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1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sin a x+\cos b x$, then $y^{\prime \prime}+b^2 y=$
A
$\left(b^2-a^2\right) \sin a x$
B
$\left(b^2-a^2\right) \cos b x$
C
$\left(a^2-b^2\right) \tan a x$
D
$\left(b^2-a^2\right) \cot b x$
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A particle moving from a fixed point on a straight line travels a distance $S$ metres in $t \mathrm{sec}$. If $S=t^3-t^2-t+3$, then the distance (in mts) travelled by the particle when it comes to rest, is
A
5
B
4
C
2
D
3
3
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\sqrt{x}(x \geq 0)$ and $g(x)=1+x^2$, then $(f \circ g)^{\prime}(1)=$

A

1

B

$1 / 2$

C

$\sqrt{2}$

D

$1 / \sqrt{2}$

4
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

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