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

If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ then the possible values of $x$ lies in the interval

A
$$\left[\frac{1}{3}, \frac{2}{9}\right]$$
B
$$\left[-\frac{1}{3}, \frac{5}{9}\right]$$
C
$$[0,1]$$
D
$$\left[-\frac{7}{9}, \frac{4}{9}\right]$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The mean of the numbers $$a, b, 8,5,10$$ is 6 and the variance is 6.80 , then which of the following gives possible values of $$a$$ & $$b$$

A
$$a=1, b=6$$
B
$$a=0, b=7$$
C
$$a=3, b=4$$
D
$$a=5, b=2$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, then $$\lambda$$ is equal to

A
$$-12$$
B
$$-6$$
C
$$12$$
D
$$6$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{x^2-4 x+2} d x=$$

A
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}+\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
B
$$ (x-2) \sqrt{x^2-4 x+2}+\frac{1}{2} \log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
C
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\sin ^{-1} \frac{x-2}{\sqrt{2}}+C $$
D
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
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