Did not pass emission

EGR (exhaust gas recirculation) valve helps to reduce the exhaust emission of automobiles. It recycles some gases discharged from the engine by returning them to the intake manifold, where the engine can burn these gases again, thus reducing emissions.
The exhaust gas recirculation valve is located in the engine compartment (under the hood). Most engines need exhaust gas recirculation to meet emission standards. If the exhaust gas recirculation valve is broken, the car will not pass the exhaust. My Suzuki Jimny has had such a question before, so I am more qualified to answer this question

The presence of a stored P2413 code means that the powertrain control module (PCM) has detected a malfunction in the exhaust gas recirculation (EGR) system. The EGR system, used in ODB-II equipped vehicles, is designed to help reduce nitrogen oxide emissions in engine exhaust, so the answer is no

What make , model an year vehicle ? engine ? Typically EGR valves open on deceleration ,not acceleration . Pupose for EGR ? do you know what it's pupose is ?

Exhaust gas recirculation In internal combustion engines, exhaust gas recirculation (EGR) is a nitrogen oxide (NOx) emissions reduction technique used in petrol/gasoline and diesel engines. EGR works by recirculating a portion of an engine's exhaust gas back to the engine cylinders.

Your best bet , take it to a qualified repair shop.

Doesn't have EGR valve . How many miles on the truck ?
What Causes High NO (NOx)? Nitrogen Oxide or NO is created when an engine's combustion chamber temperature reaches over 2500F. Vehicle manufacturers have designed several systems, which when working properly, lower nitric oxide emissions. Below are common failures which may cause your car, truck, van, suv, or motorhome to produce high high nitric oxide. 1. Lean Fuel Mixture - Lean fuel mixtures cause high NOx. A lean fuel mixture exists when less fuel then required is delivered to the combustion chambers or when more air then necessary is added to the fuel. In either case the lack of gasoline needed to cool the combustion chambers down is not present. Combustion temperatures increase causing high nitric oxide emissions. A lean fuel condition may be due to a vacuum leak/s and/or defective fuel control components, such as the Air Flow Meter, Engine Coolant Temperature Sensor, and O2 sensors. Read about Oxygen Sensor.
2. Defective EGR System- The Exhaust Gas Recirculation system is designed to reduce NO. The EGR system consists of an EGR valve, EGR pressure sensor, vacuum hoses, and one or more vacuum switching valves or solenoids. Later model vehicles may be equipped with electronically controlled EGR valves, which do not require vacuum lines or switching solenoids. Electronic EGR systems will have these components built in.
The EGR system's job is to re-route a small amount of exhaust gas back into the intake manifold to help reduce combustion chamber temperatures. As mentioned above NOx is created when combustion chamber temperatures reach above 2500F. By recirculating exhaust gas back into the intake, a small amount of the air/fuel mixture is replaced with inert gas, reducing combustion temperatures. Read about EGR System.
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3. Defective Catalytic Converter (CAT) Some vehicle manufactures have designed their cars to operate without EGR valves. Non-EGR equipped vehicles rely heavily on the Catalytic Converter to assist in the reduction of NO. These vehicles have tendencies to develop CAT problems sooner then those which are equipped. If you own a non-EGR equipped vehicle, and have failed the emissions test for high NOx, pay close attention to the Catalytic Converter. Read about Catalytic Converter
4. High Engine Mileage - Over an engine's lifetime, carbon build-up develops in the engine's combustion chambers. The more miles on your engine, the more carbon build-up on the pistons, cylinder heads and valves. Carbon build-up decreases the available space for the air/fuel mixture to combust, and causes higher cylinder compression. High compression results in high temperatures and high NOx. Keep in mind this problem is usually seen in vehicles with over 150,000 miles which have been poorly maintained. The solution to this problem is called De-Carbonizing. It usually costs around two labor hours at a smog check repair station. It will remove a good amount of carbon out of an engine. This will increase combustion space, lower compression and lower NOx.
5. Engine Overheating - Inadequate engine cooling can will high NOx. If your vehicle's cooling system is not working efficiently, (i.e. bad radiator, thermostat, hoses) high NOx will be created. Remember high NOx nitric oxide is created when an engine's combustion chamber temperatures reach over 2500F. You will want to make sure your vehicle's cooling system is working properly, and your vehicle's temperature gauge is always indicating normal.

In internal combustion engines,exhaust gas recirculation (EGR) is a nitrogen oxide (NOx) emissions reduction technique used in petrol/gasoline and diesel engines.EGR works by recirculating a portion of an engine's exhaust gas back to the engine cylinders. Thers a hose going down the rear of the engine to the exhaust pipe. It recirculates the portion of the gasses coming out of the engine by putting in back into the intake manifold, where the engine can burn it again, thereby reducing the emissions. The EGR valve is located in the engine compartment (underneath the hood). Usually on the side with the air intake manifold attatched to the side frame rail

P0401
EGR stands for Exhaust Gas Recirculation. It is part of the vehicle emmissions system, and is used to reduce combustion temperature and pressure to control Oxides of Nitrogen. There are generally three parts to the EGR system: the EGR valve, an actuator solenoid, and a differential pressure sensor EGR (DPFE). These things work together to deliver the correct amount of recirculation based on engine temperature, load, etc. The P0401 code means that OBD detected an insufficient amount of EGR.

P0402
EGR stands for Exhaust Gas Recirculation. It is part of the vehicle emmissions system, and is used to reduce combustion temperature and pressure to control Oxides of Nitrogen. There are generally three parts to the EGR system: the EGR valve, an actuator solenoid, and a differential pressure sensor (DPF). These things work together to deliver the correct amount of recirculation based on engine temperature, load, etc. The P0402 code means that OBD detected an excessive amount of EGR.

There sound like a bad EGR and need replace it.

P0755 Shift Solenoid B Malfunction and P0756 Shift Solenoid B Performance or Stuck Off. First I suggtes check leve fluids and preventive maintenance.

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An inadequate functioning egr system.The exhaust gas recirculation valve uses spent exhaust gases to line the cylinder walls with burnt gases.The purpose of this is to keep the cylinder temperature lower to reduce emissions of oxides of nitrogen.

The most likely cause of this is a faulty exhuast recirculation system.It is used to cool the combustion process preventing the formation of nitrous oxide emissions. The main building block of acidic rain.Use your emission diagram and locate the EGR valve.You will need specialized equipment to check it. Other than taking it off and checking for blocked passages from carbon build up there is little you can do yourself.