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Day 6: NDA Maths

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

  1. Question 1

    Differential Equations. This type asked 5 times: NDA 1 2017, NDA 2 2018, NDA 1 2020, NDA 1 2021, NDA 1 2026. This one: NDA 1 2026

    79
    What is the solution of the differential equation cos⁡ ⁣(dydx)=p\cos\!\left(\dfrac{dy}{dx}\right)=p when y(0)=qy(0)=q?

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  2. Question 2

    Matrices & Determinants. This type asked 5 times: NDA 1 2021, NDA 2 2021, NDA 1 2022, NDA 2 2025, NDA 1 2026. This one: NDA 1 2026

    15
    If ∣a−bp−qx−yb−cq−ry−zc−ar−pz−x∣=k∣abcpqrxyz∣\begin{vmatrix}a-b & p-q & x-y\\b-c & q-r & y-z\\c-a & r-p & z-x\end{vmatrix}=k\begin{vmatrix}a & b & c\\p & q & r\\x & y & z\end{vmatrix}, then what is the value of kk?

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  3. Question 3

    Sequence & Series. This type asked 5 times: NDA 2 2018, NDA 1 2019, NDA 1 2022, NDA 2 2024, NDA 1 2026. This one: NDA 1 2026

    45
    If pthp^{\text{th}} term of an AP is kk, then what is the sum of pthp^{\text{th}} term, (p+q)th(p+q)^{\text{th}} term and (p−q)th(p-q)^{\text{th}} term of the AP?

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  4. Question 4

    Applications of Integration. This type asked 5 times: NDA 2 2017, NDA 2 2019, NDA 2 2022, NDA 1 2023, NDA 2 2025. This one: NDA 2 2025

    98
    What is the area of the region bounded by ∣x∣≤2k|x|\leq2k and ∣y∣≤k|y|\leq k, where kk is a positive real number?

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  5. Question 5

    Definite Integration. This type asked 5 times: NDA 1 2018, NDA 2 2018, NDA 1 2024, NDA 1 2025, NDA 2 2025. This one: NDA 2 2025

    92
    What is ∫nn+1(x−[x]) dx\int_n^{n+1}(x-[x])\,dx, where [⋅][\cdot] is the greatest integer function and nn is natural number?

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