Integrals Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. is equal to
(a)
(b)
(c)
(d)
2. Let I
n
 = , n is a positive integer. Then
(a) I
n
 : I
n – 2
 = n : (n – 1)
(b) I
n
 > I
n – 2
Page 2


PART-I (Single Correct MCQs)
1. is equal to
(a)
(b)
(c)
(d)
2. Let I
n
 = , n is a positive integer. Then
(a) I
n
 : I
n – 2
 = n : (n – 1)
(b) I
n
 > I
n – 2
(c) n (I
n – 2
 – I
n
) = I
n – 2
(d) None of these
3. If , then f '(x) is equal to
(a) cos (sin
3
 x) cos x – 2 cos (8x
3
)
(b) sin (sin
3
 x) sin x – 2 sin (8x
3
)
(c) cos (cos
3
 x) cos x – 2 cos (x
3
)
(d) cos (sin
3
 x) – cos (8x
3
)
4. If  then  is equal to
(a) 2m + n
(b) m + 2n
(c) m – n
(d) m + n
5. =
(a)
(b) ln (sec ln x) + C
(c)
(d)
Page 3


PART-I (Single Correct MCQs)
1. is equal to
(a)
(b)
(c)
(d)
2. Let I
n
 = , n is a positive integer. Then
(a) I
n
 : I
n – 2
 = n : (n – 1)
(b) I
n
 > I
n – 2
(c) n (I
n – 2
 – I
n
) = I
n – 2
(d) None of these
3. If , then f '(x) is equal to
(a) cos (sin
3
 x) cos x – 2 cos (8x
3
)
(b) sin (sin
3
 x) sin x – 2 sin (8x
3
)
(c) cos (cos
3
 x) cos x – 2 cos (x
3
)
(d) cos (sin
3
 x) – cos (8x
3
)
4. If  then  is equal to
(a) 2m + n
(b) m + 2n
(c) m – n
(d) m + n
5. =
(a)
(b) ln (sec ln x) + C
(c)
(d)
6. is equal to
(a)
(b)
(c)
(d)
7. The value of is
(a)
(b)
(c)
(d)
8. If  then
,............ are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Page 4


PART-I (Single Correct MCQs)
1. is equal to
(a)
(b)
(c)
(d)
2. Let I
n
 = , n is a positive integer. Then
(a) I
n
 : I
n – 2
 = n : (n – 1)
(b) I
n
 > I
n – 2
(c) n (I
n – 2
 – I
n
) = I
n – 2
(d) None of these
3. If , then f '(x) is equal to
(a) cos (sin
3
 x) cos x – 2 cos (8x
3
)
(b) sin (sin
3
 x) sin x – 2 sin (8x
3
)
(c) cos (cos
3
 x) cos x – 2 cos (x
3
)
(d) cos (sin
3
 x) – cos (8x
3
)
4. If  then  is equal to
(a) 2m + n
(b) m + 2n
(c) m – n
(d) m + n
5. =
(a)
(b) ln (sec ln x) + C
(c)
(d)
6. is equal to
(a)
(b)
(c)
(d)
7. The value of is
(a)
(b)
(c)
(d)
8. If  then
,............ are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
9. Let  and . Then which one of the
following is true ?
(a) K < 2/3 and J < 2
(b) K > 2/3 and J > 2
(c) K < 2/3 and J > 2
(d) K > 2/3 and J < 2
10.  is equal to ([x] = greatest integer = x)
(a)
(b) e
2
(c) 0
(d)
11. The line y = a intersects the curve y = g (x), atleast at two points. If  
 then  possible value of a is/are –
(a)
(b)
(c)
(d)
12. Let the equation of a curve passing through the point (0,1) be given by
y= If the equation of the curve is written in the form x = f(y)
then f(y) is
Page 5


PART-I (Single Correct MCQs)
1. is equal to
(a)
(b)
(c)
(d)
2. Let I
n
 = , n is a positive integer. Then
(a) I
n
 : I
n – 2
 = n : (n – 1)
(b) I
n
 > I
n – 2
(c) n (I
n – 2
 – I
n
) = I
n – 2
(d) None of these
3. If , then f '(x) is equal to
(a) cos (sin
3
 x) cos x – 2 cos (8x
3
)
(b) sin (sin
3
 x) sin x – 2 sin (8x
3
)
(c) cos (cos
3
 x) cos x – 2 cos (x
3
)
(d) cos (sin
3
 x) – cos (8x
3
)
4. If  then  is equal to
(a) 2m + n
(b) m + 2n
(c) m – n
(d) m + n
5. =
(a)
(b) ln (sec ln x) + C
(c)
(d)
6. is equal to
(a)
(b)
(c)
(d)
7. The value of is
(a)
(b)
(c)
(d)
8. If  then
,............ are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
9. Let  and . Then which one of the
following is true ?
(a) K < 2/3 and J < 2
(b) K > 2/3 and J > 2
(c) K < 2/3 and J > 2
(d) K > 2/3 and J < 2
10.  is equal to ([x] = greatest integer = x)
(a)
(b) e
2
(c) 0
(d)
11. The line y = a intersects the curve y = g (x), atleast at two points. If  
 then  possible value of a is/are –
(a)
(b)
(c)
(d)
12. Let the equation of a curve passing through the point (0,1) be given by
y= If the equation of the curve is written in the form x = f(y)
then f(y) is
(a)
(b)
(c)
(d) None of these
13. The integral is equal to :
(a)
(b)
(c)
(d) None of these
14. Let f be a positive function if
where 2k – 1 >0,  then I
1
 : I
2
 is equal to
(a) 2
(b) k
(c)
(d) 1
15. The value of  is
(a)
(b)
(c)
(d) None of these
16. Given that f and g are continuous functions on [0  a] satisfying f(a–x) =
f(x) and g(x)+g(a–x) = 2.
Then   is equal to :