AP Polycet (Polytechnic) 2021 Previous Question Paper with Answers And Model Papers With Complete Analysis

6) If the diameter of a sphere is d, then its volume is

A) $\frac16\mathrm{πd}^3$
B) $\frac43\mathrm{πd}^3$
C) $\frac1{24}\mathrm{πd}^3$
D) $\frac13\mathrm{πd}^3$

View Answer

A) $\frac16\mathrm{πd}^3$

7) The sharpened edge of the pencil gives an idea about the

A) circle
B) cone
C) rectangle
D) none of these

View Answer

B) cone

8) If tanθ + cotθ = 2, then tan²θ+ cot²θ=

A) 4
B) 2
C) 6
D) 1

View Answer

B) 2

Explanation:We are given:
$\tan\theta + \cot\theta = 2$
Shortcut Trick:
Use the identity:
$\tan^2\theta + \cot^2\theta = (\tan\theta + \cot\theta)^2 - 2$
Substitute:
$(\tan\theta + \cot\theta)^2 = 2^2 = 4$
$\tan^2\theta + \cot^2\theta = 4 - 2 = 2$
Final Answer: 2

9) If tanθ = $\frac1{\sqrt3}$ then value of cosθ is

A) $\frac12$
B) $\frac{\sqrt3}2$
C) $\frac2{\sqrt3}$
D) √3

View Answer

B) $\frac{\sqrt3}2$

Explanation:We are given:
$\tan\theta = \frac{1}{\sqrt{3}}$
Shortcut Method:
Recall the standard value:
$\tan 30^\circ = \frac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ$
Now, use:
$\cos 30^\circ = \frac{\sqrt{3}}{2}$
Final Answer: $\frac{\sqrt{3}}{2}$

10) If sinθ = $\frac{12}{13}$ then tanθ =

A) $\frac{13}5$
B) $\frac5{12}$
C) $\frac{13}{12}$
D) $\frac{12}5$

View Answer

D) $\frac{12}5$

Explanation:We are given:
$\sin\theta = \frac{12}{13}$
Shortcut Method: Use Pythagorean Triplet
If $\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{12}{13}$ ,
then use the Pythagorean identity:
$\text{Adjacent} = \sqrt{13^2 - 12^2} = \sqrt{169 - 144} = \sqrt{25} = 5$
Now,
$\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{12}{5}$
Final Answer: $\frac{12}{5}$