1
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Match the values of $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ for the following system of curves in parametric form given in List-I with those of the items in List-II

List-I List-II
(i) x = a ( θ sin θ ) , y = a ( 1 cos θ ) x = a ( θ sin θ ) , y = a ( 1 cos θ ) x=a(theta-sin theta),y=a(1-cos theta) (a) 4 3 4 3 4sqrt3
(ii) x = 3 cos θ 2 cos 3 θ , y = 3 sin θ 2 sin 3 θ x = 3 cos θ 2 cos 3 θ , y = 3 sin θ 2 sin 3 θ x=3cos theta-2cos^(3)theta,y=3sin theta-2sin^(3)theta (b) 1 3 3 1 3 3 (-1)/(3sqrt3)
(iii) x = 3 cos θ cos 3 θ , y = 3 sin θ sin 3 θ x = 3 cos θ cos 3 θ , y = 3 sin θ sin 3 θ x=3cos theta-cos^(3)theta,y=3sin theta-sin^(3)theta (c) 3 3 sqrt3
(iv) x = a log sin θ , y = a tan θ x = a log sin θ , y = a tan θ x=a log sin theta,y=a tan theta (d) 1 3 1 3 (1)/(sqrt3)
(e) 1 3 3 1 3 3 (1)/(3sqrt3)
A

(i) → c, (ii) → d, (iii) → b, (iv) → a

B

(i) → c, (ii) → e, (iii) → d, (iv) → a

C

(i) → d, (ii) → c, (iii) → b, (iv) → a

D

(i) →d, (ii) → c, (iii) → e, (iv) → b

2
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=x \sin x$ and $\frac{\frac{d y}{d x}-\frac{y}{x}}{x \frac{d y}{d x}-y}$ at $x=\alpha$ is 1 , then $\alpha=$

A

$\sqrt{2}$

B

2

C

1

D

$1 / \sqrt{2}$

3
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

A ladder of length 13 m has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \mathrm{~m} / \mathrm{min}$ then the speed (in $\mathrm{m} / \mathrm{min}$ ) at which upper end falls when the bottom is 5 m away from the wall is

A

$6 / 5$

B

$12 / 5$

C

$5 / 6$

D

$5 / 12$

4
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

An angle between the curves $x^2-y^2=4$ and $x^2+y^2=4 \sqrt{2}$ is

A

$\pi / 6$

B

$\pi / 4$

C

$\pi / 3$

D

$\pi / 2$

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