Class X Session 2023-24 Question 3

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 3

The lines representing the given pair of linear equations are non-intersecting. Which of the

following statements is true? 

$$\begin{array}{rlcr}(a)& \frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}& & \\ (b)& \frac{a1}{a2}=\frac{b1}{b2}\ne \frac{c1}{c2}& & \\ (c)& \frac{a1}{a2}\ne \frac{b1}{b2}=\frac{c1}{c2}& & \\ (d)& \frac{a1}{a2}\ne \frac{b1}{b2}\ne \frac{c1}{c2}& & \end{array}$$

Explanation : 

Let us examine each choice and determine the right response.

$$(a)\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}$$

This option suggests that the ratios of the coefficients for x and y and the constant terms in the two equations are all equal . In terms of slopes, it implies that the slopes of the two lines are equal.

Additionally, it suggests that the lines pass through the same point on the y-axis. This option is not correct.

$$(b)\frac{a1}{a2}=\frac{b1}{b2}\ne \frac{c1}{c2}$$ --Correct Ans

$$\begin{array}{rlcr}& \frac{a1}{a2}=\frac{b1}{b2}:& & \end{array}$$

This part implies that the slopes of the two lines are equal. This suggests that the lines have the same steepness.

$$\begin{array}{rlcr}& \ne \frac{c1}{c2}:& & \end{array}$$

This part indicates that the constant terms (y-intercepts) of the two lines are not equal. This means that the lines do not pass through the same point on the y-axis.

Putting it together, option (b) describes a situation where the slopes of the two lines are equal, indicating that these lines have the same steepness, but they do not pass through the same point on the y-axis. This scenario is consistent with the condition of non-intersecting lines.

$$(c)\frac{a1}{a2}\ne \frac{b1}{b2}=\frac{c1}{c2}$$ 

This option suggests that the slopes of the two lines are not equal, but the constant terms (y-intercepts) are equal. In other words, the lines have different steepness, but they pass through the same point on the y-axis. - Not correct 

$$(d)\frac{a1}{a2}\ne \frac{b1}{b2}\ne \frac{c1}{c2}$$ 

This option suggests that none of the ratios of coefficients are equal. In other words, the slopes of the lines are all different, and the constant terms (y-intercepts) are also different. - Not correct 

Guess the Option and comment below  👇