Day 209: NDA Maths

5 questions. Try each one first, then open its answer.

Question 1
Binomial Theorem. Asked once: NDA 2 2019 (same type asked 6 times)
24 $(1 + 2x + x^{2})^{5} + (1 + 4y + 4y^{2})^{5}$
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Question 2
Definite Integration. Asked once: NDA 2 2022 (same type asked 6 times)
96 $\int_{-\pi/2}^{\pi/2}(e^{\cos x}\sin x+e^{\sin x}\cos x)\,dx$
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Question 3
Matrices & Determinants. Asked once: NDA 2 2023 (same type asked 6 times)
5 $A$
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Question 4
Probability. Asked once: NDA 1 2018 (same type asked 6 times)
104 $P(solves A)=0.4, P(solves B)=0.5. P(solves at least one)?$
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Question 5
Probability. Asked once: NDA 1 2018 (same type asked 6 times)
114 $Two fair dice rolled. P(sum=7)?$
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Question 1