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Day 183: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 11 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    90
    Let x0x_0 be the point of local maxima of f(x)=aˉ⋅(bˉ×cˉ)f(x) = \bar{a}\cdot(\bar{b} \times \bar{c}) where aˉ=xi^−2j^+3k^,bˉ=−2i^+xj^−k^\bar{a} = x\hat{i} - 2\hat{j} + 3\hat{k}, \bar{b} = -2\hat{i} + x\hat{j} - \hat{k} and cˉ=7i^−2j^+xk^\bar{c} = 7\hat{i} - 2\hat{j} + x\hat{k} then the value of aˉ⋅cˉ\bar{a}\cdot\bar{c} at x=x0x = x_0 is

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  2. Question 2

    Differentiation. Asked once: 13 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    66
    If y=tan⁡−1(1x2+x+1)+tan⁡−1(1x2+3x+3)+tan⁡−1(1x2+5x+7)+…y = \tan^{-1}\left(\dfrac{1}{x^2 + x + 1}\right) + \tan^{-1}\left(\dfrac{1}{x^2 + 3x + 3}\right) + \tan^{-1}\left(\dfrac{1}{x^2 + 5x + 7}\right) + \ldots upto nn terms, then y′(0)=y'(0) =

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  3. Question 3

    Trigonometric Functions. Asked once: 25 Apr 2025 S2 (same type asked 8 times) See all 8 of this type

    135
    If tan⁡−1(x+1)+tan⁡−1x+tan⁡−1(x−1)=tan⁡−13\tan^{- 1}(x+ 1) +\tan^{- 1}x+\tan^{- 1}(x- 1) =\tan^{- 1}3, then for x<0x< 0 the value of 500x4+270x2+997=500x^{4}+ 270x^{2}+ 997 =

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  4. Question 4

    Linear Programming. Asked once: 23 Apr 2025 S1 (same type asked 8 times) See all 8 of this type

    140
    The graph with correct feasible region of L.P.P. for the constraints 2x+y⩽10,y⩽x,y⩽2,x,y⩾02x+y\leqslant 10,y\leqslant x,y\leqslant 2,x,y\geqslant 0 is ...

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  5. Question 5

    Differential Equations. Asked once: 14 May 2024 S2 (same type asked 8 times) See all 8 of this type

    123
    If the slope of the tangent of the curve at any point is equal to −y+e−x-y + e^{-x}, then the equation of the curve passing through origin is

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