Qua,Trigo,Kinematics,Mole Concpaper 1

7/31/2019 Qua,Trigo,Kinematics,Mole Concpaper 1

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APEX INSTITUTE TEST PAPER-1

A

PHASE TEST-1

TIME: 3Hrs. IIT-JEE 2014 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. Three circular coins each of radii 1 cm are kept in an equilateral triangle so that all the threecoins touch each other and also the sides of the triangle. Area of the Triangle is

(a) ( ) 24 2 3 cm+ (b) ( ) 21

12 7 34

cm+

(c) ( ) 21

48 7 34

cm+ (d) ( ) 26 4 3 cm+

2. sin cos 1, 0 ,2

x xIf then

+ < <

(a) [ )2,x (b) ( ], 2x (c) [ ]1,1x (d) [ ]2, 2x

3. The number of real solutions of the equation 1 1 127 12 2.(8)x x x+ = is(a) one (b) two (c) infinite (d) zero.

4. The value of a for which the equation ( )23 32 log log 0x x a + = possess four realsolutions

(a) 2 0a < < (b)1

0 8a< < (c) 0 5a< < (d)N.O.T

Space for rough work


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5. The set of values of a for which 1 lies between the roots of 2 3 0x ax a + = is(a) (- ,-6) (b) (- ,+6) (c) (- ,-6) (2, ) (d) (2, )

6. The number of positive integral solutions of ( ) ( )( ) ( )

3 42

5 6

3 4 20

5 2 7

x x x

x x

is

(a) four (b) three (c) two (d) only one

7. If 5 7sin sin sin18 18 18

a

= and is the integral root of the equation 22 5 3 0x x + =

,then a is equal to

(a)1

4x(b)

1

6x(c)

1

8x(d)

1

10x

8. The values of a for which the equation 4 4sin cosx x a+ = has real solutions(a)

31

4

a (b)1

1

4

a (c)1

1

2

a (d) N.O.T



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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 solution set of sin cos 2x x contains(a) ,

6 6x n n

+

(b)2

x n

+

(c) ,8 8

x n n

+ (d) ,

4 4x n n

+

10. In a triangle tan A + tan B + tan C = 6 and tan A tan B = 2, then the values of tan A, tan B andtan C are

(a) 1, 2, 3 (b) 2, 1, 3 (c) 1, 2, 0 (d) none of these

11. If 3cos5

= and 5cos13

=

(a) ( )33

cos65

+ = (b) ( )56

sin65

+ =

(c)2 1sin

2 65

=

(d) ( )

63cos

65 =

12. Let a,b,c R. If 2 0ax bx c+ + = has two real roots A and B where A < 1 and B > 1, then(a) 1 0

b c

a a

+ + < (b) 1 0b c

a a

+ + <

(c) c a< (d) c a b<

13. ( )2

5 2 3 169 0x

x+

is true in the interval

(a) ( ) , 2 (b) ( )0, 2

(c) ( )2,

(d) ( )0, 4



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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-ILet us consider the quadratic equation ( ) ( ) ( )

21 2 1 3 1 8 0m x m x m+ + + + = , where m R {1}.

On the basis of above information answer the following:

14.The number of integral values ofm such that the given quadratic equation has imaginary roots are(a) 0 (b) 1 (c) 2 (d) 3

15.The set of values ofm such that the given quadratic has at least one root is negative is

(a) m (, 1) (b)

(c) m 1

1, 8

(d) m R

16. The set of values ofm such that the given quadratic equation has both roots are positive is(a) m R (b) m (1, 3)

(c) m[3, ) (d) (, 1) [3, )


1 ,

8m


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Paragraph-IIParagraph for Question Nos. 17 to 19

If ( )log 0, 1, 0x aa b x b a a b= = > > m > 0, m 1,

(i) log log logm m m

ab a b= +

(ii) log log logm m m

aa b

b

=

(iii) log logbm ma b a= (iv)

log logc cb aa b=

17.Values ofx satisfy the equation( ) ( )2 2

2 3 3 7log 6 23 21 4 log 4 12 9x xx x x x+ ++ + = + +

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

18.Value ofx satisfy equation 10 10log log 525 5 4x x= + is.(a) 1 (b) 10 (c) 1000 (d) 4

19.Values ofx satisfy the equation ( )23log 2log 9 71 1xxx x = (a) 1, 3 (b) 4, 7 (c) 9, 11 (d) 81, 2



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20. Match the following :

Columns I Columns II

A The number of roots of the equation4 23sec 8 10sec + = in[ ]0, is P 1

B The number of roots of the equation

2

5cos 2 2cos 1 02

+ + = in ( )0, Q 2

C The number of roots of the equation ( )2

sin 1x x = is R 3

D The number of roots of the equation2

1tan x

x = in[ ]2,1 is S 4

T 0

21. Match the following :


Column-I Column-II

A If 2log

2x

x thenx P (2, 3)

B If log0.4(x 5) < log0.016(x 5) Q (6, )

C

Log3(x + 2)(x + 4) + log1/3(x + 2)

Qua,Trigo,Kinematics,Mole Concpaper 1

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