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lambda MCQ Questions for Class 10

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3 questions tagged with lambda.

Question 1/3 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (\(\lambda+1\)x-2-2\(\lambda-2\)x+\(\lambda+1\)=0) के वास्तविक और समान मूलों के लिए \(\lambda\) क्या होगा?

What will \(\lambda\) be for real and equal roots of (\(\lambda+1\)x-2-2\(\lambda-2\)x+\(\lambda+1\)=0)?

Explanation opens after your attempt
Correct Answer

A. \(\lambda=\frac{1}{4}\)

Step 1

Concept

Here (D=4\(\lambda-2\)2-4\(\lambda+1\)2=12\(1-2\lambda\)). From (D=0), \(\lambda=\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\lambda=\frac{1}{4}\). Here (D=4\(\lambda-2\)2-4\(\lambda+1\)2=12\(1-2\lambda\)). From (D=0), \(\lambda=\frac{1}{2}\).

Step 3

Exam Tip

यहाँ (D=4\(\lambda-2\)2-4\(\lambda+1\)2=12\(1-2\lambda\)) है। (D=0) से \(\lambda=\frac{1}{2}\) मिलता है।

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Question 2/3 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण (x-2+2\(\lambda-1\)x+\lambda-2+1=0) के वास्तविक मूलों के लिए \(\lambda\) पर सही शर्त क्या है?

What is the correct condition on \(\lambda\) for real roots of (x-2+2\(\lambda-1\)x+\lambda-2+1=0)?

Explanation opens after your attempt
Correct Answer

A. \(\lambda\le0\)

Step 1

Concept

Here (D=4\(\lambda-1\)2-4\(\lambda^2+1\)=-8\lambda). For real roots \(D\ge0\), so \(\lambda\le0\).

Step 2

Why this answer is correct

The correct answer is A. \(\lambda\le0\). Here (D=4\(\lambda-1\)2-4\(\lambda^2+1\)=-8\lambda). For real roots \(D\ge0\), so \(\lambda\le0\).

Step 3

Exam Tip

यहाँ (D=4\(\lambda-1\)2-4\(\lambda^2+1\)=-8\lambda) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(\lambda\le0\)।

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Question 3/3 Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

\(2x^2+\lambda x+8=0\) की जड़ें समान हों, तो \(\lambda\) के मान क्या होंगे?

If \(2x^2+\lambda x+8=0\) has equal roots, what are the values of \(\lambda\)?

Explanation opens after your attempt
Correct Answer

A. (8) और (-8)(8) and (-8)

Step 1

Concept

For equal roots, put (D=0). From \(\lambda^2-64=0\), we get \(\lambda=\pm8\).

Step 2

Why this answer is correct

The correct answer is A. (8) और (-8) / (8) and (-8). For equal roots, put (D=0). From \(\lambda^2-64=0\), we get \(\lambda=\pm8\).

Step 3

Exam Tip

समान जड़ों के लिए (D=0) रखें। \(\lambda^2-64=0\) से \(\lambda=\pm8\) मिलता है।

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