CBSE MATHEMATICS • SELECTED CENTRAL & STATE COMPETITIVE EXAMS

AIMS LEARNING

Chapter 1 · APS · AR

Think first. Use AI purposefully. Verify always.

Chapter 1 · Learning journey →

APS–AR · Assertion–Reason

Judge both statements, then their explanatory relationship. Choose a short five-question session.

Session 1 · 5 questions

Question 1 of 5

Choose an answer, then check. A retry hint appears after an incorrect attempt. You can change your choice and try again.

QUESTION 01

Assertion:

(- 2, 3)

is in II. Reason: Negative x and positive y identify II.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 02

Assertion:

(0, - 3)

is in III. Reason: Every y-axis point has x = 0.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 03

Assertion: The distance from

(- 2, 1)

(3, 1)

is 5. Reason: Distance is found by adding the x-coordinates.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 04

Assertion: The origin lies on both axes. Reason: Both axes pass through their common zero.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 05

Assertion: A

(0, 0)

and B

(3, 4)

are 5 units apart. Reason: The midpoint of AB is

(1.5, 2)

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

Question 1 of 5

Feedback is based on reviewed answer keys, not AI. Completion records correct responses after any retries; it is not an exam mark.

Session 2 · 5 questions

Question 1 of 5

Choose an answer, then check. A retry hint appears after an incorrect attempt. You can change your choice and try again.

QUESTION 01

Assertion: A midpoint has integer coordinates whenever endpoints do. Reason: The average of two integers can be a half-integer.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 02

Assertion: Swapping unequal coordinates changes a point. Reason: The first coordinate is horizontal and the second vertical.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 03

Assertion: The distance formula also works for a vertical segment. Reason: The horizontal change is zero for that segment.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 04

Assertion: Equal distance from A and B alone makes P their midpoint. Reason: A midpoint lies on segment AB.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

QUESTION 05

Assertion: A

(0, 0)

, B

(1, 1)

, C

(2, 2)

are collinear. Reason: AB = BC.

Both A and R are true, and R correctly explains A.Both A and R are true, but R does not correctly explain A.A is true, but R is false.A is false, but R is true.

Think independently before checking.

Question 1 of 5

Feedback is based on reviewed answer keys, not AI. Completion records correct responses after any retries; it is not an exam mark.

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