1
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

Maximum value of $$z=12x+3y$$, subject to constraints $$x\ge0,y\ge0,x+y\ge5$$ and $$3x+y\le9$$ is

A
15
B
36
C
60
D
40
2
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If $$\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$$ and $$\mathbf{r}=\hat{i}+\hat{k}$$, then the unit vector in the direction of $$3 p+q-2 r$$ is

A
$$\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})$$
B
$$\frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k})$$
C
$$\frac{1}{3}(\hat{i}-2 \hat{j}+2 \hat{k})$$
D
$$\hat{i}+2 \hat{j}+2 \hat{k}$$
3
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

The line $$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}$$ is parallel to the plane

A
$$3 x+4 y+5 z=7$$
B
$$x+y+z=2$$
C
$$x-2 y+z=0$$
D
$$2 x+3 y+4 z=0$$
4
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{x \sqrt{a x-x^2}} d x$$ is

A
$$\frac{-3}{a} \sqrt{\frac{a-x}{x}}+C$$
B
$$-\frac{2}{a} \sqrt{\frac{x}{a-x}+C}$$
C
$$\frac{-2}{a} \sqrt{\frac{a-x}{x}}+C$$
D
None of these
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