1
MHT CET 2022 11th August Evening Shift
+2
-0

If the function $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$a \in I R$$ is increasing in $$(0,1]$$ and decreasing in $$[1,5)$$, then a root of the equation $$\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)$$ is

A
14
B
7
C
$$-$$14
D
$$-$$7
2
MHT CET 2022 11th August Evening Shift
+2
-0

A firm is manufacturing 2000 items. It is estimated that the rate of change of production $$P$$ with respect to additional number of workers $$x$$ is given by $$\frac{\mathrm{d} P}{\mathrm{~d} x}=100-12 \sqrt{x}$$. If the firm employs 25 more workers, then the new level of production of items is

A
4500
B
3000
C
2500
D
3500
3
MHT CET 2022 11th August Evening Shift
+2
-0

If the normal to the curve $$y=f(x)$$ at the point $$(3,4)$$ makes an angle $$\left(\frac{3 \pi}{4}\right)^c$$ with positive $$X$$-axis, then $$f^{\prime}(3)$$ is equal to

A
$$-1$$
B
$$\frac{4}{3}$$
C
$$-\frac{3}{4}$$
D
1
4
MHT CET 2022 11th August Evening Shift
+2
-0

If $$y=\cos \left(\sin x^2\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\sqrt{\frac{\pi}{2}}$$ is

A
0
B
2
C
$$-$$1
D
$$-$$2
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