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

$$ \text { If } x^2+y^2=t+\frac{1}{t} \text { and } x^4+y^4=t^2+\frac{1}{t^2} \text { then } \frac{d y}{d x}= $$

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

$$ \text { If } \alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right) \text { and } \beta=\tan ^{-1}\left(-\tan \frac{2 \pi}{3}\right) \text { then } $$

A
$$ 3 \alpha=4 \beta $$
B
$$ \alpha-\beta=\frac{7 \pi}{12} $$
C
$$ 4 \alpha=3 \beta $$
D
$$ \alpha+\beta=-\frac{7 \pi}{12} $$
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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