1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The maximum value of $$P=500 x+400 y$$ for the given constraints $$x+y \leq 200, \quad x \geq 20, \quad y \geq 4 x, \quad y \geq 0$$ is

A
96,000
B
84,000
C
98,000
D
82,000
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals } $$

A
$$\frac{-2 x}{\sqrt{1-x^2}}$$
B
$$\frac{-1}{\sqrt{1+x^2}}$$
C
$$\frac{1}{\sqrt{1-x^2}}$$
D
$$\frac{2 x}{\sqrt{1-x^2}}$$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the straight lines $$\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-t}$$ and $$\frac{x-1}{t}=\frac{y-4}{2}=\frac{z-5}{1}$$ are intersecting then $$t$$ can have

A
Exactly three values
B
Exactly two values
C
Any number of values
D
Exactly one value
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to } $$

A
5
B
13
C
$$-$$2
D
7
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