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Day 297: MHT-CET Maths

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

  1. Question 1

    Pair of Straight Lines. Asked once: May 2022 S1 (same type asked 5 times) See all 5 of this type

    107
    The joint equation of pair of lines through the origin and making an equilateral triangle with the line y=5y = 5 is

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  2. Question 2

    Differentiation. Asked once: 11 May 2024 S1 (same type asked 5 times) See all 5 of this type

    102
    If y=log⁡sin⁡x(tan⁡x)y = \log_{\sin x}(\tan x), then dydx∣x=π/4\left.\frac{dy}{dx}\right|_{x=\pi/4} has the value

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  3. Question 3

    Line and Plane. Asked once: 9 May 2024 S1 (same type asked 5 times) See all 5 of this type

    139
    If two vertices of a triangle are A(3,1,4)A(3,1,4) and B(−4,5,−3)B(-4,5,-3) and the centroid of the triangle is G(−1,2,1)G(-1,2,1), then the third vertex C of the triangle is

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  4. Question 4

    Vectors. Asked once: 13 May 2024 S2 (same type asked 5 times) See all 5 of this type

    119
    If the vectors pi^+j^+k^,i^+qj^+k^p\hat{i}+\hat{j}+\hat{k},\hat{i}+q\hat{j}+\hat{k} and i^+j^+rk^ (p≠q≠r≠1)\hat{i}+\hat{j}+r\hat{k}\ (p\neq q\neq r\neq1) are coplanar, then the value of pqr−(p+q+r)pqr-(p+q+r) is

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  5. Question 5

    Differential Equations. Asked once: 14 May 2024 S2 (same type asked 5 times) See all 5 of this type

    103
    The differential equation representing the family of curves y2=2c(x+c)y^2 = 2c(x + \sqrt{c}), where cc is a positive parameter, is of

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