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Day 390: MHT-CET Maths

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

  1. Question 1

    Linear Programming. Asked once: 9 May 2024 S2 (same type asked 8 times) See all 8 of this type

    149
    The graphical solution set for the system of inequations x−2y≤2,  5x+2y≥10,  4x+5y≤20,  x≥0,  y≥0x-2y \leq 2,\;5x+2y \geq 10,\;4x+5y \leq 20,\;x \geq 0,\;y \geq 0 is given by

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  2. Question 2

    Differential Equations. Asked once: 4 May 2023 S1 (same type asked 8 times) See all 8 of this type

    110
    Let y=y(x)y=y(x) be the solution of the differential equation sin⁡x dydx+ycos⁡x=4x, x∈(0,π)\sin x\,\frac{dy}{dx}+y\cos x=4x,\,x\in(0,\pi). If y ⁣(π2)=0y\!\left(\frac{\pi}{2}\right)=0, then y ⁣(π6)y\!\left(\frac{\pi}{6}\right) is equal to

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  3. Question 3

    Line and Plane. Asked once: 16 May 2023 S2 (same type asked 7 times) See all 7 of this type

    105
    The co-ordinates of the foot of the perpendicular from the point (0,2,3)(0,2,3) on the line x+35=y+12=z+43\frac{x+3}{5} = \frac{y+1}{2} = \frac{z+4}{3} is

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  4. Question 4

    Differentiation. Asked once: 13 May 2024 S2 (same type asked 7 times) See all 7 of this type

    122
    If x=log⁡e ⁣cos⁡y2−sin⁡y2cos⁡y2+sin⁡y2, tan⁡y2=1−t1+tx=\log_e\!\frac{\cos\frac{y}{2}-\sin\frac{y}{2}}{\cos\frac{y}{2}+\sin\frac{y}{2}},\ \tan\frac{y}{2}=\frac{1-t}{1+t}. Then y′ ⁣ ⁣∣t=12y'\!\!\left|_{t=\frac{1}{2}}\right. has the value

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  5. Question 5

    Line and Plane. Asked once: 11 May 2024 S1 (same type asked 7 times) See all 7 of this type

    133
    The lines x−13=y+12=z−15\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} and x+24=y−13=z+12\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}

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