G < L ≤ M

Conclusions: I. D ≤ M II. E < F

A) Only conclusion I follows.    B) Only conclusion II follows.   C) Both conclusions I an II follow.   D) Either conclusion I or conclusion II follows.    E) Neither of the conclusions follows.

Explanation: For conclusion I: D ≤ M

Combining statements ii and iii:

D < F = G < L ≤ M

As, “<”, is having highest priority, therefore, this conclusion does not follow.

For conclusion II: D < E

Combining statements i and ii E > C = D

As, “<”, is having highest priority, so the conclusion follows.

Ans: B

7. Statements: i) B = C ≤ Y ≤ Z ii) Q ≥ Y = A

iii) Y ≤ O < P > Q

Conclusions: I. Q > C II. Q = C

A) Only conclusion I follows.     B) Only conclusion II follows.   C) Both conclusions I and II follow.    D) Either conclusion I or conclusion II follows.   E) Neither of the conclusions follows.

Explanation: For conclusion I: Q > C

Combining statements i and ii: C ≤ Y ≤ Q

So, Q > C, does not follow.

For conclusion II: Q = C

Combining statements I and II: C ≤ Y ≤ Q

So, Q = C, does not follow.

Now, we can see that:

Both the objects of conclusions I and II are same i.e. ‘Q’ and ‘C’.

Both the conclusions I and II are wrong. On combining both the relations we get the actual relation i.e. Q ≥ C

So, Either conclusion I or conclusion II follows.

Ans: D

8. Statements: M = Q ≤ N ≤ W ≤ B, R ≥ S = O > Q

Conclusions: I. R > M II. O ≤ B

A) None follows.    B) Only conclusion II follows.   C) Either conclusion I or conclusion II follows.   D) Only conclusion I follows.   E) Both conclusion I and conclusion II follow.

Explanation: Given Statements: M = Q ≤ N ≤ W ≤ B, R ≥ S = O > Q

Conclusions: I. R > M II. O ≤ B

For Conclusion I, combining both the equations, we get

R ≥ S = O > Q = M ≤ N ≤ W ≤ B ........... (i)

We can observe that between R and M, the common sign of inequality is of '>' which confirms R > M which is given as conclusion I. For Conclusion II,

We can observe that between O and B the signs are getting reversed and hence we can't derive a definite conclusion between these two elements

. Conclusion II, hence, doesn't follow.

Ans: D

9. Statements: T ≤ E > R > W; N ≤ O < R = X

Conclusions: I. E ≥ N II. O < E

A) Only conclusion I follows    B) Neither conclusion I nor conclusion II follows    C) Only conclusion II follows

D) Either conclusion I nor conclusion II follows    E) Both conclusions I and conclusion II follow

Explanation: Statements: T ≤ E > R > W; N ≤ O < R = X

Conclusions: I. E ≥ N II. O < E

Combining eq (i) and (ii) for the relation between E and N & O and E, we get E > R > O ≥ N and O < R < E

Common sign between E and N is of '>'. Thus, the given conclusion E ≥ N is not valid. Now, common sign between O and E (moving from O to E) is '<' and the given conclusion is O < E.

Ans: C

Posted Date : 18-04-2023

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.