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impossibility MCQ Questions for Class 10

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2 questions tagged with impossibility.

Question 1/2 Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2-4x+k=0\) की जड़ें \(\sin \theta\) और \(\cos \theta\) हैं, तो (k) का अधिकतम संभव मान क्या है?

If the roots of \(x^2-4x+k=0\) are \(\sin \theta\) and \(\cos \theta\), what is the maximum possible value of (k)?

Explanation opens after your attempt
Correct Answer

A. ऐसा कोई वास्तविक \(\theta\) नहींNo such real \(\theta\)

Step 1

Concept

We would need \(\sin \theta+\cos \theta=4\), but its maximum is \(\sqrt{2}\). Therefore no real \(\theta\) is possible.

Step 2

Why this answer is correct

The correct answer is A. ऐसा कोई वास्तविक \(\theta\) नहीं / No such real \(\theta\). We would need \(\sin \theta+\cos \theta=4\), but its maximum is \(\sqrt{2}\). Therefore no real \(\theta\) is possible.

Step 3

Exam Tip

\(\sin \theta+\cos \theta=4\) होना पड़ेगा, पर इसका अधिकतम \(\sqrt{2}\) है। इसलिए ऐसा वास्तविक \(\theta\) संभव नहीं है।

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Question 2/2 Expert Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 16

\(\sqrt{5}\) की अपरिमेयता में (p) और (q) दोनों (5) से विभाज्य क्यों असंभव है?

Why is it impossible for both (p) and (q) to be divisible by (5) in the irrationality proof of \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि (p) और (q) सरलतम रूप में सहअभाज्य लिए गए थेBecause (p) and (q) were taken coprime in lowest form

Step 1

Concept

In lowest form, numerator and denominator are coprime.

Step 2

Why this answer is correct

Both being divisible by (5) gives a common factor.

Step 3

Exam Tip

So this situation goes against the starting condition. चरण 1: सरलतम रूप में अंश और हर सहअभाज्य होते हैं। चरण 2: दोनों का (5) से विभाज्य होना साझा गुणनखंड देता है। चरण 3: इसलिए यह स्थिति आरंभिक शर्त के विरुद्ध है।

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