Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

If \[y = \frac{ax + b}{x^2 + c}\] then (2xy₁ + y)y₃ = 

If \[y = \log_e \left( \frac{x}{a + bx} \right)^x\] then x³ y₂ =

If x = f(t) cos t − f' (t) sin t and y = f(t) sin t + f'(t) cos t, then\[\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 =\]

If \[y^\frac{1}{n} + y^{- \frac{1}{n}} = 2x, \text { then find } \left( x^2 - 1 \right) y_2 + x y_1 =\] ?

If \[\frac{d}{dx}\left[ x^n - a_1 x^{n - 1} + a_2 x^{n - 2} + . . . + \left( - 1 \right)^n a_n \right] e^x = x^n e^x\] then the value of a_r, 0 < r ≤ n, is equal to 

If y = xⁿ⁻¹ log x then x² y₂ + (3 − 2n) xy₁ is equal to

If xy − log_e y = 1 satisfies the equation \[x\left( y y_2 + y_1^2 \right) - y_2 + \lambda y y_1 = 0\]

If y² = ax² + bx + c, then \[y^3 \frac{d^2 y}{d x^2}\] is