Jee 2014 Booklet6 Hwt Integral Calculus 2
Short Description
Jee 2014 Booklet6 Hwt Integral Calculus 2...
Description
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [1]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct.
1.
5.
dx is : 5 4 cos x
(A) (C)
0
/2 /3
(A) (C)
/4 /6
(B) (D)
Let f : R R and g : R R be continuous functions. Then the value of the integral 2
3.
7.
f f 2 2
(D)
g g 2 2
1
and
f
(x)
be
a
function
f x g x dx is : e7 4
that
4.
If I1
dx and I 2 log x
(D)
1
0 120
(A)
I1 2 I 2
(B)
I 2 2 I1
(C)
I1 I 2 0
(D)
I1 I 2 0
10.
5/2 0
(B) (D)
3 5
f 3a x g x , g 3a x h x
If
h 3a x f x .
and
f x
3a
Then
f x g x h x dx is : 0
(A) (C)
VMC/Integral Calculus-2
120 120
e
1
e
(B) (D)
log e x dx is : x
(A) (C)
e2 3 e 2 2
e dx , then : x
1 2
30
e3 2
2 x
(B) (D)
|cosx|dx
(A) (C) 9.
(B)
e2 3 e 2 2 e2
1 0
30
e2
0
(C)
(B) (D)
x 1dx , where [ ] represents the greatest integer
8.
1
(A)
1 /4
1
satisfies f x g x x 2 . Then the value of the integral
2/3 5/3
sin3 x 2 x sin2 x( x2 1) x2 sin x (1 2 x2 x4 ) dx
function equals : (A) 0 (C) 1
Let g (x) be a function satisfying g x g x and =
(B) (D)
y | x 1| is :
1
1 0
(0)
2
f x f x g x g x dx
(C)
g
1/3 4/3
is: (A) (C)
2
(A) (B)
x, y : x 1
6. 2.
Area of the region
101
a 3a
(B) (D)
2a 3a/2
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [2]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. e
1.
tan 1 x log x x 1 x2 1
tan 1 e
(A) 1
2.
sin x 1
6
sin
1
log tan e
(C)
1 tan 1 e
(D)
tan 1 e
(B)
2 8 4
(C)
2 8 2
(D)
2 8 2
dx
is :
2 8 4
(A)
(B)
2
1 sin x
1
3.
dx is :
x d x , where {x} is fractional part function is : 2
0
3 8
(A) 4.
2
2
3 8
(B)
The area bounded by 2 y 1 y
2
3 2 8 (C)
2
x and its vertical asymptotes is :
(B)
(C)
2
3 2 8 (D)
(D)
2
4
Area bounded by y 2 x 3 4 4 x , the ordinate x = 3, x = 4 and above the x-axis is : 5
5 6
(A)
6.
2
(A) 5.
2
(B)
5 8
(C)
3 8
(D)
2
x x Area bounded by x-axis and the curve f x e . e|x| . e between the lines x 1 and x = 2, where [ ] represents greatest
integer function and { } represent fractional part function, is : e 1 2
(A) x
7.
If
x
(A)
8.
(B)
1 f t
2
e2 1 2
(C)
e3 1 2
(D)
e4 1 2
3 x dt f z dz t dt , [.] represents greatest integer function and f 0 1 , then f is : 2 20 (B) (C) 2 (D) 0 1
1
If f a b x f x , then
b
xf x dx is : a
(A)
ab 2
b
f x dx a
VMC/Integral Calculus-2
(B)
ab 2
b
f x dx
b
(C)
a
a b f x dx a
102
b
(D)
a b f x dx a
HWT-6/Mathematics
Vidyamandir Classes 2 3
9.
x cos 2 x3 2 dx is :
0
(A) 4
10.
If
3
f x dx 4 and
1
(A)
(B) 4
4
7 f x dx 7 , then the value of
VMC/Integral Calculus-2
6
(D)
12
(D)
3
2
f x dx is :
1
2
5
(C)
(B)
4
(C)
103
3
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [3]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.5
1.
x
2
dx , where [ ] denotes the greatest integer function, equals :
1
2 2
(A)
(B)
2 2
(C)
2.25
(D)
1.25
(B)
3
(C)
0
(D)
5
(D)
0
2
2.
n log tan x dx is : 0
2
(A)
2
x2 2
3.
The number of points at which
0
(A)
1
t 5t 4 2 et
(B)
dt has extremum is :
2
(C)
3
4.
3 2 p sin x q cos x r dx depends on the value of :
If p, q, r are constants, then the value of
3
(A)
5.
sin
2
(A) x
7.
If
0
(A)
1
p and q only
(C)
p only
(D)
all of p, q, and r
cos x cos 1 sin x dx is : 2 2
(B)
2 4
(C)
2 8
(D)
2 1 4
1
1 f t dt x tf t dt then the quadratic equation whose roots are f and f (2) is : 2
x
2
3x 7 x 2 0
(B)
3x 2 7 x 2 0
(C)
3x 2 7 x 2 0
(D)
3x 2 7 x 2 0
(C)
18
(D)
98 3
10
8.
(B)
The area of the region in the first quadrant enclosed by the x-axis, the line x 3 y and the circle x 2 y 2 4 is : 2 (A) (B) (C) (D) 4 3 2 3 5 2
6.
q and r only
x 2 x 1 x 2 x 1 dx is :
1
(A)
110
VMC/Integral Calculus-2
(B)
110 3
104
HWT-6/Mathematics
Vidyamandir Classes 9.
P(x) is a non-zero polynomial such that P(0) = 0 and P x3 x 4 P x , P 1 7 and
1
1
P x dx 1.5 then P x P x dx is :
0
(A)
10.
6
(B)
8
(C)
1 1 If for a non-zero x, af x bf 5 a b ; and x x
(A)
a log 2
VMC/Integral Calculus-2
7b 5a 2
(B)
a log 2
2
7.5
0
(D)
None of these
(D)
a log 2
f x dx a2 b2 then k is : k
1
7b 5a 2
(C)
105
a log 2
7b 5a 2
7b 5a 2
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [4]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
If [x] is the greatest integer less than or equal to x, then the area bounded by y x x and y x x , and the x-axis between x 2 to x = 2 is : (A) 1 (B) 2 (C) 3/2 (D) 1/2 2
2.
x sin x cos x sin 4 x cos 4 x
0
2 32
(A)
3.
dx
(B)
2 8
(C)
2 16
(D)
16
(B)
2 4
(C)
2 2
(D)
2
(C)
1
(D)
3 2
1 cos2 x dx x sin x
0
4.
(A)
4
If g x
1 x
(A)
1 2
x
3t 2 g t dt , then g 2 is : 2
5.
1 n n lim
2
If
e
n 1
8.
(B)
5
0
0
f t dt
f t dt where, 0 5 the interval in which H is increasing is :
5 2 , 5
(C)
5 0, 2
(D)
(1. 5)
1
(C)
1 e
(D)
0
(C)
2e 4 e
(D)
2e
(C)
1 2
(D)
1
k
k 0
e t2
log 1 n equals : (B) e4
dt , then,
1
(A)
2
(0, 5)
(A)
7.
3 4
Let f x 2 x 15 x 24 x and H 3
(A)
6.
(B)
log t dt equals :
e
e2 2
(B)
e4 e2 1
4
e
The area bounded by the curves x 2| y | 1 and x = 0 is : (A)
1 4
VMC/Integral Calculus-2
(B)
1 3
106
HWT-6/Mathematics
Vidyamandir Classes
9.
n n3 r3 1 dx r 1 , P lim Let 3 n 1 x n 3n 0
(A) 2
10.
log 2 1
1/ n
then log P is :
(B)
log 2 3 3
(C)
2 log 2
(D)
log 4 3 2
(B)
8
(C)
1
(D)
1 2
1 sin 3 x
1 2 sin x dx is : 0
(A)
2
VMC/Integral Calculus-2
107
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [5]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Let f (x) be differentiable in R and f x 2 x 2
2
2
f t dt tf t dt . Then
0
6 19
(A) 2.
(B)
f x dx is :
0
3 19
1
0
(C)
14 19
6 19
(D)
x2 8 , the x-axis and the ordinates x 3 , equals : Area enclosed by the curve f x 4 x2 4 4 4 3 1 3 8 tan 2 8 tan 1 2 (A) (B) 3 2 3 2 4 3 8 tan 1 (C) (D) None of these 3 2 log 4
*3.
If the function f x Ae
2x
39 f x cx dx 2 , then :
Be Cx satisfies the condition f 0 1, f log 2 31 and x
0
(A)
A=5 1
*4.
If I1 2
1
x3
dx, I 2 2
0
2
If A
x4
2
dx, I 3 2
0
I 2 I1
(A)
*5.
x3
(C) 2
sin x dx and B sin x cos x
(D)
B=6
4
1
I3 I 4
2
C=3
dx , and I 4 2 x dx, then :
1
(B)
0
(A)
B 6
(B)
(C)
I 4 I3
(D)
I1 I 2
(C)
A B
(D)
AB
cos x dx , then : sin x cos x
0
A+B=0
(B)
A B
2
4
2
6.
, 5 x 0 2 x 1 , 3 x 1 4 x 7 Let f x 2 and g x 2 . Then value of g f x dx equals : x 1 x0 3 x 2 , 5 x x 7 , 2 (A) 0 (B) 101/12 (C) 1991/6 (D) 1991/12
1
7.
xe x
0 1 x 2 dx (A)
/ 2 sin /2
8.
e 2
(A)
2
(B) x sin 4 x
4 15
VMC/Integral Calculus-2
1 2 e 1
(C)
1 2 e 2
(C)
(D)
None of these
(D)
2 15
sin x cos x dx is equal to : (B)
0
108
4 15
HWT-6/Mathematics
Vidyamandir Classes 9.
The values of a and b which satisfy f 1 2 , (A)
(C)
10.
3
0 f x dx 7, f x a2
1, 2 2 3 loge 2 1 1 , 2 loge 2 7 log 2
b , are :
(B)
1 ,0 log e 2
(D)
2 7 log 2 1 1 , 2 loge 2 3 log 2
3 1 If x 2 f x f 2 for all x except at x = 0, then f x dx 1/ 3 x (A) 4/3 (B) 8/3 (C) 1/3
VMC/Integral Calculus-2
x
109
(D)
None
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [6]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. /4
1.
(A) (C) 2.
1
/ 4 sec2 x 1 sinx dx
6.
/4
/2 2
(B) (D)
(A) (C)
2
2
Area common to the circle x y 64 and the
(B)
(D)
None of these
(C)
16 3 4 3
The
(A) (C)
5.
(A)
y
4.
16 3 8 3
16 3 4 3
area 2
1 x2
bounded
by
the
7.
y x and
curves
3 3 2 6
3 2
(B)
3 9.
(D)
None of these
The area enclosed between the curves y = tan x, tangent drawn to it at x and y 0 is : 4 log 4 1 log 4 1 (A) (B) 4 2 log 4 1 (C) (D) None of these 4 The area bounded by the hyperbola between the lines x = 2 and x = 4 is :
3 4 log 2 3 (D)
8 3 4 log 2 3
(C)
8
4
VMC/Integral Calculus-2
(B) (D)
0 x dx ,
1 2 None
where {} denotes the
(B) (D)
25/3 None
e x sin x dx is equal to :
(A)
e / 2 1 2
(B)
(C)
e / 2 1 2
(D)
e / 2 1 2 None
If f x min, 2 sin x, 1 cos x, 1 , then
(C)
5 6 2 1 3 3 3 1
(B) (D)
0
f x dx
2 3 5 1 3 6 3 1
bc
10.
3 2 log 2 3
4 3 2 log 2 3 (B)
0
(A)
x2 y 2 4
(A)
1 2 1
The value of
/2
8.
is :
3 3
x dx
fractional part of x is : (A) 16/3 (C) 7/3
2
1
4
parabola y 2 12 x is equal to :
3.
0 sin
a c f x c dx b (A) a f x c dx b (B) a f x dx b (C) a f a b c x dx (D)
110
None of these
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [7]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1/ 2
1.
2.
1/ 2
2
1
2
x 1 x 1 x 1 x 1 2 dx
(A)
3
(B)
(C)
3 1 cos 1
(D)
6. 3 1 cos 1 2 None of these
Area included between the parabolas y 2 4ax and 7.
x 2 4ay is equal to :
3.
(A)
8a 2 3
(C)
4a 2 3
(D)
5 2 6
(B)
(C)
5 2 6 4 2 6
2
4.
1 10100
(D)
None
Let f be real valued function such that f 2 2
(C) 2
2 4
2 2
1
1
1 1
(B) (D)
The value of the integral
(A) (C)
(D)
0 None
0 f k 1 x dx is : 1
k 1
24
(B)
dt x2 (B) 12 (D) None
1
10.
2 None of these
|cosx sinx | dx
(A)
4 2
(B)
2 2
(C)
2
(D)
None
If I1
2
0 f x dx n 0 f x dx a
(B) (D)
0 f x dx 1 n f x dx 0
a
0 x dx, I 2 0 x dx, x fractional part of
x, = G.I.F., a Z , then :
2
0
VMC/Integral Calculus-2
2
1 / 4 x tan x x dx
The area of the smaller region bounded by the
(A)
f x 4t 3
6 32
3
circle x 2 y 2 1 and the lines | y | = x + 1 is :
5.
(C)
n
9.
24
4 None of these
1 10010
3
2
(D)
(B)
(A) (C)
2 2
11 10100
4
8.
5 2 6 4 2 6
(A)
(A) (C)
Area bounded by | y | x 1, 8 y x 2 & x-axis is equal to: (A)
dx
x2
None of these
2
99
and f 2 1 , then lim
16a 2 3
(B)
0 x 1 x
111
a 1
(A)
I2
(C)
I1 a 1 I 2
I2
(B)
I1 aI1
(D)
I 2 aI1
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [8]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Area bounded by the curves | x | 2 is given by : (A) 5 (C) 9/2
2.
The
area
y | x 1|, y 0 and
(C) 3.
bounded
2
3e 2e 3
3e
3e 2
2e 3
by
3
(B)
/ 2
the
2
curves
(A) (C)
x 1
7.
e 1
If
(B) (D)
0
dx
x2 4 x2 9 k , then the value of k is : 0
e
(D)
1 1
(A) (C)
1/60 1/40
(B) (D)
1/80 1/20
None of these The area of the figure bounded by the lines x 0 x / 2 f x sin x and g x cos x is:
tangent and normal at 1, 3 and x-axis in A1 and A2.
8.
(A)
Then A1/A2 =
(C)
(C)
(B)
3 3
(D)
3
3
The value of
0
3
3
9.
3 1 2 1
3 1
(B) (D)
2
2 1
An inflection point on the graph of the function x
None of these
dx
y
1 cot x
is equal to :
t 1 t 2
2
dt is :
(B)
/2
(C)
/4
(D)
/3
(A)
x 1
(B)
x 3/ 2
(C)
x 4/ 3
(D)
x 1
2
(A)
The value of
2 2
0
/2
5.
f x f x g x g x dx
4 None
Let the circle x 2 y 2 4 divide the area bounded by
(A)
4.
If f R R g R R are continuous functions then the value of the integral /2
(B) (D)
y x 2 2 x 1, e x y 1 0 and ordinates and x = 1 is : (A)
6.
x dx
4 cos2 x 9 sin2 x
/4
10.
The value of
sin
x dx is :
0
(A) (C)
is equal to :
0 2
(B) (D)
1 None of these
0
2
(A)
/ 12
(B)
2 / 4
(C)
2 / 6
(D)
2 /3
VMC/Integral Calculus-2
112
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [9]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Let f be a periodic continuous function with period
6.
T
T 0.
I
If
f x dx ,
then
the
value
cos x If f x e2e . sin x for | x | 2 , 3
of then
0 4 4T
I1
2
f 3 x dx is :
(A) (C)
4
(A) (C) 2.
I 3I
(B) (D)
2I 4I
3 / 4
2 2 x 1 dx , where [x] is the greatest The value of x
7.
integer less than or equal to x is : (A) 2 (B) (C) 4 (D)
8/3 None of these
The area bounded by the curves y 5 x 2
/4
8.
5 2 4
(C)
5 2 2 x2 4
4.
f x
If
(B)
5 2 4
(D)
5 2
2
e t dt , then the function
1 2
(C) /4
5.
(B) (D)
0 2
9.
(C)
2 1/2
2 1 / 2
5/3 2/3
Let f x
(B) (D)
1/3 4/3
x
6 x 2 dx , then the real roots of the
(A)
x 6
(B)
x 3
(C)
x 2
(D)
x 1
1
10.
Let f be an odd function, then
| x| f x cos x dx is
1
log 1 tan 2 2 tan d log 2
(B)
log 2 2
log 2 4
(D)
log 2
VMC/Integral Calculus-2
(B) (D)
dx is equal to : 1 cos x
equation x 2 f x 0 are :
f x
equal to : (A) 0 (C) 2
0
(A)
1 3
0
(B) (D)
The area of the plane region bounded by the curves
(A) (C)
x2
increases in : (A) 0
0 2
x 2 y 2 0 and x 3 y 2 1 is equal to :
and
y | x 1| is :
(A)
(A) (C)
0
3.
f x dx otherwise :
113
(B) (D)
1 None of these
HWT-6/Mathematics
Vidyamandir Classes DATE :
TIME : 40 Minutes
MARKS : [ ___ /10]
TEST CODE : IC-2 [10]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. /4
1.
The value of the integral
sin x cos x dx is : 3 sin 2 x
0
(A)
2.
4.
(B)
log(3)
(C)
1 log(3) (D) 4
1 log(3) 8
The area of the plane figure bounded by the interval 5 / 6 of the x-axis, the graph of the function y cos x and the segment so the straight lines x 5 / 6 and x is : (A)
3.
log(2)
3/2
(B)
5/2
(C)
3/4
sin x sin 2 x sin 3x sin 2 x sin 3x /2 3 4 sin x 3 4 sin x then the value of If f x f x dx is : 1 sin x sin x 1 0 (A) 3 (B) 0 (C) 2/3
(D)
7/2
(D)
1/3
(D)
2
Let f 0 R and F x
x
f t dt . If F x 2 x 2 1 x then f 4 equals :
0
(A)
5.
5/4
(B)
7
(C)
4
The area bounded by the curve y f x x 4 2 x3 x 2 3 , x-axis and the ordinates corresponding to minimum of the function f x is : (A)
6.
1
(B)
91 30
(C)
30 9
(D)
Suppose that the graph of y f x contains the points (0 , 4) and (2, 7). If f is continuous then
4 2
f x dx is equal to: 0
(A)
2
(B)
–2
(C)
3
(D)
None of these
0
(C)
2
(D)
None of these
(D)
3/2
x
sint dt 2
7.
The value of lim 0 x 0
(A) 8.
1
sin x 2
is : (B)
The area between the curves y x 2 and y x1 3 taking x 1 1 is : (A) 1/2 (B) (C) 3/4 2
VMC/Integral Calculus-2
114
HWT-6/Mathematics
Vidyamandir Classes 9.
10.
1 22 n2 is : The value of lim .......... n 13 n3 23 n3 n3 n3 1 1 log 2 (A) (B) (C) 3 3 1 If x 2 f x f 0 for all x R ~ 0 then x
(A)
sin 2
VMC/Integral Calculus-2
(B)
1
sec
1 log 3 2
(D)
1 log 3 3
sec cos
(D)
0
f x dx =
cos
(C)
115
HWT-6/Mathematics
View more...
Comments
