Q.6 (mcq) equatio let k,l e r such that every solution of the following differential 2k+ly -0 dr satisties y) =0 then (a) 3k+l<0 and k >0 (c)-<0 and k >0 (b) k

Q.6 (McQ) equatio Let k,l E R such that every solution of the following differential 2k+ly -0 dr satisties Y) =0 then (a) 3k+l<0 and k >0 (c)-<0 and k >0 (b) k +l>0 and k <0 (d) k- I > 0, k > 0,1 >0 Q.7 (MCQ) The general solution of the following differential equation with con- stant coetficient dr2 d y approaches zero as r tends to infnity, it (a) b>0 and c < 0 (c) b>0 and c > 0 (b) b>0 and c < 0 (d) b0 and c <0 Q.8 (NAT) Given that there exists common solution to the following problems +29-'f u0)=1 2.-2+ay = 0 then value of a is Q.9 (NAT) Let y(r) be the solution of following differential equation dy dr y(0) = 2, (0) = 20 Find the value of a E |0, 1)) such that the intimum of the set ulr)}; r € R} is greater han or equal to l. Q.10 (NAT) Find the real number such that the following differential equation d+2a- 1)(a -3)+(a-2)y= 0 has a solution of the form of y(r) = Ci cos ir +C2 sin jr for some constats C1, C2, in R