Practice Test

1) If 9 times the 9th term of an AP is equal to 13 times the 13th term, then the 22nd term of the AP is

2) In an AP, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. The 20th term is

3) If a, b, c,d, e, f are in AP, then the value of e - c will be

4) If the sum of a certain n number of terms of the AP, 25,22,19,.....is 116, then the last term is

5) If the ratio of the sum of n terms of two AP's be (7n + 1) : (4n + 27), then the ratio of their 11th terms will be

6) A man saved Rs. 66000 in 20 yr . In each succeeding year after the first year he saved Rs. 200 more than what he saved in the previous year. How much did he save in the first year ?

7) A carpenter was hired to build 192 windows frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How much days did it take him to finish the job ?

8) If the first term of an AP is a and the sum of the first p terms is zero, then the sum of its next q terms is

9) In a cricket tournament 16 schools term participated. A sum of Rs.8000 is to be awarded among themselves as prize money . If the last placed team is awarded Rs.275 in prize money and the award increase by the same amount for successive finishing places, amount will the first place team received is

10) If a, b, c are in AP, then the straight line ax + by + c = 0 will always pass through the point

11) The solution of the equation (x + 1) + (x + 4) + (x + 7) + ..... + (x + 28) = 155 is .

12) The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is ....

13) The sum of integers from 1 to 100 that are divisible by 2 or 5 is

14) The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is

15) Insert three arithmetic means between 3 and 19

16) If the 4th,10th,and 16th terms of a GP are x, y and z respectively, then x, y , z are in

17) The sum of n terms of the sequences 8, 88, 888, 8888, .... is

18) Find four numbers forming a GP in which the third term is greater than the first term by 9 and the second term is greater than 4th by 18

19) The number which should be added to the numbers 2, 14, 62, so that the resulting numbers may be in GP, is

20) The third term of GP is 4. The product of its first 5 terms is

21) If x, 2y and 3z are in AP, where the distinct numbers x, y, z are in GP, then the common ratio of the GP is

22) The sum of 100 terms of the series 0.9 + 0.09 + 0.009 +... will be

23) The value of 0.234 is

24) 0.14189189189 ... can be expressed as a rational number

25) The sum of the geometric progression 0.15, 0.015, 0.0015, ... 20 terms is

26) In the four number first three are in GP and last three are in AP whose common difference is 6. If the first and last number are same, then first number will be

27) In a GP the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number the series becomes AP, then the greatest number is

28) Which of the following statement is correct ?

29) If the AM and GM of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be

30) Three numbers from a GP. If the 3rd term is decreased by 64, then the three numbers thus obtained will constitute an AP. If the second term of this AP is decreased by 8, a GP will be formed again, then the numbers will be

31) The number 111...1 (91 times ) is a / an

32) Let two number have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

33) If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is

34) An infinite GP has the first term 'x' and sum 5, then x belongs to

35) If the altitudes of a triangle are in AP, then the sides of the triangle are in

36) If a, b and c are in AP and p, p' are the AM and GM respectively between a and b, while q, q' are the AM and the GM respectively between b and c, then

37) The product of n positive numbers is unity. Their sum is

38) Sum of n terms of series 12 + 16 + 24 + 40 + .... will be

39) Number of identical terms in the sequences 2, 5, 8, 11, .... upto 100 terms and 3, 5, 7, 9, 11, .... upto 100 terms, are

40) Jairam purchased a house in Rs. 15,000 and paid Rs. 5,000 at once. Rest money he promised to pay in annual instalment of Rs. 1,000 with 10% per annum interest. How much money is to be paid by Jairam ?

41) 150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

42) After striking the floor, a certain ball rebounds (4 / 5)th of height from which it has fallen. Then, the total distance that it travels before coming to rest, if it i gently dropped from a height of 120 m is

43) concentric circles of radii 1, 2, 3, .... , 100 cm are drawn. The interior of the smallest circle is coloured red and the angular regions are coloured alternately green and red, so that no two adjacent region are of the same colour. Then, the total era of the green region in sq.cm is equal to

44) The sum of n terms of an AP is a n(n - 1). The sum of the squares of these terms is

45) If the ratio of AM between two positive real numbers a and b to their HM is m : n, then a : b is equal to

46) The consecutive digits of a three digit number are in GP. If the middle digit be increased by 2, then they form an AP. If 792 is subtracted from this, then we get the number constituting of same three digits but in reverse order. Then, number is divisible by

47) If an increasing GP is consider, then the number of terms in GP is

48) If the decreasing GP is considered, then the sum of infinite term is

49) In any case, the difference of the least and greatest term is

50) Statement I 3, 6, 12 are in GP, then 9, 12, 18 are in HP.
Statement II If middle term is added in three consecutive terms of a GP, resultant will be in HP.

51) Statement I There are infinite geometric progression for which 27, 8 and 12 are three of its terms (not necessarily consecutive ).
Statement II Given terms are integers.

52) If 100 times the 100th term of an AP with non-zero common difference equals the 50 times its 50th term , then the 150th term of this AP is

53) A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increase by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs.11040 after

54) The first two terms of a geometric progression add upto 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then first term is

55) 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 is equal to

56) The sum of first two terms of an infinite G.P. is 1 and every term is twice the sum of the successive terms. Its first term is

57) If three numbers are in H.P., then the numbers obtained by subtracting half of the middle number from each of them are in

58) Three non-zero real numbers form an A.P. and the squares of these numbers taken in the same order form a G.P. Then, then number of all possible values of common ratios of the G.P. is

59) If the sum of an infinitely decreasing G.P. is 3, and the sum of the squares of its terms is 9/2, the sum of the cubes of the terms is

60) the AM of two numbers be A and GM be G, then the numbers will be

61) If twice the 11th term of an AP is equal to 7 times its 21st term, then its 25th term is equal to

62) If the AM and GM between two numbers are in the ratio m : n, then the numbers are in the ratio

63) If the sum of the first n natural numbers is 1/5 times the sum of their squares, then the value of n is

64) If the sides of sides of a right angled triangle are in AP, then the sides are proportional to

65) If p, q, r are in A.P., then p th, q th and r th terms of any G.P. are in

66) If the sum to first n terms of the AP 2, 4, 6,… is 240, then the value of n is

67) Three numbers whose sum is 15 are in AP. If they are added by 1, 4 and 19 respectively they are in GP. The numbers are

68) If n geometric means be inserted between a and b, then the n th geometric mean will be

69) If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is

70) If the p th term of an AP be q and q th term be p, then its r th term will be

71) The first term of a GP is 7, the last term is 448 and sum of all term is 889, then the common ratio is

72) Sum of infinite number of terms of a G.P. is 20 and sum of their squares is 100. The common ration of the G.P. is

73) If three real numbers a, b, c are in harmonic progression, then which of the following is true?

74) If a, b, c are three unequal positive quantities in H.P., then

75) The sum of all 2 digit odd numbers is

76) If arithmetic mean of two positive numbers is A, their geometric mean is G and harmonic mean is H, then H is equal to

77) The sum of a GP with common ratio 3 is 364 and last term is 243, then the number of terms is

78) If a and b are two different positive real numbers, then which of the following statements is true?

79) 0.5737373… is equal to

80) If the sum of the series 2, 5, 8, 11,… is 60100, then n, the number of terms, is

81) Fifth term of a G.P. is 2, then the product of its 9 terms is

82) GM and HM of two numbers are 10 and 8 respectively. The numbers are

83) The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to

84) The sum of the integers from 1 to 100 which are divisible by 3 and 5, is

85) The n th term of the sequence 4, 14, 30, 52, 80, 114, ..., is

86) Three numbers are in GP such that their sum is 38 and their product is 1728. The greatest number among them is

87) If three numbers are in G.P., then the numbers obtained by adding the middle number to each of these numbers are in

88) If sum of the first 2n terms of an AP series 2, 5, 8, ... is equal to the sum of the first n terms of the AP series 57, 59, 61, ..., then n equals

89) In a G.P. with alternatively positive and negative terms, any term is the A.M. of the next two terms. Then, the common ratio of the G.P. is

90) If a, b, c are in H.P., then

91) Consider the sequence of numbers 121, 12321, 1234321, . . . Each term in the sequence is

92) A student read common difference of an AP as - 3 instead of 3 and obtained the sum of first 10 terms as - 30. Then, the actual sum of first 10 terms is equal to

93) If the sum to 2 n terms of the AP 2, 5, 8, 11, ... is equal to the sum to n terms of the AP 57, 59, 61, 63, ..., then n is equal to

94) The sum of the first and third term of an arithmetic series is 12 and the product of first and second term is 24, then first term is

95) If a, b, c are in A. P., b - a, c - b and a are in G. P., then a : b : c is

96) If a, b, c, d be in HP, then

97) In an AP the sum of any two terms, such that the distance of one of them from the beginning is same as that of the other from the end, is

98) In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2. If the middle term of AP be equal to the middle term of the GP, then the middle term of the entire sequence is

99) The difference between two numbers is 48 and the difference between their arithmetic mean and their geometric mean is 18. Then, the greater of two numbers is

100) Three numbers are in AP such that their sum is 18 and sum of their squares is 158. The greatest number among them is

101) The arithmetic mean of first n odd natural number is

102) A GP consists 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

103) The sum of all the products of the first n natural numbers taken two at a time is

104) The 4th term of a HP is 3/5 and 8th term is 1/3, then its 6th term is

105) After inserting n A.Ms between 2 and 38, the sum of the resulting progression is 200. The value of n is

106) If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of the AP is

107) 99th term of the series 2 + 7 + 14 + 23 + 34 ... is

108) In a geometric progression (GP) the ratio of the sum of the first three terms and first six terms is 125:152 the common ratio is

109) If S is the sum of an infinite GP, the first term a, then the common ratio r is given by

110) The sum of 11 terms of an A.P. whose middle term is 30, is

111) 7th term of an AP is 40. Then, the sum of first 13 terms is

112) If the first, second and last terms of an arithmetic series are a, b and c respectively, then the number of terms is

113) The sum of the series 6 + 66 + 666 + ... upto n term is

114) The value of 0.423, is

115) a, b, c, d, e are five numbers in which the first three are in A.P. and the last three are in H.P. If the three numbers in the middle are in G.P., then the numbers in the odd places are in

116) An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is

117) The sum of n terms of two arithmetic series are in the ratio 2 n + 3 : 6 n + 5, then the ratio of their 13 th terms is

118) If a, b and c are in AP, then which one of the following is not true?

119) If a, b, c, d are in H P, then

120) If the sum of two extreme numbers of an AP with four terms is 8 and product of remaining two middle terms is 15, then greatest number of the series will be

121) An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

122) If the third term of a GP is P. Then, the product of the first 5 terms of the GP is

123) In an arithmetic progression, the 24th term is 100. Then, the sum of the first 47 terms of the arithmetic progression is

124) The sum of all odd numbers between 1 and 1000 which are divisible by 3, is

125) The correct statement is