1
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
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If the line $$\frac{1-x}{-3}=y=\frac{z+2}{2}$$ is perpendicular to the line $$\frac{3 x-1}{2 b}=3-y=\frac{z-1}{a}$$, then find the value of $$3 a+3 b$$

A
3
B
$$\frac{3}{2}$$
C
4
D
$$\frac{1}{2}$$
3
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

The lines $$\vec{r}=(2 \hat{\jmath}-3 \hat{k})+\lambda(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})$$ and $$\vec{r}=(2 \hat{\imath}+6 \hat{\jmath}+3 \hat{k})+\mu(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})$$ are

A
Intersecting lines
B
Skew lines
C
co-incident lines
D
Parallel lines
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

A line makes the same angle $$\theta$$ with each of the $$x$$ and $$z$$-axes. If the angle $$\beta$$, which it makes with the $$y$$-axis is such that $$\sin ^2 \beta=3 \sin ^2 \theta$$, then $$\cos ^2 \theta$$ equals

A
$$\frac{2}{5}$$
B
$$\frac{1}{5}$$
C
$$\frac{3}{5}$$
D
$$\frac{2}{3}$$
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