NCERT Exemplar - MCQs

Chapter 6 Class 12 Application of Derivatives
Serial order wise

## (D) π/2

### 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)