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

$$\text { If } y=\sqrt{\sin x+y} \text { then find } \frac{d y}{d x} \text { at } x=0, \quad y=1$$

A
0
B
1
C
2
D
$$-$$1
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals }$$

A
$$\frac{-2 x}{\sqrt{1-x^2}}$$
B
$$\frac{-1}{\sqrt{1+x^2}}$$
C
$$\frac{1}{\sqrt{1-x^2}}$$
D
$$\frac{2 x}{\sqrt{1-x^2}}$$
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7 x^2+10$$

A
$$-39.995$$
B
$$-38.995$$
C
$$-37.335$$
D
$$-40.995$$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }$$

A
$$2 \log 2$$
B
$$\frac{2}{3} \log 2$$
C
0
D
$$\log 2$$
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