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Day 36: NDA Maths

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

  1. Question 1

    Matrices & Determinants. This type asked 3 times: NDA 1 2020, NDA 1 2022, NDA 1 2024. This one: NDA 1 2024

    11
    Consider the following statements in respect of two nonsingular matrices AA and BB of the same order nn: A. adj(AB)=(adj A)(adj B)\text{adj}(AB)=(\text{adj }A)(\text{adj }B) B. adj(AB)=adj(BA)\text{adj}(AB)=\text{adj}(BA) C. (AB) adj(AB)−∣AB∣In(AB)\,\text{adj}(AB)-|AB|I_n is a null matrix of order nn How many of the above statements are correct?

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  2. Question 2

    Matrices & Determinants. This type asked 3 times: NDA 1 2021, NDA 2 2021, NDA 1 2024. This one: NDA 1 2024

    21
    What is the number of different matrices, each having 4 entries, that can be formed using 1,2,3,41,2,3,4 (repetition is allowed)?

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  3. Question 3

    Permutation & Combination. This type asked 3 times: NDA 1 2017, NDA 2 2018, NDA 1 2024. This one: NDA 1 2024

    3
    What is the sum of all four-digit numbers formed by using all digits 0,1,4,50,1,4,5 without repetition of digits?

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  4. Question 4

    Properties of Triangle. This type asked 3 times: NDA 2 2017, NDA 2 2021, NDA 1 2024. This one: NDA 1 2024

    46
    In a triangle ABCABC, AB=16AB=16 cm, BC=63BC=63 cm and AC=65AC=65 cm. What is the value of cos⁡2A+cos⁡2B+cos⁡2C\cos2A+\cos2B+\cos2C?

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  5. Question 5

    Statistics. This type asked 3 times: NDA 1 2018, NDA 2 2019, NDA 1 2024. This one: NDA 1 2024

    107
    An edible oil is sold at 150, 200, 250, 300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family every year, what is the average price of oil (approximately) per litre?

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