1
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The maximum value of $$Z=12 x+13 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 5$$ and $$3 x+y \leq 9$$ is

A
63
B
65
C
60
D
117
2
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is

A
$$\frac{1}{3}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$
B
$$\frac{1}{2}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})$$
C
$$\frac{1}{3}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}})$$
D
None of these
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The place $$x-2 y+z=0$$ is parallel to the line

A
$$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-3}{6}$$
B
$$\frac{x-2}{1}=\frac{y-2}{-2}=\frac{z-3}{1}$$
C
$$\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{4}$$
D
$$\frac{x-4}{3}=\frac{y-5}{4}=\frac{z-6}{3}$$
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{x d x}{2(1+x)^{3 / 2}}$$ is equal to

A
$$\frac{2+x}{\sqrt{1+x}}+C$$
B
$$\frac{2+x}{x \sqrt{1+x}}+C$$
C
$$\frac{x}{\sqrt{1+x}}+C$$
D
$$-\frac{x}{\sqrt{1+x}}+C$$
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