Test: Inequalities - 2 - Class 10 MCQ

Test: Inequalities - 2 - Class 10 MCQ

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15 Questions MCQ Test The Complete SAT Course - Test: Inequalities - 2

Test: Inequalities - 2 for Class 10 2024 is part of The Complete SAT Course preparation. The Test: Inequalities - 2 questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Inequalities - 2 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inequalities - 2 below.
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Test: Inequalities - 2 - Question 1

A statement is given followed by two conclusions. Find which conclusion is true based on the given statement. Statement: C < A ≤ T = D ≥ O; G ≥ D < S; T ≥ A Conclusions: I: A ≤ O II: C < G

Detailed Solution for Test: Inequalities - 2 - Question 1

The given statement is: C < A ≤ T = D ≥ O; G ≥ D < S; T ≥ A

Combine the statement: C < A ≤ T = D ≥ O; G ≥ D < S

Conclusions:

I: A ≤ O → False (as A ≤ T = D ≥ O gives; as A ≤ D and D ≥ O → clear relationship between A and O cannot be determined).

II: C < G → True (as C < A ≤ T = D ≥ O; G ≥ D < S gives; as by combinatin C < A ≤ T = D ≤ G so C < G True).

Hence, the correct answer is “Only II”.

Test: Inequalities - 2 - Question 2

Directions: In the following question assuming the given statements to be true, find out which of the following two conclusions definitely true. Statements: A ≤ P = B; C = P; F < B Conclusions: I. B < A II. F = P

Detailed Solution for Test: Inequalities - 2 - Question 2

Given: A ≤ P = B; C = P; F < B

On combining: A ≤ P = B = C

I. B < A → False as A ≤ B.

II. F = P → False as F < P.

Hence both conclusions are false.

Test: Inequalities - 2 - Question 3

Directions: In the following question assuming the given statements to be true, find which of the given conclusions is definitely true. Statement: C < O > K; Z < R < N = C

Detailed Solution for Test: Inequalities - 2 - Question 3

Given:

C < O > K; Z < R < N = C

On Combining:

Z < R < N = C < O > K

Conclusions:

1. R < C → True (as R < N = C)

2. Z > N → False (as Z < R < N; therefore Z < N)

3. O = R → False (as R < N = C < O; therefore R < O)

4. C < K → False (as C < O > K; thus, a clear relation between C and K cannot be established)

Hence, “R < C” is definitely true among the given options.

Test: Inequalities - 2 - Question 4

If A + B = C + D and A + D > B + C, then which one of the following is definitely wrong?

Detailed Solution for Test: Inequalities - 2 - Question 4

Given : A + B = C + D

⇒ A - D = C - B ----- (i)

Also, it is given that A + D > B + C ----- (ii)

Subtracting (i) from (ii), we get :

D > B

Therefore, B > D is definitely wrong.

Hence, option 4 is the correct answer.

Test: Inequalities - 2 - Question 5

In the given question, relationship between different elements is shown in the statement. The statement is followed by two conclusions. Study the conclusions based on the given statements and select the correct answer.

Statements:

U > H = G ≥ N; E < N > W ≥ O

Conclusion:

I. G > E

II. H > N

Detailed Solution for Test: Inequalities - 2 - Question 5

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 (b) is correct.
Mistake Points:
As from the equation H = G ≥ N.
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.

Test: Inequalities - 2 - Question 6

In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statements:
Q > J ≥ M > L = K < S

Conclusions:

I. Q > L

II. J > K

III. L < S

Detailed Solution for Test: Inequalities - 2 - Question 6

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)

Hence, the answer is ‘All follow’.

Test: Inequalities - 2 - Question 7

Given below is an inequality, which of the following condition is TRUE?

If A > B > C > D = F ≥ G < H

Detailed Solution for Test: Inequalities - 2 - Question 7

From the given conditions, A > B > C > D = F ≥ G < H.

1. G > C → C > D = F ≥ G, C > G → False.

2. B > F → B > C > D = F, B > F → True.

3. G > F → D = F ≥ G < H, F ≥ G → False.

4. D < G → D = F ≥ G, D ≥ G → False.

So, B > F is the correct inequality.

Test: Inequalities - 2 - Question 8

Given below is an inequality, which of the following condition is TRUE?

If P > Q ≤ R = S ≥ T

Detailed Solution for Test: Inequalities - 2 - Question 8

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.

So, none of the options are correct.

Test: Inequalities - 2 - Question 9

Read the given statement and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions is true based on the given statement.

Statement:

S = Q > R ≤  U = M > B

Conclusions:

I. Q > U

II. R < S

Detailed Solution for Test: Inequalities - 2 - Question 9

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".

Test: Inequalities - 2 - Question 10

Given below is an inequality, which of the following condition is TRUE?

If P ≤ Q ≥ R; E ≥ Q; L < Q = D

Detailed Solution for Test: Inequalities - 2 - Question 10

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.

Hence, E ≥ R, is the correct inequality.

Test: Inequalities - 2 - Question 11

In the following question, Few statements are given which are followed by some conclusions. According to the given statements, which conclusion is/are definitely true?

Statements:

M ≤ N = O ; M ≤ P ; O < Q

Conclusions:

I. Q > N

II. M ≥ O

Detailed Solution for Test: Inequalities - 2 - Question 11

According to given information:

Statements: M ≤ N = O ; M ≤ P ; O < Q

Combining the statement:> M ≤ N = O < Q

Here, P is greater than or equal to M which is less than or equal to N equal to O which is less than Q.

Conclusions:

I.  Q > N → True (In the given statement, P > M ≤ N = O < Q ,It clearly mentioned Q is greater than O which is equal to N .So, Q is greater than N too. Thus, the conclusion I is true).

II. M ≥ O → False (In the given statement, M ≤ N = O, It is clearly mentioned that M is less than or equal to N which is equal to O. So, M can never be greater than O. Thus, conclusion II is a false).

Hence, "Option b" is the correct answer.

Test: Inequalities - 2 - Question 12

In the following question, a statement is being followed by two conclusions. Find which of the two conclusion is/are true according to the given statement.

Statement:

J = K ≥ L > X ≥ Y ;  J ≥ P ; P ≥ Z

Conclusions:

I: J < L

II: P ≤ Y

Detailed Solution for Test: Inequalities - 2 - Question 12

The given statement is: J = K ≥ L > X ≥ Y ;  J ≥ P ; P ≥ Z

Combining the statement: < P J = K ≥ L > X ≥ Y

Here, Z is smaller than or equal to P which is Smaller than or equal to J which is equal to K which is greater than or equal to L which is greater than X and X is greater than or equal to Y.

Conclusions:

I: J < L → False (as J = K ≥ L gives as J = K and K ≥ L which implies that J ≥ L and J cannot be less than L . Thus, Conclusion I is false.).

II:  P ≤ Y → False (as Z < P J = K ≥ L > X ≥ Y  → clear relationship between P and Y cannot be determined. Thus, Conclusion II is false.)

Hence, the "Option c" is the correct answer.

Test: Inequalities - 2 - Question 13

Assuming the given statements to be true in the following question , find which of the given conclusion is/are definitely true and then give your answers accordingly.

Statements:
V < Z ≥ Y ≥ X = A < B  < C < D

Conclusions:

I. X < B

II. Y > A

III. V < Y

Detailed Solution for Test: Inequalities - 2 - Question 13

Given statements: V < Z ≥ Y ≥ X = A < B  < C < D

Conclusions:

I. X < B → True (As X = A < B  which implies X < B . So, Conclusion I is true.)

II. Y > A → True (As Y ≥ X = A  which implies Y > A . So, Conclusion II is true.)

III. V < Y → False (As V < Z ≥ Y  there is no direct relation between V and Y. So, Conclusion II is false)

Thus, Conclusions I or II are true.

Hence, "Option a" is the correct answer.

Test: Inequalities - 2 - Question 14

In the following question, Few statements are given which are followed by some conclusions. According to the given statements, which conclusion is/are definitely true?

Statements:

S = R ≥ Q ≤ P ; N ≤ P ; M < N

Conclusions:

I. M < S

II. M ≥ S

Detailed Solution for Test: Inequalities - 2 - Question 14

Given the logic, M<S (Conclusion I) follows from the statements. Therefore: Only  I follows.

Test: Inequalities - 2 - Question 15

Solve problems using substitution (Mathematical Operations): If A > B, B > C and C > D, then which of the following conclusions is definitely wrong?

Detailed Solution for Test: Inequalities - 2 - Question 15

Given: A > B, B > C and C > D

After combining the operators,

we get: A > B > C > D

Now, checking the options:

Option A: A > D → True (As, A > B > C > D gives A > D)

Option B: A > C → True (As, A > B > C > D gives A > C)

Option C: D > A → False (As, A > B > C > D gives A > D)

Option D: B > D → True (As, A > B > C > D gives B > D)

So, Option C, D > A is definitely wrong.

Hence, the correct answer is "Option c".

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