Page 12 - ECAT Past Paper 2006

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A) 2 B) 1
C) 0 D) -2 (Correct)
Explanation:
f(x)=cotx
Diff. w.r.t “x”
First of all;
f’(x)= -cosec x
2
Now ;
f’(π/4)= -(cosec (π/4)) =-(√2) = -2 (Answer)
2
2
Q.52 ∫ . . =?
A) e secx +c B) e tanx +c
C) e cosecx +c D) None of these
Explanation:-
Using the back solving method and taking the derivative of given option and later
match with given
notation.
Let y=e secx +c
Diff. w.r.t. “x”
dy/dx= e secx .secx.tanx (Answer)

Q.53 ∫ 2 =?
4
0
A) ½ (Correct) B) 2/3
C) 0 D) 3/2
Explanation:

As ∫ 2 =?
4
0
On integrating:
2
= − [ ]
2
Now x π/4 and 0
π
2( ) 2(0)
= -([ 4 ]-[ ])
2 2
= -0+1/2 =1/2 (Answer)
Q.54 The slope of the line with inclination 120* is
A) 0 B) 1
C) −√3 (Correct) D) Undefined
Explanation:
As we know that
tanθ=m
As =120*
nd
Also in 2 quadrant tan is negative and so = 180° −
tan(180° − 120°)=m
m=tan60*
nd
As tangent value in 2 Quadrant is negative.
So, m= −√3 (Answer)
Q.55 Equation of a line passing through (a,b) and perpendicular to ax+by+c=0 is
A) bx+ay=0 B) bx-ay=0 (Correct)
C) ax-by=0 D) ax+by=0
Explanation:
Equation of a line passing through (a,b) and perpendicular to ax+by+c=0 is bx-
ay+k=0 whereas k can be
any number.
So in this case, k=0 so bx-ay=0 (Answer)
Q.56 A line segment whose endpoints lie on a circle is called