Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10 Important

Misc 11 Important

Misc 12 Important

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16 (MCQ)

Question 1 (a)

Question 1 (b) Important

Question 2

Question 3 Important

Question 4 (MCQ) Important

Question 5 (MCQ) Important You are here

Question 6 (MCQ)

Question 7 (MCQ) Important

Question 8 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken & Given Equation of tangent 𝑦=𝑚𝑥+1 & Curve is 𝑦^2=4𝑥 We know that Slope of tangent to the Curve is 𝑑𝑦/𝑑𝑥 𝑦^2=4𝑥 Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken Since (𝒉 , 𝒌) lies on line 𝑘=𝑚ℎ+1 Since (𝒉 , 𝒌) lies on curve 𝑘^2=4ℎ ℎ=𝑘^2/4 Putting (2) in (1) 𝑘=𝑚(𝒌^𝟐/𝟒)+1 4𝑘=𝑚𝑘^2+4 𝑚𝑘^2−4𝑘+4=0 Since tangent touches the curve at only one point There is only one value of k So, this quadratic equation has only one root Thus, Discriminant of Quadratic equation = 0 𝒃^𝟐−𝟒𝒂𝒄=𝟎 (−4)^2−4 × 𝑚 × 4=0 16−16𝑚=0 𝑚=16/16 𝑚=1 Hence Correct Answer is (A)