1
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\sqrt{x-x y}+\sqrt{y-x y}=1$, then $\frac{d y}{d x}=$

A

$-\sqrt{\frac{y-y^2}{x-x^2}}$

B

$-\sqrt{\frac{1-y^2}{1-x^2}}$

C

$-\sqrt{\frac{1-y}{1-x}}$

D

$-\sqrt{\frac{x-y}{x+y}}$

2
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x=2 \cos ^3 \theta$ and $y=3 \sin ^2 \theta$, then $\frac{d y}{d x}=$

A

$-\sec \theta$

B

$\cos \theta$

C

$-\operatorname{cosec} \theta$

D

$\sin \theta$

3
AP EAPCET 2025 - 22nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) If $y=f(x)=(|x|-|x-1|)^2$, then $\left(\frac{d y}{d x}\right)_{x=1}=1$

Reason (R) $\mathop {\lim }\limits_{x \to a} \frac{f(x)-f(a)}{x-a}$ exist, then it is called derivative of $f(x)$ at $x=a$.

A

(A) is true, (R) is true, (R) is correct explanation to (A)

B

(A) is true, (R) is true, (R) is not the correct explanation to (A)

C

(A) is true, (R) is false

D

(A) if false, (R) is true

4
AP EAPCET 2025 - 21st May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$

A

$\frac{y}{x}$

B

$\frac{y^2}{x^2}$

C

$\sqrt{\frac{y}{x}}$

D

$-\frac{y}{x}$

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