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Day 43: MHT-CET Maths

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

  1. Question 1

    Differential Equations. This type asked 5 times: 2 May 2023 S2, 11 May 2023 S2, 12 May 2024 S2, 19 Apr 2025 S1, 22 Apr 2025 S1. This one: 22 Apr 2025 S1 See all 5 of this type

    101
    If y=y(x)y=y(x) and (2+sin⁡xy+1)dy dx=−cos⁡x,y(0)=1\left( \frac{2 + \sin x}{y+ 1} \right)\frac{dy}{\text{ }dx}= - \cos x,y(0) = 1, then y(π2)=y\left( \frac{\pi}{2} \right)=

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  2. Question 2

    Probability Distribution. This type asked 5 times: 2 May 2023 S1, 11 May 2023 S2, 16 May 2023 S2, 20 Apr 2025 S2, 21 Apr 2025 S1. This one: 21 Apr 2025 S1 See all 5 of this type

    111
    A random variable X takes values 0,1,2,30,1,2,3, ____\_\_\_\_ with probabilities. P(X=x)=k(x+1)(12)x,kP(X =x) = k(x+ 1)\left( \frac{1}{2} \right)^{x},k is a constant, then P(X=1)=P(X= 1) =

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  3. Question 3

    Linear Programming. This type asked 5 times: 16 May 2023 S2, 10 May 2024 S2, 12 May 2024 S1, 13 May 2024 S2, 20 Apr 2025 S2. This one: 20 Apr 2025 S2 See all 5 of this type

    105
    A scholarship amount is given by z=550x+300yz= 550x+ 300y and is to be distributed among xx boys and yy girls. From the graph given below the maximum amount of scholarship is ____\_\_\_\_

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  4. Question 4

    Applications of Derivative. This type asked 5 times: 2 May 2023 S2, 3 May 2023 S2, 11 May 2023 S2, 9 May 2024 S2, 14 May 2024 S1. This one: 14 May 2024 S1 See all 5 of this type

    111
    The maximum value of the function f(x)=3x3−18x2+27x−40f(x)=3x^3-18x^2+27x-40 on the set S={x∈R ∣ x2+30≤11x}S=\{x\in\mathbb{R}\,|\,x^2+30\leq11x\} is

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  5. Question 5

    Vectors. This type asked 5 times: 2 May 2023 S1, 10 May 2023 S2, 16 May 2023 S2, 10 May 2024 S1, 11 May 2024 S2. This one: 11 May 2024 S2 See all 5 of this type

    145
    If a⃗=2i^+3j^+2k^\vec{a}=2\hat{i}+3\hat{j}+2\hat{k}, b⃗=2i^+j^−k^\vec{b}=2\hat{i}+\hat{j}-\hat{k} and c⃗=3i^−j^\vec{c}=3\hat{i}-\hat{j} are such that a⃗+λb⃗\vec{a}+\lambda\vec{b} is perpendicular to c⃗\vec{c}, then the value of λ\lambda is

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