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MATHEMATICS DPP

DPP

TARGET : JEE (Advanced) 2015
T EST INFORM ATION

Course : VIJETA & VIJAY (ADP & ADR)

Date : 11-04-2015

NO
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Time : 112 min
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1 to 15
Multiple choice objective (no negative marking) Q
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33 to 40

1
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(5 marks, 3 min
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[45, 45]
[85, 51]
[24, 16]

Let f be a continuous real function such that f(11) = 10 and for all x, f(x) f(f(x)) = 1 then f(9) =
1
10
9
(A) 9
(B)
(C)
(D)
9
9
10
n2

2
...




2 


sin 
1
n 
 where [
...
} = FPF, is
The value of Lim
 2
n  
1 
1  n  cos n 
 2n tan  tan 



n 
n


(A) 1
(B) 2
(C) 3
(D) 0

If f(x) =
(A) 0

4
...


6
...


If real numbers a and b satisfy equation |a – 1| + |b – 1| = |a| + |b| = |a + 1| + |b + 1| then minimum
value of |a – b| is
(A) 3
(B) 0
(C) 1
(D) 2

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2

–1

The least positive integral solution of x – 4x > cot x is
(A) 1
(B) 2
(C) 5



(D) 4




– sin –1 2x 1– x 2
3
The value of lim
is
3
3
x
x–
2
2
(A) 1
(B) 2

(C) 3

(D) 4

m

11
...
] denotes GIF) is equal to
 n

r 1  2  

(A) 0 for mR
(B) 0 for m > 0
(C)  for m 0
(D) 1 for m = 0





12
...


If f(x) is a differentiable function satisfying f(x + y) = f(x) f(y)  x, y  R and f(0) = 2 then f(x) =
(A) e2x
(B) 2ex
(C) –e2x
(D) –2ex

14
...






24  2x  x2
25  x 2
If a =
and loga
> 1, then x
16
14
(A) (0, 1)
(B) (–3, 1)  (3, 4)
(C) (–– 17)  (1, ) (D) (4, 5)

16
...


If f(x) = 1   x   x x where [x] and {x} denote the integral part and fractional part of x respectively and
 
a = Lim f(x), b = Lim f(x), c = Lim f(x) then



1

x 0

x 0

x 0

(A) only 'a' exists
(C) a and c does not exist
18
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x 0

x   0 , where [
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1
 1

, x0

If f(x) =  x 2 x 2
then at x = 0, f(x) is
sin 1x  b  , x  0

(A) continuous if b = 0
(B) discontinuous for any real b
(C) differentiable for b = ± 1
(D) non-differentiable for any real b

Consider a continuous function f:[0, )  [0, )
...


If f(x) =

sin



(C)

 f r  = 11

(D) f'(2) = 0

r 0



x  1  2 then

(A) f(x) is continuous at x = 2
(C) f'(2) = cos1

(B) f(x) is differentiable at x = 2
(D) f(x) is non-differentiable at x = 0

23
...
Which
one is correct?
(A) f'(1) = 0
(B) af'(1) < 0
(C) c  0
(D) abc  0

24
...


For all   R, the quadratic equation ax2 + (b – )x + (a – b – ) = 0 has real roots
...


Which of the following is a subset of solution set of inequality |x2 – 2x| + |x – 4| > |x2 – 3x + 4|
(A) (0, 2)
(B) (4, )
(C) (0, 3)
(D) [4, 5)

27
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(n + 2–n+1)}n then which of the following is true?

2

n

(A) p is irrational
 1 x 
(C) p > Lim

x   x 

(B) integer nearest to p is 7
n x  x

(D) all of these

28
...
] denotes GIF and {
...


The equation 2log(x + 3) = log (x) has only one solution if
(A) = 12
(B) (–, 0)
(C) (0, )

30
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Comprehension # 1 (Q
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By changing origin we can say that if f(x – a) is
continuous at x = a then (x – a) f(x – a) is differentiable at x = a
33
...


If f(x) =

x sin | x |

is differentiable is
1 | x |2
(A) R – {0, 1, –1}
(B) R
(C) R – {1, –1}
(D) None of these
34
...

Let f(x) = |x|, g(x) = sinx and h(x) = g(x) f(g(x)) then
(A) h(x) is continuous but not differentiable at x = 0
(B) h(x) is continuous and differentiable everywhere
(C) h(x) is continuous everywhere and differentiable only at x = 0
(D) all of these
Comprehension # 2 (Q
...
36 to 37)
If left hand derivative and right hand derivative of a function is same and finite then the function is
continuous as well as differentiable
...
If one of the derivatives is infinite then the function may
be continuous but not differentiable
...


f(x) =

x

is
1  21/ x
(A) continuous at all points
(C) continuous for x  R – {0}

(B) differentiable at all points
(D) non-differentiable at x = 0, 1

Comprehension # 3 (Q
...
38 to 40)

38
...


40
...

2
 4
The graph of y = (x) is a
(A) parabola
(B) ellipse
(C) hyperbola
(D) circle
One of the vertices of the conic is
 1 1
(A) (1, 0)
(B) (0, 1)
(C) (1, 1)
(D)  , 
2 2
Length of latus rectum of conic is
9
16
16
25
(A)
(B)
(C)
(D)
16
25
9
16
ANSWER KEY

DPP # 1
1
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(D)

3
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(A)

5
...


(C)

7
...


(D)

9
...


(C)

11
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(BD)

13
...


(ACD)

15
...


(ABCD)

17
...


(ABCD)

19
...


(ACD)

21
...


(BC)

23
...
(ABD)

25
...


(AB)

27
...


(ABC)

29
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(ABD)

31
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(ACD)

33
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(A)

35
...


(C)

37
...


(A)  (p), (B)  (p), (C)  (p, q, s), (D)  (s)

39
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4

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