CUET · MATHS · PYQ PAPER 2023

How many times a person must toss a fair coin so that the probability of having at least one head is more than 80% ?

Verified Solution

Answer & Solution

Correct Answer

(C) 3

Step-by-step Solution

Detailed explanation

\(P(\text{at least one head}) = 1 - P(\text{no heads})\) \(1 - (0.5)^n > 0.8\) \((0.5)^n \((1/2)^n \(2^n > 5\) For \(n=1\), \(2^1 = 2 \not> 5\) For \(n=2\), \(2^2 = 4 \not> 5\) For \(n=3\), \(2^3 = 8 > 5\) \(n = 3\)

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

Consider the LPP,
Maximize \(z=2 x+3 y\), subject to the conditions,
\(\begin{array}{l}x+y \leq 2 \\x \leq 2 \\x \geq 0, y \geq 0\end{array}\)
then maximum value of the objective function is:

CUET 2023 Hard

Match List - I with List - II.

List - I	List - II
(A) \(\left(y^{\prime \prime}\right)^3+\sin \left(y^{\prime}\right)=e^x\)	(I) 2
(B) \(\left(y^{\prime \prime}\right)^2+\left(y^{\prime}\right)^3=\sin x\)	(II) 1
(C) \(y^{\prime \prime \prime}+5 y^{\prime \prime}+6 y^{\prime}+3 y=\cos x\)	(III) Not defined
	(IV) 3

Choose the correct answer from the options given below :

CUET 2023 Easy

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