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Day 122: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked 2 times: 19 Apr 2025 S1*, 22 Apr 2025 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    115
    If the sum of the squares of the distances of a point P(x,y,z)P(x,y,z) from the three co-ordinate axes is 324 , then the distance of point P from the origin is ...

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  2. Question 2

    Vectors. Asked 2 times: 3 May 2023 S1, 22 Apr 2025 S1 See all 2 times it was asked

    107
    a‾=i^−j^,b‾=j^−k^,c‾=k^−i^\overline{a}=\widehat{i}-\widehat{j},\overline{b}=\widehat{j}-\widehat{k},\overline{c}=\widehat{k}-\widehat{i} then a unit vector d‾\overline{d} such that a‾⋅d‾=0=[b‾c‾d‾]\overline{a}\cdot\overline{d}= 0 = \lbrack\overline{b}\overline{c}\overline{d}\rbrack is

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  3. Question 3

    Binomial Distribution. Asked 2 times: 16 May 2023 S2*, 21 Apr 2025 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    101
    Numbers are selected at random, one at a time from the two-digit numbers 00,01,02,……−00,01,02,\ldots\ldots -, 99 with replacement. An event EE occurs only if the product of the two digits of a selected number is 24. If four numbers are selected, then probability, that the event E occurs at least 3 times, is

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  4. Question 4

    Definite Integration. Asked 2 times: 11 May 2024 S1*, 21 Apr 2025 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    107
    ∫−13(tan⁡−1(xx2+1)+tan⁡−1(x2+1x))dx=\int_{- 1}^{3} \left( \tan^{- 1}\left( \frac{x}{x^{2}+ 1} \right)+\tan^{- 1}\left( \frac{x^{2}+ 1}{x} \right) \right)dx=

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  5. Question 5

    Differential Equations. Asked 2 times: 16 May 2023 S2*, 21 Apr 2025 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    150
    In a culture bacteria count is 1,00,0001,00,000 initially. The number increases by 10%10\% in first 2 hours. In how many hours will the count reach 2,00,0002,00,000, if the rate of growth of bacteria is proportional to the number present?

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