Page 9 - ECAT Past Paper 2006

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+
= +
2
+1 − +1
3
:. ℎ + 1
2
2
+ 1 = ( − + 1) + (Bx+C) (x+1)
Now put x+1=0  x=-1
2
2
(−1) + 1 = ((−1) − (−1) + 1) +(B(-1)+C) ((-1)+1)
So 2=A(3)  A=2/3
Now simplifies the notation:-
2
2
2
+ 1 = − + +Bx +Bx+Cx+C
Comparing the co-efficient now.
1=A+B
1-2/3=B  B=1/3 (Answer)
st
Q.36 If a is 1 Term and d is common difference of an A.P. Then its Common difference of an
th
A.P. Then its (2m+1) term is
A) a+2md (Correct) B) a+m
C) a+m+1 D) None of these
Explanation:-
a1=a , n=2m+1
Using the formula:-
a2m+1 = a+(2m+1-1)d
a2m+1 = a+2md (Answer)
̅̅̅̅
Q.37 If common fraction form , the recurring decimal 0. is written as:
A) 7/33 (Correct) B) 11/9
C) 33/7 D) 9/11
Explanation:-
Using the shortcut:
Number of repeating in Decimal part in Denominator 2 so no. of 9’s =2
 Whole fraction- Non-decimal part in Nominator=Product
e.g. 021-0/99= 21/99=7/33 (Answer)
Q.38 n Pr=?
A) n!/(n+1)! B) n!/(n+r)!
C) Pr-1 (Correct) D) n! (n+1)!
n
Explanation:-
On solving all the notation:-
n Pr-1= !
( − +1)!
On Expanding the notations
= ( −1)( −2)…..( − +1)( − )( − −1)…..3.2.1 ( −1)( −2)…..( − +1)( − )…..3.2.1 = !
=
( − +1)( − )! ( − )! ( − )!
(Answer)
n
Q.39 If expansion of (x+y) in every term , the sum of exponents of x and y is:
A) n B) n+1
C) n-1 D) 2n+1
Note: There should be one more option as all the given options are wrong.
E) n(n+1) (Correct)
Explanation:-
As Index =n
and Total number of terms=n+1
n
So, Sum of all exponents in expansion of (x+y) =Index (No. of Terms)= n(n+1)
(Answer)
Q.40 If the sine of angle is √ times its cosine of angle then angle will be:
A) 30* B) 60 * (Correct)
C) 45* D) 75*
Explanation:-
sinθ=√3 cosθ