1 Infomaths/Mca/Maths/Old Questions

OLD QUESTIONS-CW1

1 INFOMATHS/MCA/MATHS/OLD QUESTIONS

SEQUENCE & SERIES

1.If a, b, c are in A.P. and a2, b2, c2 are in H.P. then :

PU-2015

(a) 2b = 3a + c (b) b = 3a + c

2.If the sum of eleven consecutive numbers is 2761, than the middle number is :

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(a) 250 (b) 249(c) 252 (d) 251

3.If a, b and c are in geometric progression, then logax x, logbx x and logcx x are in NIMCET-2015

(a) Arithmetic progression

(b) Geometric progression

(d) Arithmetic-geometric progression

4.If the mean deviation of the numbers 1, 1 + d, 1 + 2d, …, 1 + 100d from their mean is 225, then the value of d is NIMCET-2015

(a) 20.0(b) 10.1(c) 20.2(d) 10.0

5.The nth term of the series

is : BHU-2015

(a) (b)

6. The geometric mean of the numbers 5, 10, 40, 80 is :

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(A) 10 (B) 30(C) 40 (D) 20

7. is equal to

HCU-2014

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

8.If G1, G2 are the geometric means of two series of observations and G is the geometric mean of the ratios the corresponding observations, then G is equal to :

BHU-2014

(a) (b) log G1 – log G2

©(d)

9.If are in AP, then :

BHU-2014

(a) a, b, c are in AP (b) a, b, c are in HP

10.If , Then equals :

BHU-2014

(a) (b)

©(d)

11.If s = 1 + a + a2 + ……, (a < 1), then a = ?

BHU-2014

(a) (b)

©(d)

12.The sum of integers from 1 to 60 that are divisible by 2 or 3 is

BHU-2014

(a) 330(b) 1230

13.The fifth, tenth and fifteenth terms of a GP are p, q, r respectively. Then:

BHU-2014

(a) p2 = qr (b) q2 = pr

14.The sum of n terms of is :

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(a) n + 2n – 1 (b) n + 2-n – 1

15. Let

Which of the following is true?

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(A) Y < Z < X (B) X < Y < Z

16.The value of the sum is

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(A) 2020/10101(b) 3030/10101

17. Given that  is not a root of a x2 + bx + c = 0 then is not invertibleif:

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(A)a, b, c are· in AP (B) a, b, care in GP

©a, b, c are in HP(D) a+b+c= 0

18.a, b, c, d and e are integers such that 1 a < b < c < d < e are geometric progression and lcm (m, n) is the least common multiple of m and n, then the maximum value of

BHU-2013

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

19.The number of common terms in the two sequences 17, 21, 25, ….., 417 and 16, 21, 26, ……, 466 is

BHU-2013

(a) 78(b) 19(c) 20(d) 77

20.

is BHU-2013

(a) (b)

©(d)

21.Let a1, a2, a3, ….. be terms of an AP. If

then equals BHU-2013

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

22.If a1, a2, ……., an are in HP, then the expressions a1a2 + a2a3 + …… + an – 1 an is equal to BHU-2013

(a) n(a1 – an) (b) (n – 1) (a1 – an)

23.If a1, a2, ……., an, …… are in GP, then the value of the determinant

is BHU-2013

(a) 0(b) 1(c) 2(d) – 2

24.If the sum of first n terms of an AP is cn2, then the sum of squares of these n terms is BHU-2013

(a) (b)

©(d)

25.The value of is BHU-2013

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

26.13 – 23 + 33 – 43 + …… + 93 = BHU-2013

(a) 425 (b) – 425 (c) 475 (d) – 475

27.In a G.P. consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the G.P. is NIMCET-2013

(a) (b)

©(d)

28.Let f(x) be a polynomial function of second degree and f(1) = f(-1). If a, b, c are in A.P., then f ‘(a), f ‘(b), f ‘(c) are in NIMCET-2013

(a) GP(b) HP (c) AGP (d) AP

29.The sum of n terms of an arithmetic series is 216. The value of the first term is n and the value of the nth term is 2n. The common difference, d is

NIMCET-2013

(a) 1(b) 2/3(c) 3/2(d) 12/11

30.The value of …….  is NIMCET-2013

(a) 3(b) 6(c) 9(d) None of these

31.Sum of 20 terms of the series – 12 + 22 – 32 + 42 - …. Is NIMCET-2013

(a) 180(b) 200(c) 210(d) 220

SEQUENCE & SERIES

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
D / D / C / - / D / D / C / A / C / A
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
C / B / C / B / C / - / - / C / C / A
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
B / D / A / C / B / A / D / D / D / A
31
C

SOLUTIONS

1.Ans. (d)

From choices its true only if a = b = c

2.Ans. (d) a, a + 1, ….., a + 10

11  Middle No. = 2761

Middle No.

3.Ans. (c) Since, a, b and c are in GP.

 ax, bx and cx will also in GP.

and log ax, log bx and log cx are in AP.

a, b, c are in GP, then log a and log b and log c are in AP]

Hence, logaxx, logbxx and logcxx, are in HP.

4.Ans. () Mean

Mean

 Mean

5.Ans. (d) We have,

Now, are in HP

are in AP

Whose common difference is .

 nth terms of series is

6.Ans. (d)Geometric mean of 5, 10, 40, 80

= (5.10.40.80) 1/4 = (160000)1/4  20

7.Ans. (c)

8.Ans. (a) Let the 2 no.s be a and b

 a, G, b are in GP

 G2 = ab

And ac, G2, d are in GP

Also

9. are in AP

ac + 2bc + c2 + a2 + 2ab + ac = 2[ab + b2 + ac + bc]

c2 + a2 = 2b2

 a2, b2, c2 are in AP

10.

11.

12.S2 + S3 – S6

= {2, 4, 6, 8, 60} +{3, 6, 9, 12…..60} – {6, 12, 18, ….60}

= 15  60 + 10(63) – 5(66)

= 30 + 630 - 330

= 1230

13.In a GP. The terms equidistant from each other are in GP as well

 q2 = pr

14. terms.

15.Ans. (c) D as 100X = 50Y +50Z  X lies between Y and Z

Also Y < Z

 Y < X < Z

16.Ans. (-)

17.Ans. (-)

18.Ans. (c)

19. Ans. (c)

20.Ans. (a)

21. Ans. (d)

22. Ans. (d)

23. Ans. (a)

24. Ans. (c)

25. Ans. (b)

26. Ans. (a)

27. Ans. (d)Let the terms be a, ar, ar2, ar3….

According to the condition we have

a = ar + ar2 1 – r – r2 = 0

Since r is positive, hence

28. Ans. (d)Suppose the 2 degree polynomial is f(x) = px2 + qx + r

Given that f (1) = f (-1)

p + q + r = p - q + r q = 0

Hence f ' (x) = 2px and f '(a), f '(b), f '(c) will be 2pa,

2pb and 2pc, will be in AP.

29. Ans. (d)According to the question Tn = 2n, a = n

2n = n + (n – 1)d n = (n – 1)d

We have

 n2 = 2  72  n = 12

30. Ans. (a)The number

= 91/2 = 3.

31. Ans. (c)The series can be written as

(-12 + 22) + (-32 + 42) + …. (-192 + 202)

= 3 + 7 + 11 +…….+ 39

There will be 10 terms in the series given above.

Hence the required sum

1 INFOMATHS/MCA/MATHS/OLD QUESTIONS