TS Polycet (Polytechnic) 2015 Previous Question Paper with Answers And Model Papers With Complete Analysis

31)cos⁴ A – sin⁴ A =

32)sin 35° cos 35° sin 47° cos 47° cos 90° =

33)tan 5°.tan 30°.4 tan 85° =

34)If x tanθ + y secθ = p and x secθ + y tanθ = q, then

35)Two towers heights h1 and h2 subtend angles 60° and 30° respectively, at the midpoint of the line joining their feet. Then h₁ : h₂ =

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B) 3:1
Explanation:In ΔABE
tan 60° = h₁/EA

√3 = h₁/EA ⇒ EA =h₁/√3
In ΔCDE
1/√3 = h₂/CE ⇒ CE = √3h₂
CE = EA
√3h₂ = h₁/√3 ⇒ h₁/h₂ = 3 ⇒h₁ : h₂ = 3 : 1

36)Two poles are ‘a’ meters apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller pole is

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B) a/2√2 m
Explanation:In ΔABE
tanθ = h/EA
EA =h/tanθ
In ΔCDE
tan (90° – θ) = 2h/CE
cotθ = 2h/CE
CE = 2h/cotθ = 2h tanθ
a/2.a/2 = 2h² ⇒ h² = a²/8 ⇒ h = a/2√2

37)If A and B are supplementary angles, then A + B =

38)The probability of a certain event is

39)A number is selected from the first 5 natural numbers. What is the probability that it is a multiple of 3?

40)If three coins are tossed simultaneously then the probability of getting at least two heads, is