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

11) $\frac{\sin\left(18^\circ\right)}{\cos\left(72^\circ\right)}$

A) 1
B) $\frac14$
C) 0
D) ∞

View Answer

A) 1

Explanation:We are asked to evaluate:
$\frac{\sin(18^\circ)}{\cos(72^\circ)}$
Shortcut Observation:
Use the identity:
$\sin(x) = \cos(90^\circ - x)$
So,
$\cos(72^\circ) = \sin(18^\circ)$
Therefore:
$\frac{\sin(18^\circ)}{\cos(72^\circ)} = \frac{\sin(18^\circ)}{\sin(18^\circ)} = 1$
Final Answer: 1

12) If sinθ = $\frac12$ and θ is acute, then the value of sin2θ is

A) 1
B) $\frac{\sqrt3}2$
C) $\frac12$
D) $-\frac{\sqrt3}2$

View Answer

B) $\frac{\sqrt3}2$

Explanation:We are given:
$\sin\theta = \frac{1}{2}, \quad \theta \text{ is acute}$
Shortcut Step 1: Recall standard values
$\sin\theta = \frac{1}{2} \Rightarrow \theta = 30^\circ \quad \text{(since acute)}$
Step 2: Find $\sin 2\theta$
$2\theta = 60^\circ \Rightarrow \sin(60^\circ) = \frac{\sqrt{3}}{2}$
Final Answer: $\frac{\sqrt{3}}{2}$

13) If sinα = cosα, then the value of α is

A) 30°
B) 45°
C) 60°
D) 90°

View Answer

B) 45°

Explanation:We are given:
$\sin\alpha = \cos\alpha$
Shortcut Method: Use standard angles
$\sin\alpha = \cos\alpha \Rightarrow \tan\alpha = 1 \Rightarrow \alpha = 45^\circ \quad \text{(since in acute angles, only at 45° this holds)}$
Final Answer: 45°

14) The angle of elevation of the sun, when shadow of a pole of ‘h’ meter height is √3h metre long is

A) 60°
B) 30°
C) 45°
D) 50°

View Answer

B) 30°

Explanation:We are given:
Height of the pole = h
Length of the shadow = $\sqrt{3}h$
Shortcut Method: Use basic trigonometry
From the triangle formed by the pole and its shadow:
$\tan(\theta) = \frac{\text{height}}{\text{shadow}} = \frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ$
Final Answer: 30°

15) The probability that a non leap year will have 53 Thursdays is

A) $\frac1{121}$
B) $\frac17$
C) $\frac67$
D) $\frac9{13}$

View Answer

B) $\frac17$

Explanation:To solve this quickly, let’s apply a shortcut method using the concept of distribution of days in a non-leap year:
Step 1: Total days in a non-leap year = 365
That’s 52 weeks + 1 extra day
So, every non-leap year has 52 Thursdays for sure, and whether it has 53 Thursdays depends on that 1 extra day.
Step 2: What can the extra day be?
The extra day could be: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday (7 possibilities).
Out of these 7, only if the extra day is a Thursday, then we will get 53 Thursdays.
Probability =
$\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{7}$
Final Answer: $\frac{1}{7}$

Spread the love

Leave a Reply Cancel reply