Page 10 - ECAT Past Paper 2006

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sinθ /cosθ=√3
tanθ=√3 θ=arc tan (√3)= 60* (Answer)

4
−1+√−3
Q.41 ( ) =?
2
2
−1+√−3 −1+√−3
A) ( ) (Correct) B) ( )
2 2
2
−1−√−3
C) ( ) D) None of these
2
Explanation:-
−1+√−3
As we know that ( ) =
2
=w =w .w=w :. w =1
3
4
3
−1+√−3
Hence, ( ) (Answer)
2

Q.42 The period of 3sin5x is
A) 2π B) 5π/2
C) 2π/5 (Correct) D) 5π
Explanation:-
As we know that :-
2
Generated Period= = (Answer)
| | 5
Q.43 cos15*-sin15*=?
1
−1
A) B) (Correct)
√2 √2
C) −√2 D) √2
Explanation:-
As cos15*-sin15*=?
Extracting the formula:
=cos(45*-30*)-sin(45*-30*)
=(cos45.cos30+sin45.sin30) –(sin45.cos30-cos45.sin30)
1 √3 1 1 1 √3 1 1
= ( . + . ) − ( . − . )
√2 2 √2 2 √2 2 √2 2
1 √3 1 1 1 √3 1 1
=( . + . ) − ( . + . )
√2 2 √2 2 √2 2 √2 2
:.Cancelling the terms
1
1
= 1 . + 1 . = 2 = 1 ( )
√2 2 √2 2 2√2 √2
Q.44 tan (45+θ)=?
A) +1 B) 1+ (Correct)
−1 1−
2
C) 1+ D) 1−
2
1− 1+
Explanation:-
As tan(45+θ)=?
Using the formula:
tan(45+θ)= 45+ = 1+ (Answer)
1− 45. 1−
Q.45 A triangle which has not a right angle is called ____triangle.
A) Obtuse B) Oblique
C) Equilateral D) None of these
Note: There should be one more MCQ because all the options are correct so that.
E) All of these (Correct)
-Explanation:-
A) Obtuse triangle is one whose one angle is obtuse (greater than 90* but less than
180*)
B) Oblique triangle is one whose no angle is of 90*.