1
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

A
$$\frac{1}{3}$$
B
0
C
3
D
1
2
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ has minimum value at the point.

A
on the line $$2 x+3 y=15$$
B
on X-axis
C
on Y-axis
D
origin
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines of $$\overline{\mathrm{OP}}$$ are

A
$$\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$$
B
$$\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$$
C
$$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$$
D
$$\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$$
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$

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