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ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

IIT JEE 2014 TW TEST MARKS:57

TIME: 1 HR TOPICS: SNS DATE: 07/12/12

SECTION-IThis section contains 19multiple choice questions. Each question has 4 choices (A), (B), (C)

and (D) for its answer, out which ONLY ONE is correct.(+3, - 1)

1. The fourth term of the sequence 3,3

2, 1, is

(a)3

4 (b)

4

3 (c)

2

3 (d) none of these

2. The eleventh term of the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ..is

(a)89 (b)66 (c)72 (d)none of these

3. In a geometric progression consisting of positive terms, each term equals the sum of the next two

terms. Then the common ratio of this progression equals

(a) 512

1 (b) 5

2

1 (c) 5 (d) 15

2

1

4. A boy goes to school from his home at a speed of x km/hour and comes back at a speed of y

km/hour, then the average speed is equal to

(a)A.M. ofx, y(b)G.M. ofx, y(c)H.M. ofx, y(d)none of these

5. The arithmetic mean of nobservations is X . If the first observation is increased by 1, second by 2

and so on, then new arithmetic mean is

(a) nX (b) nX2

1 (c) 1

2

1 nX (d) 1

2

1 nX

6. If 21, AA be two A.M.s and 21 , GG be two G.M.s between aand b, then21

21

GG

AA is equal to

(a)ab

ba

2

(b)

ba

ab

2 (c)

ab

ba (d)

ab

ba

7. Let 1......,1

2

aaap 1......,12

bbbq , then ......122

baab is equal to

(a)1 qp

pq (b)

qp

pq

(c)

pqqp

pq

(d)none of these

8. Let a, b, cbe in A.P. and 1,1,1 cba . If

.......12 aax to

.......1 2 bby to

......12 ccz to , thenx, y, zare in


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(a)A.P. (b)G.P. (c)H.P. (d)none of these

9. The arithmetic mean of square of first nnatural numbers is

(a)6

1n

(b)

6

12 n (c)

6

121 nn (d)none of these

10. The numbers2log

1,

2log

1,

2log

1

1263

are in


Section B

11.

n

r

rnr1

is equal to

(a) )12(16

1 nnn (b)

2

2

1

nn(c)

6

12 nn (d)none of these

12. Let positive numbers a, b, c, dbe in A.P. Then abc,abd, acd,bcdare in

(a)A.P. (b) G.P. (c)H.P. (d)none of these

13. A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the

terms occupying odd places, then the common ratio will be equal to

(a)2 (b)3 (c)4 (d)5

14. The interior angles of a convex polygon are in arithmetic progression with common difference 5. If

smallest angle is3

2, then number of sides is

(a) 9 (b)7 (c)16 (d)20

15. If the mth term of an H.P. is nand nth term bem, then nm th term is

(a)nm

mn

(b)

nm

m

(c)

nm

n

(d)

nm

nm

16. If ,......,3,2,1,0 nixi then

n

nxxx

xxx1

......11

.......21

21 is

(a)equal to n2 (b) 2n (c)2

n (d)none of these

17. If real numbers 4321 and,, kkkk are G.M.s between a and b, then roots of the equation

04131

22

32

kkxkk

kxkk are

(a)one positive, one negative (b)both negative

(c) both positive (d)imaginary

18. A person purchased one kg of potatoes from each of 4 places at the rate of 1 kg, 2 kg, 3 kg and 4 kg

per rupee respectively. If he has purchased x kg of potatoes per rupee, then x is

(a)1.92 (b)2.08 (c) 2.10 (d)none of these

19. The first term of an A.P. of consecutive integers is 12 p . The sum of 12 p terms of this series

can be expressed as


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(a) 21p (b) 31p (c) 2

112 pp (d) 33 1 pp

20. Let rT be the rth term of an arithmetic progression, whose first term is aand common difference is d.

If for some positive integers m, n, mn,n

Tm1

andm

Tn1

, then da equals

(a)0 (b)1 (c)mn

1 (d)

nm

11

21. If a, b, c, dare positive real numbers such that ,2 dcba then dcbaM satisfies the

relation

(a) 10 M (b) 21 M (c) 32 M (d) 43 M

Section C

22. If ,.... 1015321 2222 n then the value of n is equal to

(a)13 (b)14 (c)15 (d)none of these

23. The third term of a G.P. is 4. The products of the first five term is

(a)46 (b)4

3 (c)4

5 (d)4

4

24. If the sum of first npositive integers is5

1times the sum of their squares, then nis equal to

(a) 5 (b)6 (c)7 (d)8

25. If HM : GM = 4 : 5 for two positive numbers, then the ratio of the numbers is

(a)4 : 1 (b)3 : 2 (c)3 : 4 (d)none of these

26. If cba ,, are in H.P., thencbab

11is equal to

(a)ba

11 (b)

ca

11 (c)

cb

11 (d)none of these

27. Ifx, y, zare three real numbers of the same sign, then the value ofx

z

z

y

y

x lies in the interval

(a)[2,

) (b)[3,

) (c)(3,

) (d)(

, 3)

28. The A.M., G.M. and H.M. of two distinct numbers are x, yand z respectively. Then which of the

following is true?

(a)z< y < x (b)y < x < z (c)x < y < z (d)z < x < y

29. If the sum of the first 2nterms of the A.P. 2, 5, 8, , is equal to the sum of the first nterms of the

A.P., 57, 59, 61, , then nmust be equal to

(a)10 (b)12 (c) 11 (d) 13


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30.xxx bca log

2

log

1

log

1 , then a, b, care in


31. If

2,0 then

xxxx

2

22 tan is always greater than or equal to

(a)2 tan (b)1 (c)2 (d)sec2

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