Hare Krishna,
The following is the story of how Drona was deceived:
Krishna replied, “What you say is true, O King. Drona cannot be checked as long as he stands with his weapons raised. But if he lowers them, he can be slain. I think if he hears that his son has been killed, he will lose all heart for the fight. Tell him that Asvatthama is dead. Then he will lower his bow and we will kill him.”

Arjuna was shocked. “I cannot accept this, O Madhava.” But Bhima, upon hearing Krishna’s words, immediately broke away. He raced into a nearby Kaurava elephant division. At its head rode Indravarma, the Malava ruler. Bhima knew his elephant was named Asvatthama. Whirling his iron mace, the Pandava smashed the beast and slew it and its rider together. He then rushed over to Drona and bellowed out, “Asvatthama is slain! Asvatthama is slain!” As he deceived Drona, his voice was tremulous and his heart wavered, but he knew it was Krishna’s instruction, so he called out, again and again, telling Drona that Asvatthama was dead.
Hearing Bhīma’s words, Drona stopped fighting. His limbs seemed to dissolve like sand in water. However, recalling his son’s prowess, he decided it could not be true. Bhima was known to be capricious. It would not be beyond him to speak an untruth in anger or in jest. Drona rallied himself and resumed his assault on the Pandavas. Dristadyumna had reached him and they had begun to fight again. Holding off Dristadyumna’s attack, the Kuru general continued annihilating the Pandava forces. He invoked the terrible Brahma weapon. Warriors fell to the earth like trees uprooted in a tempest. Heads and arms flew about as Drona’s arrows fell on his enemies. In a short time, he had killed ten thousand chariot fighters before Yudhisthira’s eyes, even while Dristadyumna assailed him with all his strength. Drona stood on the battlefield like a blazing fire without a single curl of smoke.

Drona looked around. Dristadyumna was still near him, roaring out his challenge. Perhaps the time for the prophesy’s fulfilment had arrived. Drona’s arms fell to his side. He could not continue. Bhīma’s words still troubled him, and the sages’ speech pained him even more. Could Asvatthama actually be dead? Who could he ask and be sure to receive the truth? Seeing Yudhisthira not far away, the Kuru general went toward him. He was the one to ask––Yudhisthira would speak no lie.
Krishna saw Drona coming toward Yudhisthira and said, “Save us from Drona, O King. If he fights for even a half-day more, your army will be finished. Under the circumstances, falsehood is better than truth. Speaking falsehood in order to preserve life is not a sin.”

Krishna cited a scriptural passage that sanctioned lying under certain circumstances, including times when life was endangered. Yudhisthira reflected on Krishna’s words. He could not ignore them. He had never in his life spoken even an ambiguity. The thought of a lie was difficult to face. Yet if Drona was not checked, his forces would be defeated. The Pandava remembered Drona’s own prophetic statement at the beginning of the war: that he would be overpowered at a time when he heard something disagreeable from a creditable source. Reluctantly, Yudhisthira agreed to Krishna’s suggestion. As the Kuru preceptor approached him, he gave him the false news. “Asvatthama is dead,” he called out, adding inaudibly at the end, “the elephant,” as he could not tell an utter untruth under any circumstances.

As soon as Yudhisthira spoke, Drona felt his heart sink into fathomless grief. His agony was compounded by the sages’ words, which made him feel like he had offended the Pandavas. Distracted by sorrow, he moved away from Yudhisthira with his weapons lowered. Dristadyumna attacked. Drona was struck all over, but he did not resist. He was plunged into despair. Dristadyumna attacked him with even more force and the old Kuru chief, incited to anger, finally raised his bow to fight back. Displaying his incomparable lightness of hand, he cut down all of Dristadyumna’s arrows. He chanted mantras, invoking celestial weapons to destroy Dristadyumna, but they no longer appeared at his command. Marvelling, he fired volleys of ordinary arrows at his foe. Suddenly, he saw that his stock of shafts, inexhaustible for the last fifteen days, was empty.

Arjuna had been shouting at Dristadyumna to capture Drona and bring him alive to Yudhisthira. He was mortified by Dristadyumna’s viciousness. His heart melted with sorrow at the cruel killing of his beloved teacher. Bhima, however, cheered and ran over to joyfully embrace Dristadyumna. Yudhisthira was afflicted by different emotions. Overjoyed that the hostilities would soon end, he was nevertheless full of misgivings that Drona’s death had been brought about by deceit. Like Arjuna, he was also saddened to see Dristadyumna mercilessly butcher his preceptor.

Krishna Gyan to Guru Drona | Difference between Love and Attachment | प्रेम और मोह के बीच का अंतर