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

The area of the upper half of the circle whose equation is $$(x-1)^2+y^2=1$$ is given by

A
$$ \frac{\pi}{4} \text { sq units } $$
B
$$ \int_\limits0^2 \sqrt{2-x^2} d x \text { sq units } $$
C
$$ \int_\limits0^2 \sqrt{2x-x^2} d x \text { sq units } $$
D
$$ \int_\limits0^1 \sqrt{2x-x^2} d x \text { sq units } $$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

In the set $$\mathrm{W}$$ of whole numbers an equivalence relation $$\mathrm{R}$$ is defined as follows $$\mathrm{aRb}$$ iff both $$\mathrm{a}$$ & $$\mathrm{~b}$$ leave the same reminder when divided by 5. The equivalence class of 1 is given by.

A
$$ \{2,7,12,17------\} $$
B
$$ \{1,6,11,16------\} $$
C
$$ \{4,9,14,19------\} $$
D
$$ \{0,5,10,15------\} $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)= $$

A
$$ \frac{4}{5} $$
B
$$ \frac{1}{2} $$
C
1
D
$$ \frac{1}{5} $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The function defined by } f(x)=\left\{\begin{array}{cc} \frac{\sin x}{x}+\cos x & x>0 \\ -5 k & x=0 \\ \frac{4(1-\sqrt{1-x})}{x} & x<0 \end{array} \quad \text { is continous at } x=0, \quad \text { then } k\right. \text { equals } $$

A
$$ -\frac{2}{5} $$
B
$$-2$$
C
2
D
$$ -\frac{5}{2} $$
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