NCERT Exemplar - MCQs

Chapter 6 Class 12 Application of Derivatives
Serial order wise

## (D) Ο/2

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### Transcript

Question 3 The tangent to the curve given by x = et . cost, y = et . sint at t = π/4 makes with x-axis an angle: 0 (B) π/4 (C) π/3 (D) π/2 Given curve π=π^π.ππππ and π=π^π.ππππ Finding slope of tangent ππ/ππ=(ππ/ππ)/(ππ/ππ) π=π^π.ππππ Differentiating π₯ π€.π.π‘ π‘ ππ₯/ππ‘=π^π‘ πππ π‘βπ^π‘ π πππ‘ ππ/ππ=π^π‘ (πππ π‘βπ πππ‘) π=π^π.ππππ Differentiating y π€.π.π‘ ππ¦/ππ‘=π^π‘ π πππ‘+π^π‘ πππ π‘ ππ/ππ=π^π‘ (π πππ‘\+πππ π‘) Now, ππ/ππ=(ππ/ππ)/(ππ/ππ) ππ¦/ππ₯=(π^π‘ (π πππ‘\+πππ π‘)" " )/(π^π‘ (πππ π‘βπ πππ‘)" " ) ππ¦/ππ₯=( (ππππ\+ππππ)" " )/( (ππππβππππ)" " ) Putting π­=π/π β ππ/ππβ€|_(π=π/π)=( (π ππ π/4 \+ πππ  π/4)" " )/( (πππ  π/4 β π ππ π/4)" " ) = (1/β2+1/β2)/(1/β2β1/β2) = (2/(β2))/0 = β Let π½ be the angle made by tangent with the π₯- axis. Slope = π­ππ§β‘π½ β = tanβ‘π tanβ‘γπ=βγ β΄ π½= π/π So, the correct answer is (D)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.