CUET · MATHS · PYQ PAPER 2023

If the points \((2,1),(-1,4)\) and \((a, 3)\) are collinear then the value/(s) of a is/(are) :

A [1,2]
B [3,0]
C [0]
D [2,1]

Verified Solution

Answer & Solution

Correct Answer

(C) [0]

Step-by-step Solution

Detailed explanation

\(m_{12} = \frac{4-1}{-1-2} = -1\) \(m_{13} = \frac{3-1}{a-2} = \frac{2}{a-2}\) \(m_{12} = m_{13} \Rightarrow -1 = \frac{2}{a-2}\) \(-(a-2) = 2\) \(-a+2 = 2\) \(-a = 0\) \(a = 0\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If A and B are two independent events then,
Match List I with List II

List - I	List - II
(A) \(P(A \cup B)\)	(I) \(P\left(A^{\prime}\right) P\left(B^{\prime}\right)\)
(B) P(not A or not B)	(II) \(P(A) ; P(B) \neq 0\)
(C) \(P(A / B)\)	(III) \(1-P\left(A^{\prime}\right) P\left(B^{\prime}\right)\)
(D) P(neither A nor B)	(IV) \(1-P(A) P(B)\)

Choose the correct answer from the options given below:

CUET 2023 Easy

For the set of all straight lines in a plane, the relation of "perpendicularity" is:
(A) reflexive but neither symmetric nor transitive.
(B) symmetric but neither reflexive nor transitive.
(C) transitive but neither reflexive nor symmetric.
(D) neither reflexive nor symmetric nor transitive.
(E) reflexive, symmetric but not transitive.
Choose the correct answer from the options given below:

CUET 2023 Easy

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