Statement-1 (A): 13 20 14 20 and 15 20 are three rational numbers… - Vidyadip

MCQ

Statement-1 (A): $\frac{13}{20}$ $\frac{14}{20}$ and $\frac{15}{20}$ are three rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$
Statement-2 (R): A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.

✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.

✓

Answer

Correct option: A.

Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3

(a)
Statement-2 is true. Using statement-2, a rational number between $\frac{1}{2}$and $\frac{4}{5}$ is $\frac{1}{2}\left(\frac{1}{2}+\frac{4}{5}\right)=\frac{13}{20}$. But, $\frac{4}{5}=\frac{16}{20}$, So, rational numbers between $\frac{13}{20}$ and $\frac{16}{20}$ are $\frac{14}{20}$ and $\frac{15}{20}$
Hence, $\frac{13}{20}$, $\frac{14}{20}$ and $\frac{15}{20}$ are rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$.Hence, statement-1 is true and statement-2 is correct explanation for statement-1. So, option (a) is correct.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Number System→Number System — all question types→Maths STD 9 question papers→CBSE Board STD 9 question papers→CBSE Board question paper generator→

Similar questions

Assertion (A): Two opposite angles of a parallelogram are $(3 x-2)^{\circ}$ and $(50-x)^{\circ}$. The measure of one of the angle is $37^{\circ}$.
Reason (R): Opposite angles of a parallelogram are equal.

Statement-1 (A): If two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle, then the two triangles are congruent.
Statement-2 (R): If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles are congruent.

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The point $(2, 2)$ is the solution of $x + y = 4$.
Reason: Every point which satisfy the linear equation is a solution of the equation.

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A point both of whose coordinates are negative will lie in third quadrants.
Reason: If the ordinate of a point is equal to its abscissa, then the point lies either in the first quadrant or in the second quadrant.

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The square root of any primenumber is irrational.
Reason: The rationlizong factor of $ 2+\sqrt7$ is $5+\sqrt3$

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Abscissa of a point is positive in $I$ and $IV$ quadrant.
Reason: If $(x + 2, 4) = (5, y - 2)$, then coordinates $(x, y)$ are $(3, 6).$

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In $\triangle\text{ABC}, E$ and $F$ are the midpoints of $AC$ and $AB$ respectively. The altitude $AP$ at $BC$ intersects $FE$ at $Q.$ Then, $AQ = QP.$
Reason: $Q$ is the midpoint of $AP.$

Statement-1 (A): If $x+2 a$ is a factor of $f(x)=x^5-4 a^2 x^3+2 x+2 a+3$, then $2 a-3=0$.
Statement-2 (R): If $f(x)$ is divisible by $(a x+b)$, then $f\left(-\frac{b}{a}\right)=0$.

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.
Reason: If the pair of lines are parallel, then the pairs has solution and is called inconsistent pair of equations.

Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $2x + 3y = 4.37$ is a linear equation in two variable.
Reason: $ax + b$ is also written as $ax + 0y + b$.