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

The general solution of the differential equation $$\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$$

A
$$ x=\tan ^{-1} y-1+c e^{\tan ^{-1} y} $$
B
$$ x=\tan ^{-1} y-1+c e^{-\tan ^{-1} y} $$
C
$$ x=\tan ^{-1} y+c e^{\tan ^{-1} y} $$
D
$$ x=c \tan ^{-1} y+e^{-\tan ^{-1} y} $$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The function $$f(x)=\frac{x}{2}+\frac{2}{x}$$ has a local minimum at

A
$$ x=2 $$
B
$$ x=-2 $$
C
$$ x=0 $$
D
$$ x=1 $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The scalar components of a unit vector which is perpendicular to each of the vectors $$\hat{\imath}+2 \hat{\jmath}-\hat{k}$$ and $$3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$$ are

A
$$ -\frac{3}{\sqrt{83}}, \quad-\frac{5}{\sqrt{83}}, \quad \frac{7}{\sqrt{83}} $$
B
$$ -3, \quad-5, \quad 7 $$
C
$$ \frac{3}{\sqrt{83}}, \quad-\frac{5}{\sqrt{83}}, \quad-\frac{7}{\sqrt{83}} $$
D
$$ 3, \quad-5, \quad-7 $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

A
1272
B
780
C
640
D
820
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