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Day 540: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 3 May 2023 S1

    138
    The image of the line x−13=y−31=z−4−5\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5} in the plane 2x−y+z+3=02x-y+z+3=0 is the line

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  2. Question 2

    Trigonometric Functions. Asked once: 16 May 2023 S2

    109
    In a triangle ABC, l(AB)=23l(AB) = \sqrt{23} units, l(BC)=3l(BC) = 3 units, l(CA)=4l(CA) = 4 units, then cot⁡A+cot⁡Ccot⁡B\frac{\cot A + \cot C}{\cot B} is

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  3. Question 3

    Vectors. Asked once: 10 May 2024 S2

    112
    If (a⃗×b⃗)×c⃗=−5a⃗+4b⃗(\vec{a}\times\vec{b})\times\vec{c}=-5\vec{a}+4\vec{b} and a⃗⋅b⃗=3\vec{a}\cdot\vec{b}=3, then the value of a⃗×(b⃗×c⃗)\vec{a}\times(\vec{b}\times\vec{c}) is

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  4. Question 4

    Indefinite Integration. Asked once: 11 May 2024 S1

    149
    ∫log⁡(cot⁡x)sin⁡2x dx=\int \frac{\log(\cot x)}{\sin 2x}\,dx =

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  5. Question 5

    Line and Plane. Asked once: 2 May 2023 S2

    144
    Let P be the image of the point (3,1,7)(3,1,7) with respect to the plane x−y+z=3x-y+z=3. Then the equation of the plane passing through P and containing the straight line x1=y2=z1\frac{x}{1}=\frac{y}{2}=\frac{z}{1} is

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