Lista de Exercicios Matematica-35

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[17]Quest Tutorials
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Quest
Q.121 The true solution set of the inequality, 






 π
+−− ∫
x
0
2 dz
2
x6x5 > ∫
π
0
2
dxxsinx is :
(A) R (B) ( 1, 6) ( C ) ( − 6, 1) (D) (2, 3)
Q.122 If ∫
−
1
0
2x1
xn�
 dx = k 
0
π
∫ ln (1 + cos x) dx then the value of k is :
(A) 2 (B) 1/2 (C) − 2 (D) − 1/2
Q.123 Let a, b and c be positive constants. The value of 'a' in terms of 'c' if the value of integral
∫
++ +
1
0
5b331b dx)bxaacx( is independent of b equals
(A) 
2
c3
(B) 
3
c2
(C) 
3
c
(D) 
c2
3
Q.124 θθ+θθ∫ d)tan(secsec 22
(A) C)]tan(sectan2[
2
)tan(sec
+θ+θθ+
θ+θ
(B) C)]tan(sectan42[
3
)tan(sec
+θ+θθ+
θ+θ
(C) C)]tan(sectan2[
3
)tan(sec
+θ+θθ+
θ+θ
(D) C)]tan(sectan2[
2
)tan(sec3
+θ+θθ+
θ+θ
Q.125 ∫ +
+2
1
4
2
1x
1x
 dx is equal to:
(A) 
1
2
 tan−1 2 (B) 
1
2
 cot−1 2 (C) 
1
2
 tan−1 
1
2
(D) 
1
2
 tan−1 2
Q.126
1xx
Limit
→
1
xx
x
− ∫
x
x1
f(t) dt is equal to :
(A) 
( )f x
x
1
1
(B) x
1
 f (x
1
) (C) f (x
1
) (D) does not exist
Q.127 Which of the following statements could be true if, f ′′ (x) = x1/3.
I II III IV
f (x) =
28
9 x7/3 + 9 f ′ (x) =
28
9 x7/3 − 2 f ′ (x) =
4
3
 x4/3 + 6 f (x) =
4
3
 x4/3 − 4
(A) I only (B) III only (C) II & IV only (D) I & III only