1
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
$$ A \text { and } B \text { are independent } $$
2
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
$$\frac{\lambda}{1+\lambda}$$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=f(x), \quad p=\frac{d y}{d x} ; q=\frac{d^2 y}{d x^2} \text { then } \frac{d^2 x}{d y^2} \text { is equal to } $$

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

$$ \text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are } $$

A
$$\sqrt{3}, \quad \sqrt{14}$$
B
$$\sqrt{13}, \sqrt{14}$$
C
$$\sqrt{21}, \quad \sqrt{3}$$
D
$$\sqrt{21}, \quad \sqrt{13}$$
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