Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2023 · Mathematics · Indefinite Integration

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are...

Paragraph: Let f(x)=Pex+Qe2x+Re3xf(x)=P e^x+Q e^{2 x}+R e^{3 x}, where P,Q,RP, Q, R are real numbers. Further f(0)=6,f′(ln⁡3)=282f(0)=6, f^{\prime}(\ln 3)=282 and ∫0ln⁡2f(x)dx=11\int_0^{\ln 2} f(x) d x=11
Question: What is the value of R ?

Options

  1. A11
  2. B22
  3. C33
  4. D44

Correct answer

C. 33

Step-by-step solution

∵Q=2∴R=30−3Q8=30−68=3\because Q=2\therefore \quad R=\frac{30-3 Q}{8}=\frac{30-6}{8}=3
Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026What is ∫ dx 10^x + 10^ -x equal to? NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . Consider… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . What is u +… NDA 2025Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of β ? NDA 2024Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is U(x)… NDA 2024Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of α ? NDA 2024Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further… NDA 2023What is ∫(x^x)^2(1+ x) d x equal to? NDA 2022What is ∫ e^ x (1+ x+x x) d x equal to? NDA 2022If I_1=∫ e^x d x e^x+e^ -x and I_2=∫ d x e^ 2 x +1 , then what is I_1+I_2 equal to? NDA 2022 Full Indefinite Integration list Indefinite Integration JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs