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Day 462: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 13 May 2026 S2

    91
    a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} represent three concurrent edges of a rectangular parallelopiped whose lengths are 5,25, 2 and 33 units respectively, then (a⃗+b⃗+c⃗)⋅(a⃗×b⃗+b⃗×c⃗+c⃗×a⃗)=(\vec{a} + \vec{b} + \vec{c}) \cdot (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}) =

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  2. Question 2

    Applications of Definite Integral. Asked once: 11 May 2024 S2

    123
    The slope of the tangent to a curve y=f(x)y=f(x) at (x,f(x))(x,f(x)) is 2x+12x+1. If the curve passes through the point (1,2)(1,2), then the area (in sq.units), bounded by the curve, the X-axis and the line x=1x=1, is

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  3. Question 3

    Applications of Derivative. Asked once: 19 Apr 2026 S2

    75
    Rolle's theorem holds for monic quadratic polynomial f(x)f(x) on the interval [α,α+3][\alpha, \alpha + 3] where f(α)=0f(\alpha) = 0. Similarly, g(x)=f(x)+2g(x) = f(x) + 2 also follows Rolle's theorem in the interval [β,3][\beta, 3] where g(3)=0g(3) = 0, such that the value of cc is the same for both f(x)f(x) and g(x)g(x). Then the value of (f∘g)(α)(f \circ g)(\alpha) is...

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  4. Question 4

    Circle. Asked once: 12 May 2024 S1

    146
    If λ\lambda is the perpendicular distance of a point PP on the circle x2+y2+2x+2y−3=0x^{2}+y^{2}+2x+2y-3=0 from the line 2x+y+13=02x+y+13=0 then maximum possible value of λ\lambda is

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  5. Question 5

    Complex Numbers. Asked once: 16 May 2023 S1

    148
    Let z=x+iyz = x+iy be a complex number, where x and y are integers and i=−1i = \sqrt{-1}. Then the area of the rectangle whose vertices are the roots of the equation zzˉ3+zˉz3=350z\bar{z}^3 + \bar{z}z^3 = 350 is

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