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Day 350: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 9 May 2023 S1 (same type asked 5 times) See all 5 of this type

    113
    If the vectors ai^+j^+k^a\hat{i}+\hat{j}+\hat{k}, i^+bj^+k^\hat{i}+b\hat{j}+\hat{k}, i^+j^+ck^\hat{i}+\hat{j}+c\hat{k} (a≠b,c≠1a\neq b, c\neq1) are coplanar, then 11−a+11−b+11−c\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c} has the value

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  2. Question 2

    Linear Programming. Asked once: 10 May 2024 S2 (same type asked 5 times) See all 5 of this type

    105
    The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function 3x+5y3x+5y, subject to the linear constraints given by this system of inequations is

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  3. Question 3

    Applications of Derivative. Asked once: 11 May 2023 S1 (same type asked 5 times) See all 5 of this type

    114
    If f(x)=x3−6x2+9x+3f(x) = x^3 - 6x^2 + 9x + 3 is monotonically decreasing function, then x lies in

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  4. Question 4

    Complex Numbers. Asked once: 2 May 2023 S2 (same type asked 4 times) See all 4 of this type

    125
    If P(x,y)P(x,y) denotes z=x+iyz=x+iy and ∣z−1z+2i∣=1\left|\frac{z-1}{z+2i}\right|=1, then the locus of P is

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  5. Question 5

    Line and Plane. Asked once: 15 May 2023 S2 (same type asked 4 times) See all 4 of this type

    141
    The foot of the perpendicular drawn from origin to a plane is M(2,1,−2)M(2,1,-2), then vector equation of the plane is

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