Day 14: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

Question 1 (case study, 2 parts)
Limits & Continuity. This type asked 4 times: NDA 2 2021, NDA 2 2023, NDA 1 2024, NDA 1 2025. This one: NDA 1 2025
Let the function $f(x) = \sin[x]$ , where $[\cdot]$ is the greatest integer function and $g(x) = |x|$ .
83 $\lim_{x\to 0}\{f(x) \cdot g(x)\}$
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84 $\lim_{x\to 0} \frac{f(x)}{g(x)}$
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Question 2
Matrices & Determinants. This type asked 4 times: NDA 2 2017, NDA 2 2019, NDA 2 2023, NDA 1 2025. This one: NDA 1 2025
27 $A = \begin{pmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{pmatrix}$
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Question 3
Permutation & Combination. This type asked 4 times: NDA 1 2019, NDA 1 2020, NDA 1 2022, NDA 1 2025. This one: NDA 1 2025
28 $r$
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Question 4
Permutation & Combination. This type asked 4 times: NDA 1 2020, NDA 1 2022, NDA 2 2024, NDA 1 2025. This one: NDA 1 2025
18 $In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?$
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Question 5 (case study, 2 parts)
Probability. This type asked 4 times: NDA 1 2017, NDA 2 2017, NDA 1 2020, NDA 1 2025. This one: NDA 1 2025
A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
109 $What is the probability that the committee includes exactly 3 gentlemen?$
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110 $What is the probability that the committee includes at least 2 ladies?$
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Question 1 (case study, 2 parts)

Question 2

Question 3

Question 4

Question 5 (case study, 2 parts)