Assertion :Three points $A (x_{1}, y_{1})$ , $B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$ are collinear if $x_{1} + x_{2} + x_{3} = y_{1} + y_{2} + y_{3} .$ Reason: The points $A (x, - x)$ , $B (7, - 5)$ , $C (- 5, 3)$ are collinear if $x = 1$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is incorrect but Reason is correct

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is incorrect but Reason is correct
Assertion is False as the condition for collinearity is $∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$ , using in reason we have $∣ ∣ ∣ ∣ \begin{matrix} x & - x & 1 7 & - 5 & 1 - 5 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow 4 x - 4 = 0 \Rightarrow x = 1$ and reason is True.

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Similar questions

Q. Assertion (A)
If the points A(8, 1), B(k, −4) and C(2, −5) are collinear, then k = 4.

Reason (R)
Three points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are collinear only when x₁(y₂− y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) = 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.
Reason: Equation of the x-axis is y = 0

Choose the correct option.

Q. Assertion: The compressibility factor for

H_{2}

and

H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

H_{2}

and

H e

can be derived from Van der Waal's equation.

Assertion (A) Order and molecularity are same.

Reason (R) Order is determined experimentally and molecularity is the sum of the stoichimetric coeffcient of rate determining elementary step.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Assertion (A) Order of the reaction can be zero or fractional.

Reason (R) We cannot determine order from balanced chemical equation.

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Assertion :Three points A(x1,y1), B(x2,y2) and C(x3,y3) are collinear if x1+x2+x3=y1+y2+y3. Reason: The points A(x,−x), B(7,−5), C(−5,3) are collinear if x=1.

The correct option is C Assertion is incorrect but Reason is correctAssertion is False as the condition for collinearity is ∣∣ ∣∣x1y11x2y21x3y31∣∣ ∣∣=0, using in reason we have ∣∣ ∣∣x−x17−51−531∣∣ ∣∣=0⇒4x−4=0⇒x=1 and reason is True.

Assertion :Three points $A (x_{1}, y_{1})$ , $B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$ are collinear if $x_{1} + x_{2} + x_{3} = y_{1} + y_{2} + y_{3} .$ Reason: The points $A (x, - x)$ , $B (7, - 5)$ , $C (- 5, 3)$ are collinear if $x = 1$ .