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

The line joining two points $$A(2,0) B(3,1)$$ is rotated about $$A$$ in anticlockwise direction through an angle of $$15^{\circ}$$. If $$B$$ goes to $$C$$ in the new position, then the coordinates of $$C$$ is

A
$$ \left(2+\frac{1}{\sqrt{3}}, \sqrt{\frac{3}{2}}\right) $$
B
$$ \left(2, \sqrt{\frac{3}{2}}\right) $$
C
$$ \left(2+\frac{1}{\sqrt{3}}, 1\right) $$
D
$$ \left(2+\frac{1}{\sqrt{2}}, \sqrt{\frac{3}{2}}\right) $$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \lim _\limits{x \rightarrow 1} \frac{x^{15}-1}{x^{10}-1}= $$

A
$$\frac{2}{3}$$
B
1
C
$$\frac{3}{2}$$
D
Does not exist
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$\mathrm{A}$$ and $${B}$$ be two events such that $$P(A / B)=\frac{1}{2}$$ and $$P(B / A)=\frac{1}{3}$$ and $$P(A \cap B)=\frac{1}{6}$$ then, which one of the following is not true?

A
$$ \mathrm{A} \text { and } \mathrm{B} \text { are not independent } $$
B
$$ P(A \cup B)=\frac{2}{3} $$
C
$$ P\left(A^{\prime} \cap B\right)=\frac{1}{6} $$
D
$$ A \text { and } B \text { are independent } $$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y= $$

A
$$\frac{1+\lambda}{1-\lambda}$$
B
$$\frac{1-\lambda}{1+\lambda}$$
C
$$\frac{\lambda}{1-\lambda}$$
D
$$\frac{\lambda}{1+\lambda}$$
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