Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

STATEMENT 1: If y= (m ⁻¹ x ) then (1-x^2 ) y_ n+2 -(2 n+1) x y_ n+1 + (n^2-m^2 ) y_n=0 [ y_n is n th derivative of y w.r.t. x ] STATEMENT 2: d^n d x^n [u(x) v(x)]=u_n v₀+ ^n C₁ u_ n-1 v₁+ ^n C₂ u_ n-2 v₂+ . .+ ^n C_n u₀ v_n [u_n, v_n . denote nth derivative of u(x), v(x) w.r.t. x ]

Options

  1. ABoth the statements are true and Statement 2 is correct explanation of Statement 1.
  2. BBoth the Statements are true and Statement 2 is not the correct explanation of Statement 1.
  3. CStatement 1 is true and Statement 2 is false.
  4. DStatement 1 is false and Statement 2 is true.

Correct answer

D. Statement 1 is false and Statement 2 is true.

Step-by-step solution

y₁= (m ⁻¹ x ) m 1-x^2 aligned & 1-x^2 y₁=m (m ⁻¹ x ) & (1-x^2 ) y₂-x y₁+m^2 y=0 & [ (1-x^2 ) y_ n+2 +n(-2 x) y_ n+1 + n(n-1) 2 (-2) y_n ]- [x y_ n+1 +n 1 y_n ]+m^2 y_n=0 aligned Simplifying we get, (1-x^2 ) y_ n+2 -(2 n+1) y_ n+1 - (n^2-m^2 ) y_n=0

Practice Differentiation on Quantrex Academy →

More from Differentiation

Let R denote the set of all real numbers. Consider the polynomial function f: R R defined by f(x) = d¹⁰ dx¹⁰ ((x^2 - 1)¹⁰ ) , for all x R . Here d¹⁰ dx¹⁰ ((x^2 - 1)¹⁰ ) is the 10th 2026Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x R , f'(1) = 2g'(1) = 4 and g(2) = 3f(2) = 9 . Then f(25) - g(25) is equal to : 2026Let f be a real polynomial of degree n such that f(x) = f'(x) f''(x) , for all x R . If f(0) = 0 , then 36 (f'(2) + f''(2) + ₀^2 f(x) ,dx ) is equal to: 2026Let f(x)=x³+x² f^ (1)+2 x f^ (2)+f^ (3), x R . Then the value of f^ (5) is: 2026Let R denote the set of all real numbers. Let f: R R and g: R (0,4) be functions defined by f(x)= _e (x^2+2 x+4 ) , and g(x)= 4 1+e^ -2 x Define the composite function f g⁻¹ by (f 2025Let f: R R be a twice differentiable function such that ( x y)(f(2 x+2 y)-f(2 x-2 y))=( x y )(f(2 x +2 y )+f(2 x -2 y )) , for all x , y R . If f^ (0)= 1 2 , then the value of 24 f 2025If _e y=3 ⁻¹ x , then (1-x^2 ) y^ -x y^ at x= 1 2 is equal to 2024Let f(x)=a x^3+b x^2+c x+41 be such that f(1)=40, f^ (1)=2 and f^ (1)=4 . Then a ^2+ b ^2+ c ^2 is equal to: 2024 Full Differentiation list All Most Important Selected Qs for JEE Advanced PYQs