CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## (a) ±  1  (b) −1      (c) ±  1/2  (d) 1/2

This question is inspired from -   Question 21 - CBSE Class 12 Sample Paper for 2021 Boards

### Transcript

Question 2 The value of k (k < 0) for which the function f defined as π (π₯)={β((1 βcosβ‘ππ₯)/(π₯ sinβ‘π₯ ),π₯β 0@1/2, π₯=0)β€ is continuous at x = 0 is : (a) Β± 1 (b) β1 (c) Β± 1/2 (d) 1/2 Given that function is continuous at x = 0 π(π₯) is continuous at x = 0 i.e. (π₯π’π¦)β¬(π±βπ) π(π)=π(π) Limit at x β 0 (πππ)β¬(π₯β0) f(x) = (πππ)β¬(ββ0) f(h) = limβ¬(hβ0) (1 β cosβ‘πβ)/(β (sinβ‘β) ) = limβ¬(hβ0) (π γπ¬π’π§γ^πβ‘γππ/πγ)/(β (sinβ‘β)) = limβ¬(hβ0) (2 sin^2β‘γπβ/2γ)/1 Γ1/(β (sinβ‘β)) = (πππ)β¬(π‘βπ) (π γπππγ^πβ‘γππ/πγ)/(ππ/π)^π Γ (ππ/π)^π/(π (πππβ‘π)) = limβ¬(hβ0) (2 sin^2β‘γπβ/2γ)/(πβ/2)^2 Γ (π^2 β^2)/(4β (sinβ‘β)) = limβ¬(hβ0) sin^2β‘γπβ/2γ/(πβ/2)^2 Γ (π^π π)/(π(πππβ‘π)) = π^π/π limβ¬(hβ0) sin^2β‘γπβ/2γ/(πβ/2)^2 Γ β/sinβ‘β = π^2/2 limβ¬(hβ0) sin^2β‘γπβ/2γ/(πβ/2)^2 Γlimβ¬(hβ0) β/sinβ‘β = π^2/2 Γ 1 Γ 1 = π^π/π Now, (π₯π’π¦)β¬(π±βπ) π(π)=π(π) π^2/2 = 1/2 π^2 =1 π =Β±π But, given that k < 0 Thus, only value is k = β1 So, the correct answer is (b)

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.