Will diode be turned on?
I assumed that D1 conducts and found the current 0.003A.But I assumed D1 conducts it may not what should I do from here?

If

you are using an &quot;on/off&quot; model of diode conduction (as opposed to an exponential current/voltage relationship)
and you have calculated all the voltages and currents in the circuit assuming all the diodes conduct,
and for every node in your circuit, the sum of all currents entering that node is equal to the sum of all the currents leaving that node,
the (conventional) current through each diode flows from positive to negative

then

you are done.

For example if you have this circuit:



simulate this circuit &ndash; Schematic created using CircuitLab
and you assume that there is 0.7V across D1, and you calculate that the currents through the components are

\$I_{R1} = 20\$ mA
\$I_{R2} = 7\$ mA
\$I_{R3} = 13\$ mA (which is positive)

and the voltages across components are

\$V_{R1} = 2\$ V
\$V_{R2} = 0.7\$ V
\$V_{D1} = 0.7\$ V

And the sum of voltages around any loop is 0, and the algebraic sum of currents into any node is 0 and the (conventional) current through the diode D1 is from positive to negative. So you are done.
However, suppose you are analyzing the following circuit



simulate this circuit
And you calculate as follows:

D1 has a drop of 0.7V
R2 is in parallel with D1, so it also has a drop of 0.7V
R1 has a voltage drop of V1 - \$V_{D1}\$ = 2.7 - 0.7 = 2V
R1 has a current of \$\frac{2V}{440\Omega} = \$ 4.545 mA
R2 has a current of \$\frac{0.7V}{100\Omega} = \$ 7 mA
D1 has a current of \$I_{R1} - I_{R2} = 4.545-7 = -2.455\$ mA

Then you would see that the (conventional) current in D1 is flowing from the negative to the positive. So, the assumption that D1 conducting is invalid, and you need to recalculate the voltages and currents in the circuit using the assumption that D1 is not conducting.
Now, it is possible that you calculated the voltages and currents in the circuit in a different way that presented here. Calculating in a different way may result in different values. However, in the end, the signal that the diode is not conducting is one of the following.

the algebraic sum of voltages around a loop is not 0
the algebraic sum of currents into a node is not 0
the (conventional) current through the diode is from negative to positive

Any of these conditions signify that the assumption about the diode is incorrect.