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Day 320: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 4 May 2023 S1 (same type asked 3 times) See all 3 of this type

    128
    A wire of length 2 units is cut into two parts, which are bent respectively to form a square of side xx units and a circle of radius rr units. If the sum of the areas of square and the circle so formed is minimum, then

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  2. Question 2

    Line and Plane. Asked once: 19 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    135
    The coordinates of the foot of the perpendicular drawn from a point P(−1,1,2)P( - 1,1,2) to the plane 2x−3y+z−11=02x- 3y+z- 11 = 0 are

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  3. Question 3

    Applications of Derivative. Asked once: 16 May 2023 S2 (same type asked 3 times) See all 3 of this type

    120
    If f(x)=asin⁡x+bcos⁡xcsin⁡x+dcos⁡xf(x) = \frac{a\sin x + b\cos x}{c\sin x + d\cos x} is decreasing for all xx, then

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  4. Question 4

    Determinants and Matrices. Asked once: 11 May 2024 S2 (same type asked 3 times) See all 3 of this type

    144
    If A=(i110)A=\begin{pmatrix}i&1\\1&0\end{pmatrix} where i=−1i=\sqrt{-1} and B=A2029B=A^{2029}, then B−1=B^{-1}=

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  5. Question 5

    Applications of Derivative. Asked once: 14 May 2024 S2 (same type asked 3 times) See all 3 of this type

    124
    The function f(x)=x3−6x2+9x+2f(x) = x^3 - 6x^2 + 9x + 2 has maximum value when xx is

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