List I | List II | ||
---|---|---|---|
A | Pterophyllum | I | Hag fish |
B | Myxine | II | Saw fish |
C | Pristis | III | Angel fish |
D | Exocoetus | IV | Flying fish |
List-I | List-II | ||
A | Rhizopus | I | Mushroom |
B | Ustilago | II | Smut fungus |
C | Puccinia | III | Bread mould |
D | Agaricus | IV | Rust fungus |
A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )
Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]