Day 410: MHT-CET Maths

1. A.
   $x+2y\leq6,\;5x+3y\geq15,\;x\leq7,\;y\leq6,\;x,y\geq0$
2. B.
   $x+2y\geq6,\;5x+3y\geq15,\;x\leq7,\;y\leq6,\;x,y\geq0$
3. C.
   $x+2y\geq6,\;5x+3y\leq15,\;x\geq7,\;y\leq6,\;x,y\geq0$
4. D.
   $x+2y\leq6,\;5x+3y\leq15,\;x\leq7,\;y\geq6,\;x,y\geq0$

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1. A.
   $xy\frac{d^{2}y}{dx^{2}} - x\left(\frac{dy}{dx}\right)^{2} - y\frac{dy}{dx} = 0$
2. B.
   $xy\frac{d^{2}y}{dx^{2}} - x\left(\frac{dy}{dx}\right)^{2} + y\frac{dy}{dx} = 0$
3. C.
   $xy\frac{d^{2}y}{dx^{2}} + x\left(\frac{dy}{dx}\right)^{2} + y\frac{dy}{dx} = 0$
4. D.
   $xy\frac{d^{2}y}{dx^{2}} + x\left(\frac{dy}{dx}\right)^{2} - y\frac{dy}{dx} = 0$

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1. A.
   0
2. B.
   $[\vec{a}\,\vec{b}\,\vec{c}]$
3. C.
   $2[\vec{a}\,\vec{b}\,\vec{c}]$
4. D.
   $-[\vec{a}\,\vec{b}\,\vec{c}]$

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1. A.
   $xy+\cos x=\sin x+c$, where c is a constant of integration.
2. B.
   $x(y+\cos x)=\sin x+c$, where c is a constant of integration.
3. C.
   $y(x+\cos x)=\sin x+c$, where c is a constant of integration.
4. D.
   $xy+\sin x=\cos x+c$, where c is a constant of integration.

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1. A.
   24
2. B.
   46
3. C.
   56
4. D.
   36

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