B p q r s c q p s r d s q p r 38 tangent is drawn at

(B) p q r s
(C) q p s r
(D) s q p r
38. Tangent is drawn at any point (x
i
, y
i
) on the curve
(x,y) = 0, which intersects the x-axis at (x
i +1
,0).
Now again, tangent is drawn at (x
i+1
, y
i+1
) which
intersects the x-axis at (x
i+2
,0) and so on (i = 1,2, .... n)
match the following List-I with List-II
to each of the questions is a single digit integer, ranging
from 0 to 9. The appropriate bubbles below the respective
question numbers in the ORS have to be darkened. For
example, if the correct answers to question numbers X, Y
and Z(say) are 6, 0 and 9, respectively, then the correct
darkening of bubbles will look like the following :
List - I List - II
(A) xy 2 = 1 (P) The sequence x
1
, x
2
...... x
4
are
terms of G.P.
(B) y = e –3x (Q) The sequence x
1
, x
2
, x
3
..... x
4
is periodic with period 2
(C) y = –cot –1 x (R) The sequence x
1
, x
2
........ x
4
forms an increasing A.P.
(D) y 2 = x (S) The sequence x
1
, x
2
, x
3
.....
is decreasing
39. Match the following
Column – I Column – II
(A) The most appropriate (P) [–1, 2)
interval of a for which the
equation ax
2
=logx has
real roots
(B) The most appropriate interval (Q)
1
,
2e
 



 
of a for which the equation
|log x| – ax = 0 posses
three root
(C) The most appropriate interval (R) (1,  )
of a for which the equation
x
3
–3x+[a] = 0 (where [
.
]
denotes the greatest integer
function) will have three real
and distinct roots
(D) The interval of x in which (S) (0, 1/e)
exlnx >
lnx
ex
SECTION-E
Integer Answer Type
This section contains Integer type questions. The answer
to each of the questions is a single digit integer, ranging
from 0 to 9. The appropriate bubbles below the respective
question numbers in the ORS have to be darkened. For
example, if the correct answers to question numbers X, Y
and Z(say) are 6, 0 and 9, respectively, then the correct
darkening of bubbles will look like the following :
0
X Y Z
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9

Application of Derivatives Aakash Institute
(10)
40. The maximum value of
 
 
2
2
2
3 4x x 4 x 5      
(where
1 x 3  
)
is
41. If the tangent at any point P (4m
2
, 8m
3
) of y
2
= x
3
is
a normal also to the curve, then find the value of
27m
2
42. The set of values of p for which the equation
   n x px 0 possess three distinct roots is
1
0,
 
 

 
, then floor(  ) =
43. If 4x
2
+ y
2
= 1, then the maximum value of
12x
2
– 3y
2
+16xy is ...........
44. Let y = f(x) be a parametrically defined expression
such that x = 3t
2

18t + 7 and y = 2t
3

15t
2
+ 24t +
10  t

[0, 6]. If the minimum and maximum val-
ues of y = f(x) be m and M respectively then
M
m
 
 
 
is ............
45. If f is continuous function satisfying f(f(x)) = 1 + x

x

R. then f

(1) is equal to _____.
46. The minimum value of k (k  I ) for which the equa-
tion e
x
= kx
2
has exactly three real solutions, is
________.
  

Aakash Institute Application of Derivatives
(11)
ANSWERS
LEVEL-1
CPP-06
SS JEE(M) &
ADVANCED
  
LEVEL-2
1. (D) 2. (D) 3. (A) 4. (B) 5. (A) 6. (A)
7. (C) 8. (C) 9. (D) 10. (A) 11. (C) 12. (A,B,D)
13.(A,B,D) 14. (A,B,D) 15. (B,C) 16. (A,C) 17. (D) 18. (A)
19. (D) 20. (D) 21. (3) 22. (1) 23. (9) 24. (3)
25.(5) 26. (2)
1. (B) 2. (C) 3. (D) 4. (D) 5. (B) 6. (D)
7. (A) 8. (A) 9. (A) 10. (C) 11. (C) 12. (B)
13. (B) 14. (A,C) 15. (A,B) 16. (B,C,D) 17. (C) 18. (A)
19. (B,C) 20. (A,D) 21. (A) 22. (B,C,D) 23. (C,D) 24. (A,C)
25. (C,D) 26. (A,B,D) 27. (B,D) 28. (B,D) 29. (A,D) 30. (B)
31. (D) 32. (D) 33. (D) 34. (C) 35. (B) 36. (D)
37. (B) 38.(A-P B-R C-S D-Q) 39.(A-Q B-S C-P D-R) 40. (6)
41. (3) 42. (2) 43. (5) 44. (7) 45. (1) 46. (1)