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QUEST TUTORIALS
Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. The coefficient of xr in the expansion
of, 1 +
a b x
+
1!
+
( )
!
a bx+2
2
+ ...... +
( )
!
a bx
n
n
+
+ ...... is :
(A)
( )
!
a b
r
r
+
(B)
b
r
r
!
(C)
e b
r
n r
!
(D)
e
a br
+
2. If ex = y +
12
+y
, then y =
(A)
e e
x x
+−
2
(B)
e e
x x
−−
2
(C) ex + e - x (D) ex - e - x
3. If y = x −
x x
2 3
2 3
+
− ...... ∞ , then x =
(A) y −
y y
2 3
2 3
+
- ...... ∞
(B) y +
y y
2 3
2 3! !
+
+ ...... ∞
(C) 1 +
y y
2 3
2 3! !
+
+ ......
(D) None of these
4.
a b
a
a b
a
a b
a
−
+−
+−
1
2
1
3
2 3
+ ....
is equal to :
(A) loge
(a - b) (B) loge
a
b
(C) loge
b
a
(D)
e
a b
a
−
5. If y = −
xx x
3
6 9
2 3
+ + +
......
, then
x =
(A)
1
3
+ey
(B)
1
3
−ey
(C) (1 - ey)1/3 (D) (1 - ey)3
6.
2
1!
+
2 4
2
+
!
+
2 4 6
3
+ +
!
+ ...... ∞ =
(A) e (B) 2 e
(C) 3 e(D) None of these
7.
1
3
+
1
2 32
.
+
1
3 33
.
+
1
4 34
.
+ ..... ∞ =
(A) loge 2 - loge 3
(B) loge 3 - loge 2
(C) loge 6(D) None of these
8. 1 +
1
3
1
5
1
7! ! !
+ +
+ ...... ∞ =
(A) e -1 (B) e
(C)
e e+
−1
2
(D)
e e−−1
2
9. 1 +
2
2
3
3
4
4
3 3 3
! ! !
+ +
+ ...... ∞ =
(A) 2 e(B) 3 e
(C) 4 e(D) 5 e
10.
2
3
4
5
6
7! ! !
+ +
+ ...... ∞ =
(A) e (B) 2 e
(C) e2(D)
1
e
LOGARITHM
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