Page 11 - ECAT Past Paper 2006

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C) Equilateral triangle is one whose all angles are of 60*
Q.46 If cosθ=-1 , then _____n∈Z
A) θ=(2n+1)π (Correct) B) θ≠(2n+1)π
C) θ=nπ/2 D) None of these
Explanation:
For such question just put the n value in the options and satisfies the given equation
In this case.
After putting value n=0 in all the options, the one satisfied solution is θ=(2n+1)π
 θ=(2(0)+1)π =) θ=π
So Put in the given equation
cos(π)=-1
-1=-1 (Answer)
Q.47 =?
A) tan56* (Correct) B) sin56*
C) cos56* D) None of these
Explanation:-
1) For Quick Analysis, as the notation is in fraction that’s meant it should be Option
A.
2) Back Solving Method:
Solve the options by extracting the formulas and satisfies with given notation. i.e.
11°
=
tan (56*)=tan(45*+11*)= 45°+ 11° = 1+ 11° 1+ 11° = 11°+ 11° (Answer)
1− 45° 11° 1− 11° 1− 11° 11°− 11°
11°
Q.48 Due to periodicity, the trigonometric equations have ______ number of solutions.
A) Finite B) Infinite (Correct)
C) Two D) None of these
Explanation:-
The basic reason is already stated in the MCQ.
Q.49 6 + 2 =?
5 + 3
A) −√2 B) 0
C) 1 (Correct) D) √2
Explanation:-
As after putting x0 in the given notation 0/0 form will come. So we use here
L’Hopital Rule
( )
L’Hopital Rule is applied where lim forms 0/0 or ∞/∞ form and it will equal to
→0 ( )
′( )
lim
→0 ′( )
6 6 +2 2
= lim
→0 5 5 +3 3
Putting the limit x0
8
= 6 6(0)+2 2(0) = = 1(Answer)
5 5(0)+3 3(0) 8
2
Q.50 The Solution of dy/dx=-cosec x is
A) c B) y=cotx+c (Correct)
C) y=tanx+c D) y=cos x+c
2
Explanation:-
Using the back solve method and taking the derivative of options where the derivate
notation match then
that’s our Answer.
In this case,
y=cotx+c
diff.w.r.t. “x”
2
dy/dx= -cosec x (Answer)
Q.51 If f(x)=cotx then find f’(π/4)?