Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 1

7/31/2019 Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 1

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A

PHASE TEST-1

TIME: 3Hrs. IIT-JEE 2013 MAX. MARKS: 240

Paper-1

MARKING SCHEME In Section I(Total Marks: 24), for each question you will be awarded3 marks if you

darken ONLYthe bubble corresponding to the correct answer andzero marks if no

bubble is darkened. In all other cases,minus one (-1) mark will be awarded.

In Section II(Total Marks: 20), for each question you will be awarded4 marks if youdarkenALL the bubble(s) corresponding to the correct answer(s) ONLYandzero

marks otherwise. There areno negative marks in the section.

In Section III(Total Marks : 24), for each question you will be awarded4 marks ifyou darken ONLYthe bubble corresponding to the correct answer andzero marks if

no bubble is darkened. In all other cases,minus one (-1) mark will be awarded.

In Section IV(Total Marks: 12), for each question you will be awarded6 marks ifyou darken ONLYthe bubble corresponding to the correct answer andzero marks

otherwise, There areno negative marks in this section

NAME OF THE CANDIDATE CONTACT NUMBER

CODECODECODECODE


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MATHEMATICS

Section - I

This section contains 8 multiple choice questions. Each question has 4 choices.(a),

(b),(c) and (d), out of which ONLY ONE is correct.

1. If ( ) [2 7sin ],0 ,f x x x = + < < then the no. of points at which the function is discontinuous(a) 13 (b) 7 (c) 6 (d) 1

2. ( )[ ]

cos

12 /

2

xf x

x

=

+

, where x is not an integral multiple of and [.] denotes the

greatest integer function, is

(a) An odd function (b) An even function

(c) Neither odd nor even (d) None

3. ( ) 2 1lim sin ( )2

n

nf x x x

= + +

where [.] denotes the greatest integer function.

(a) Continuous at x= 1 but discontinuous at 32

x =

(b) Continuous at x = 1 and3

2x =

(c) Discontinuous at x = 1 and3

2x = (d) Discontinuous at x = 1 but continuous at

3

2x =

4. The number of points at which the function ( ) 0.5 1 tanf x x x x= + + does not have aderivative in the interval (0, 2) is

(a) 1 (b) 2 (c) 3 (d) 4

Space for rough work


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5.If the function2 ( 2)

, 2( ) 2

2, for x=2

x A x Afor x

f x x

+ + +

is continuous for all x, then

(a) A = 0 (b) A=1 (c) A = -1 (d) none of these

6.The domain off(x) = sin log24

1

x

x

is

(a) (0, 5) (b) (1, 5) (c) (2, 1) (d) (2, 3)

7. Define a function { }: 9 / 4f R R by f(x) = 23 9 4

x

x

+. The number of

values ofR such thatf(f(x)) =x is

(a) 1 (b) 2 (c) 3 (d) 4

8.The value of0

100 99sinlim

sinx

x x

x x

+

where [] represents greatest integral function, is

(a) 199 (b) 198 (c) 0 (d) none of these



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Section II

(Multiple Correct Answer (s) Type)

This section contains4 multiple choice questions.Each question has four choices (a), (b),(c),

and (d) out of which ONE or MORE may be correct.

9. The function, [ ]( )f x x x = where [ x ] denotes greatest integer function(a) is continuous for all positive integers

(b) is discontinuous for all non positive integers

(c) has finite number of elements in its range

(d) is such that its graph does not lie above the x axis

10.3

2

1cos4tan , 0

( ) 2 , 0

, 016 4

xx x

x

f x a x

xx

x

+

The possible value of a so thatf(x) is continuous function atx = 0

(a) 1 (b) 2 (c) 2 (d) 1

11. Ifp(x) is a polynomial such thatp(x2 +1) = {p(x)}2 + 1 andp(0) = 0 then(a) p(x) =x (b) p(0) = 1 (c) p(1) = 1 (d) p(1) = 0

12. Iff(x) = sin2x + cos4x then which of the following are true ?(a)

3( )

4f x (b) f(x) is an even function

(c) f(x) 1 (d) f(x) = 0 has exactly one root in (0, )

13.Let :f A B and :g B C be two mappings. Then which of the following statement(s) is(are) true ?

(a) gof:A Cis oneone impliesfis oneone

(b) gof:A Cis onto implies g is onto

(c) gof:A Cis oneone andfis onto implies g is oneone

(d) gof:A Cis onto and g is oneone impliesfis onto



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Section III

(Paragraph Type)

This section containstwo paragraphs. Based upon3 multiple choice questions to each

have to be answered. Each of these questions has four choices (a), (b), (c) and (d), out of

which ONLYONE is correct.

Paragraph-IIf

20

1 cos( ( )) 1lim

( ( )) 2x

f x

f x= as

0lim ( ) 0x

f x

= . If,, are the real roots ofax3 + bx2 + cx + d= 0.

On the basis of above information, answer the following.

14. 3 22

1 cos( )lim

( )x

ax bx cx d

x + + +

=

(a) a2( )2( )2 (b) a( )( )

(c) a( + + ) (d)2

2 2( ) ( )2

a

15.40

1 cos1 cos(cos ) s in1 sin(cos )limx

x x

x

=

(a) 1/8 (b) 1/6 (c) 1/6 (d) 1

16. 2 2 2 26

0

1 cos (sin ) cos (sin ) cos (sin )cos(sin )limx

x x x x x

x

+=

(a) 1/16 (b) 1/8 (c) 1/4 (d) 1/2



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20. Match the following :

Columns I Columns II

A f(x) = sin([x]) where [.] denote G.I.F

P Differentiable every

where

B f(x) = sin((x [x])) (where [.] denotes G.I.F) QNot differentiable atx

= 2

C1

sin , if 0( )

0 , if 0

x xf x x

x

= =

R

Not differentiable at

1 and 1

D f(x) = |2 x| + [2+x] (where [.] denote G.I.F) SContinuous at x = 0

but not differentiable

atx = 0

21. Match the following :


Column-I Column-II

A f(x) = {x}, the fractional part ofx P f1

(x) =1

2(4

x 4

x)

B f(x) =16 1

4

x

x Q f is an even function

C f(x) = log4 ( )2 1x x+ + R f is a periodic function

D f(x) =x3 1

3 1

x

x + S f is an odd function


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Answers

Section-1(Only one Option is correct)

1. a 2.a 3.c 4.c 5.a 6.c 7.b 8.bSection II (Multiple Correct Answer (s) Type)

9. a,b,c,d 10.b,c 11.a,b,c,d 12.a,b,c 13.a,b,c,d

14. d 15.a 16.d 17.d 18.b 19.b

20. A P B R C S D Q

21. A R B S C S D Q

Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 1

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