EXERCISE - A
1) Write first 4 terms in each of the sequences:
A) aₙ = (5n+2). 7, 12, 17, 22
B) aₙ = =(2n-3)/4. -1/4,1/4,3/45/4
C) aₙ = =(-1)ⁿ⁻¹ x 2ⁿ⁺¹. 4,-8,16,-32
2) find first five terms of the sequence defined by
a₁= 1, aₙ= aₙ₋₁+3 for n≥2. 1, 4, 7, 10, 13
3) find first five terms in the sequence, defined by
a₁= -1, aₙ= (aₙ₋₁)/n for n≥2. -1, -1/2,-1/6,-1/24,-1/120
EXERCISE - B
** FIND
1) 2, 6, 10, ...... 20th term.
a) 78 b) 75 c) 67 d) 90 e) none
2) 1, 3, 5 ..... 100th term.
a) 100 b) 199 c) 201 d) 107 e) none
3) 23rd term of 7,5,3,1,....
a) -25 b) -30 c) 35 d) -37 e) none
4) 20th term √2, 3√2, 5√2,...
a) √2 b) 15√2 c) 30√2 d) 39√2 e) none
5) nth term 8, 3, -2,-7,.......
a) 2n b) 2n-6 c) 13-5n d) 5n+1 e) none
6) (a-3b), (a- b),(a+b) ... r th term.
a) a b) a+2r c) a+ 2br - 5b d) a+5b e) n
7) 13, 8, 3,-2.... nth term.
a) 18 b) 2- 3n c) 18-5n d) 5n e) none
8) 3,5,7,9,... 8th
a) 15 b) 23 c) 25 d) 17 e) 10
9) 3,5,7,9.....nth term.
a) 2n b) 2n+3 c) 2n+2 d) 2n+1 e) none
10) 2, 3/2, 1,.....nth term
a) n b) n+3 c) n/2 d) (5 - n)/2 e) none
11) 2,3/2,1,....10th term.
a) 13/2 b) 13 c) 2 d) -2 e) none
12) 1, (n+2)/n, (n+4)/n, (n+6)/n, .... 12th
a) n b) n+22 c) (n+22)/2 d) n/2 e) n/3
13) 1, (n+2)/n, (n+4)/n, (n+6)/n, .... n th.
a) n b) 3n c) 3n -2 d)(3n-2)/n e) (3n-2)/2
EXERCISE - C
**Which term of the sequences:
1) 5, 2, -1, ......is -22.
a) 10 b) 8 c) 9 d) 7 e) 6
2) 148, 146, 144 ..... is 30.
a) 20 b) 30 c) 40 d) 50 e) 60
3) 5, 8,11, 14,.... is 320 ?
a) 100 b) 102 c) 104 d) 105 e) 106th
4) 64, 60, 56,...is 0 ?
a) 12 b) 13 c) 14 d) e) 17
5) 10,13,16, ...., 43 ?
a) 12 b) 13 c) 24 d) 15 e) none
6) 5/6, 1, 7/6 ,.... 10/3 ?
a) 12 b) 16 c)15 d) 21 e) none
7) 4,9,14,19,.... is 109?
a) 22 b) 20 c) 21 d) 23 e) none
8) 7,13,19,...., 205.
a) 30 b) 34 c) 35 d) 36 e) none
9) 84,80,76,....... Is 0 . 22
j) 2,5,8..... is 92. 31
k) -1,-5/6,-2/3,-1/2,...10/3. ? 27
l) 12+i,11+6i,10+4i,. ...is (i) purely real (ii) purely imaginary.
EXERCISE - D
1) a) Is 305 a term of the series 7, 10, 13, 16?
a) yes b no c) series is in GP d) series in HP e) none
2) Find nearest term of the above
a) 100 b) 101 c) 102 d) 103 e) none
3) Is 90 a term of the series 4,7, 10, 13 .... ?
a) yes b) No c) series in GP d) series in HP e) none
4) Is 68 a term of A.P 7,10,13,..
a) yes b) No c) series in GP d) series in HP e) none
5) Is 302 a term of 3,8,13.....?
a) yes b) No c) series in GP d) series in HP e) none
6) Is 301 a term of the AP 5, 11, 17, 23.....?
a) yes b) No c) series in GP d) series in HP e) none
EXERCISE - E
** Find the value of k if series in AP:
1) 2k-1,k+1,3-k.
a) 0 b) 1 c) 2 d) 3 e) none
2) 5k-1, 3k+7,8k+1.
a) 0 b) 1 c) 2 d) 3 e) none
3) k²+2k+2,3k²+6k+6,4k²+5k+4.
a) 0 b) 1 c) 2 d) 3 e) none
EXERCISE - F
** Find
1) 15th term from the end of the AP 3,5,7,9,... 201.
a) 173 b) 176 c) 178 d) 201 e) none
2) 19th term from the end of the AP 2,6,10,14,...86.
a) 45 b) 35 c) 55 d) 65 e) none
3) 15th term from the end of 7,10,13, ....130.
a) 88 b) 58 c) 78 d) 68 e) none
4) 20th term from the end of 3,8,13, ..... 253.
a)148 b) 168 c) 138 d) 158 e) none
5) 12 th term from the end of 3,5,7,9,......201.
a) 139 b) 159 c) 159 d) 169 e) 179
6) 12 th term from the end of 1,4,7,10,....,88.
a) 55 b)45 c) 35 d) 25 e) 15
EXERCISE - G
1) Find 10th term of the AP where 1st term is 5 & common difference is 2.
a)22 b) 21 c) 20 d) 19 e) 23
2) 1st term of an AP is 6, common difference is 2. find 15th term.
a) 32 b) 62 c) 82 d) 92 e) none
3) The 20th term of an A. P is 79. If 1st term is 3, find 10th term.
a) 19 b) 29 c) 39 d) 49 e) 59
4) The 5th and 13th terms of an AP are 5 and - 3 respectively. find this AP
a) 6,7,8,9 b) 9,8,7,6 c) 5,7,9,11 d) 11,9,7,5 e) none
5) The 5th and 13th terms of an AP are 5 and - 3 respectively, Obtain its 16th term.
a) -6 b)-8 c) -9 d) -10 e) -11
6) Find 15th term of an AP whose 10th term is - 25 & 20th term is - 55.
a) 50 b) -40 c) -39 d) -29 e) -10
7) Find 2nd term and rth term of the A. P whose 6th term is 12 and 8th term is 22.
a) -5 b) -6 c) -7 d) -8 e) none
8) Find rth term of the A. P whose 6th term is 12 and 8th term is 22.
a) 5r - 18 b) 5r c) 5r+18 d) r+18 e) none
9) The 6th & 16th term of AP are 9√2/2 and 19√2/2. Find its 20th term.
a) 2 b) 23 c) 2√2 d) 23/√2 e) none
10) The 2nd, 31st and the last terms of an AP are 31/4,1/2 and -13/2 respectively. find 1st term
a) 8 b) 9 c) 10 d) 12 e) 14
11) The 2nd, 31st and the last terms of an AP are 31/4,1/2 and -13/2 find the number of terms.
a) 59 b) 60 c) 61 d) 62 e) 63
12) If the 9th term of an AP is 0, prove that its 29th term is ____to 19th term.
a) equal b) double c) triple d) half e) two and half times
13) how many two digit numbers are divisible by 7 ?
a) 10 b) 11 c) 12 d) 13 e) none
14) The 4th terms of an AP is three times the first and the 7th term exceeds twice the third term by 1. find the first term
a) 2 b) 3 c) 4 d) 5 e) 6
15) The 4th terms of an AP is three times the first and the 7th term exceeds twice the third term by 1. find the common difference.
a) 2 b) 3 c) 4 d) 5 e) 6
16) if 7 times the 7th term of an AP is equals to 11 times its 11th term, then Find its 18th term
a) 0 b)1 b) 2 c) 3 d) 4
17) If 9th term of an A. P. Is zero, then its 29th term is double the___
a) 19 b) 20 c) 21 d) 22 e)23
18) If 10th times the 10th term of an AP is equal to 15 times 15th term, then its 25th term is.
a) 0 b)1 b) 2 c) 3 d) 4
19) How many Numbers of two digits are Divisible by 3.
a) 11 b) 21 c) 31 d) 41 e) none
20) The first term of an AP is 5, 11th term is 125. The common difference is
a) 5 b) 6 c) 7 d) 8 e) none
21) The 4th and 8th term is 2 and 10. Find 11th term.
a) 6 b) 8 c) 10 d) 12 e) none
22) The 4th and 8th term is 2 and 10. Find the first term.
a) -6 b) -8 c) -2 d) -4 e) none
23) A certain series in AP. Every
term of it is multiplied by 3. resultant series in ?
a) AP b) GP c) HP d) AM e) GM
24)** In an AP 3rd term: 5th term=1: 4 Find 7th term: 12th term.
25) If 7 times the 7th term is equal to 11 times of the 11th term. Find the 18th term ?
a) 26 b) 42 c) 65 d) 102 e) none
26) The 4th term is equal to 3 times the first term and the 7th term exceeds twice the third term by 1. Find 1st term.
a) 2 b) 22 c) 12 d) 32 e) none
27) The 4th term is equal to 3 times the first term and the 7th term exceeds twice the third term by 1. Find its common difference.
a) 2 b) 22 c) 12 d) 32 e) none
28) if the mth term of an AP be 1/n and its nth term be 1/m then Find its mn th term.
a) mn b) 1+ mn c) 1+m+n d) (1+m+n/mn e) (1+m-n)/mn
29) If the mth term of a given AP is n and its nth term is m then its pth term is.
a) m+n b) m+n+p c) n+ m -p d) m-n-p e) none
30) If m times the mth term of an AP is equal to n times its nth term, then m + n th term of the AP is.
a) 0 b) 22 c) 12 d) 32 e) none
31) If the pth, qth and rth term of an AP be a, b, c respectively. Then find the value of (q-r)a + (r-p)b +(p-q)c.
a) 0 b) 22 c) 12 d) 32 e) none
32) If x th term of AP is y and y th term is x. Find (x+y) th term.
a) 2xy b) (x+y)/xy c) xy/2 d) 2(x+y)/xy e) none
33) If x th term of AP is y and y th term is x. m th term.
a) m/2 b) m+ x+ y c) (m+ x+ y)/3 d) (m+ x+ y)/2 e) none
34) if (m+1) th term of an A. P. is twice the (n+1)th term, then (3m+1)th term is ____ the (m+n+1)th term.
a) equal b) one and half c) twice d) none
35) The 4th term of an A. P is is three times the first and the 7th term exceeds twice the third term by 1. Find the first term
a) 12 b) 32 c) 56 d) 67 e) none
36) The 4th term of an A. P is is three times the first and the 7th term exceeds twice the third term by 1. Find the common difference.
a) 12 b) 32 c) 56 d) 67 e) none
EXERCISE - H
1) Which term of the AP 19, 91/5, 92/5, ........is the negative term ?
a) 22 b)32 c) 28 d) 21 e) none
2) Which term of the sequence 20, 77/4, 37/2,71/4 is the 1st negative term ?
a) 22 b) 31 c) 28 d) 21 e) none
3) Which term of the sequence 24,93/4,45/2,87/4 is the first negative term ?
a) 22 b) 31 c) 28 d) 21 e) none
EXERCISE - I
** Find A. M between:
1) 9 and 19.
a) 12 b) 14 c) 16 d) 18 e) 20
2) 12 and -8.
a) 2 b)4 c) 6 d) 8 e) 10
3) -13 and -7.
a) -10 b)-2 c) -4 d) -7 e) -9
4) 14 and 18.
a) 16 b) 20 c) 22 d) 24 e) 26
5) (a-b) and (a+b).
a) a b) b c) a+ 2b d) 2a + b e) none
** Fill up the gap :
6) 4 , _ , _ , 10
a) 6,8 b) 5,7 c) 8,9 d) -2,-4
7) _ , _ , _ , -2 , -10.
8) 34, _ , _ , _ , 48.
*** Insert 3 AM between:
9) 3 and 19.
a) 7,11,15 b) 6,10,14 c) 5,7,9
10) 2 and 14.
11) - 24 and 0
12) 13/4 and 5/4
** Insert 5 arithmetic means between
13) 8 and 26.
a) 11,14,17,20,13 b) 10,12,14,16,18 c) 13,15,17,19,21 d) 14,16,28,20,22
14)17 and 29.
15) 2 and 26
** Insert 4 A. M between:
16) 4 and 29.
a) 6,11,16,21 b) 7,12,17,22 c) 9,14,19,24 d) none
17) (a - b)² and a² + b² + 8ab.
18) 4 and 19.
a) 5,8,11,14 b) 6,9,12,15 c) 7,10,13,16 d)
none
** Find the middle term of:
19) 1,6,11,......101.
a) 11th, b) 51 c) 21st d) 54 e) none
20) 4,7,10, ....73.
a) 12th b) 13th c) both a and b d) 24 e) none
21) 5,8,11, ...., 95.
a) 15 b) 12 c) 14 d) 16 e) none
EXERCISE - J
1) Find three numbers in AP whose sum is 24 and product of extreme is 55.
a) 5,8,11 b) 11,8,5 c) either a or b d) both a and b e) neither a nor b
2) three numbers are in AP. If their sum is 27 and the product 648, find the numbers.
b) 6,9,12 b) 12,9,6 c) either a or b d) both a and b e) neither a nor b
3) the sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. find these terms.
a) 4,7,10 b) 10,7,4 c) either a or b d) both a and b e) neither a nor b
4) The three Numbers are in 3:7:9 if 5 is substracted from the second the resulting Number are in AP. Find the original number.
a) 56 b) 65 c) 45 d) 54 e) none
5) The sum of three terms of an A. P. is 21 and the product of the first and the third term exceeds the second term by 6, find three nos.
a) 4,7,10 b) 10,7,4 c) either a or b d) both a and b e) none
6) The sum of three Numbers in AP is 12 and sum of their cubes is 408. Find the numbers.
a) 2,4,6 b) 6,4,2 c) either a or b d) both a and b e) neither a nor b
7) Divide 12 into 3 parts in AP as
their squares is 56.
a) 2,4,6 b) 6,4,2 c) either a or b d) both a and b e) neither a nor b
8) find the four numbers in AP whose sum is 20 and the sum of whose squares is 120.
a) 2,4,6,8 b) 8,6,4,2 c) either a or b d) both a and b e) neither a nor b
9) divide 32 into 4 parts which are in AP such that the product of the extremes is to product of means as 7:15.
a) 2,6,10,14 b) 14,10,6,2 c) either a or b d) both a and b e) neither a nor b
10) the angles of a quadrilateral are in AP whose common difference is 10°. find the angles.
a) 65,75,85,95 b) 75,85,95,105 c) 85,95,105,115 e) none
11) Find the four numbers in A. P., Whose sum is 50 and in which the greatest number is 4 times the least.
a) 5, 10,15,20 b) 9,12,21,22 c) 8,12,16,18 e) none
12) The sum of four numbers in AP is 24. Sum of their squares is 164. Find the numbers.
a) 2,4,6,8 b) 3,5,7,10 c) 1,3,5,7 d) 1,4,7,11 e) none
f) Divide 20 into four parts in AP
and such that the product of first and fourth is to the product of second and third in the ratio 2:3.
g) Divide 32 into four parts which
are in AP. Such that the product of extremes is to the product of mean is 7:15.
EXERCISE - K
** Find the sum of the series:
1) 1,3, 5, 7... 24th term.
a) 576 b) 656 c) 566 d) 756 e) 545
2) 2+5+8+..... 30th term
a) 124 b) 321 c) 423 d) 654 e) none
3) 6, 16/3, 14/3... 10th term.
a) 30 b) 35 c) 40 d) 45 e) 50
4) 0.8+1.2+1.6+... to 25th terms.
a) 12.5 b) 31.2 c) 23.6 d) 56.4 e) none
5) 2+ 7 +12+ .... upto 20 terms.
a) 102 b) 132 c) 144 d) 154 e) none
6) √2,2√2,3√2...20th term.
a) 100√2 b) 120√2 c) 165√2 d) 210√2 e) none
7) 0.7,0.71,0.72...100th term.
a) 115.5 b) 116.5 c) 117.5 d) 119.5 e) n
8) (n-1)/2 + n/n + (n+1)/n + .... upto n terms.
a) n b) n+1 c) (n+1)/2 d) 2n+1 e) none
9) 101+99+97+....+47.
a) 1072 b) 2062 c) 2072 d) 3072 e) n
** How many term :
10) 26+21+16+11.....to get 11.
a) 9 b) 10 c) 87 d) 11 e) none
11) 18+16+14+12....to get 78.
a) 6 b) 7 c) 8 d) 9 e) 10
EXERCISE - L
1) Find the series
a) 3p²+5p.
b) an²+bn.
c) 2n+ 3n²
d) 2p² + p
e) The sum of n terms of an AP is 3n²+5n. Find p th term. Find which term of the A. P is 152.
2) Find the series if
a) 4r - 3.
b) 10 - 3n
EXERCISE - M
1) The first and the last terms of an A. P having finite number of terms are respectively - 2 and 124 and the sum of the A. P is 6161. Find the number of terms.
2) The first and the last term of an A. P are respectively - 4 and 146, and the sum of A. P= 7171. Find the number of terms, common difference.
3) If the sum of first m terms of an AP is equal to the sum of the first n terms, prove that the sum of the first (m+n)th term is zero.
4) In an AP if the 12th term is -13
and sum of first four terms is 24. What is the sum of its first 10 terms.
5) If the first term of an AP is 2 and sum of the first five terms is equal to one-fourth of the sum of the next five terms. Find the sum of first 30 terms. Also find its 20th term.
6) If the sum of p terms of an AP is q and the sum of q terms is p. Show that the sum of p+q terms is -(p+q). Also find the sum of first p-q terms.
7) How many terms of an AP -6, -11/2, -5,... make the sum -25 ?
8) How many terms of the sequence 18,16,14, ... Should be taken that sum is zero.
EXERCISE - N
1)a) Find the sum of all Numbers between 100 to 300 which are Divisible by 8.
b) Find the sum of all integer from 200 to 400 not Divisible by 7.
c) Find the sum of all odd numbers of four digits which are Divisible by 9.
d) Find the sum of all integers between 50 and 500 which are Divisible by 7 ?
e) Find the sum all natural
numbers between 100 and 1000 (excluding both) which are Divisible by 5 ?
f) The first, second and the last terms of an AP are a, b, 2a. Find its sum.
EXERCISE - O
1) If a,b,c are in A. P prove the following are in A. P.
a) b+c, c+a, a+b.
b) a²(b+c),b²(c+a), c²(a+b).
c)a(1/a+1/c),b(1/c+1/a),c(1/a+1/b)
d) {(b+c)²-a²},{(c+a)²-b²},{(a-b)²-c²}.
e) (a- c)² = 4(b² - ac).
f) a³ + 4b³+ c³= 3b(a²+c²).
g) a²(b+c), b²(c+a), c²(a+b) .
h) b+c -a, c+a - a, a+b - c.
i) b c - a², ca - b² , ab - c².
j) (a - c)² = 4(a - b)(b - c).
k) a² + c² +4ac = 2(a b+ b c+ c a).
l) a³+c³+6abc = 8b³.
2) If a², b²,c² are in A. P then prove that the following are in also in A. P.
3) 1/(b+c), 1/(c+a), 1/(a+b).
b) a/(b+c), b/(c+a), c/(a+b)
c) a/(b+c),b/(c+a), c/(a+b).
4) If a²(b+c), b²(c+a), c²(a+b) are in A. P prove that either a,b,c are in A. P or ab+b c+ca=0.
5) 1/a, 1/b, 1/c are in A. P prove following are in A. P.
a) (b+c)/a, (c+a)/b, (a+b)/c
b) a(b+c), b(c+a), c(a+b).
6) (b+c)/a, (c+a)/b, (a+b)/c are in A. P prove following are in A. P.
a) 1/a, 1/b, 1/c.
b) b c, c a, a b
EXERCISE -P
1) Find the sum of
a) 3.7+5.10+7.13+...... n terms.
b) 7²+8²+9²+ ...20².
c) 10²+11²+12²+......30².
d) 6³+7³+8³+.....20³.
e) 1.2²+3.5²+5.8²+.....n terms.
Mg. A.R -1
1) Find the 10th term of 2, 6, 10,...
A) 34 B) 36 C) 38 D) 42
2) What term of the AP 1,5,9,13,.... is 101 ?
A) 25th term B) 26th term
C) 28th term. D) 30th term
3) if the 5th and the 12th terms of an AP are 14 and 35 respectively, What is the sum of the first term and the common difference.
A) 2. B) 5. C) 6. D) 8
4) The 5th and the 11th term of an AP are 41 and 20 respectively. The first term of is..
A) 55 B) 27 C) 41 D) 14
5) If the pth term of an AP is q and the qth term is of p, then the mth term is.
A) p+q. B) p+q+m C) p+q-m D) N
6) If Ram saves ₹1 today, ₹2 rupees the next day, ₹ 3 the succeeding day and so on, what will be Ram's total savings in 365 days ?
A) ₹66700 B) ₹66895
C) ₹65495 D) ₹66795
7) insert three arithmatic means between 2 and 10.
A) 4,6,8. B) 3,6,9
C) 5,7,9. D) 1,2,3
8) Insert 4 arithmatic means between 52 and 77.
A) 56,61,66,71. B) 57,62,67,72
C) 58, 63, 68, 73. D) none
9) The sum of the three numbers in AP is 15 and their product is 80, find them.
A) 2,4,9. B) 2,6,7
C) 2,5,8. D) 1,5,9
10) Find the three integers in AP such that their sum is 27 and their product is 504.
A) 4,9,14 B) 14,9,4
C) 14,4,9. D) both A and B
11) The sum of three numbers in AP is 12 the sum of the squares is 66. Find the numbers.
A) 7,4,1. B) 8,6,2
C) 7,5,2. D) 2,5,7
12) Find the increasing AP, the sum of whose first three terms is 27 and the sum of their squares is 275.
A) 5,10,15,20,.... B) 4,9,14,19,...
C) 5,9,13,17,.. D) 3,9,15,21,...
13) The first and the last and the last terms of an AP having finite numbers of terms are respectively -2 and 124 and the sum of the AP in 6161. Find the number of the terms in the AP.
A) 98. B) 99. C) 100. D) 101
14) If the pth term of an AP is 4p - 1, find the 40th term and the sum of the first 40 terms.
A) 159, 3420. B) 159,3240
C) 168, 3240. D) 186, 3240
15) In an AP, the sum of n terms, the common difference and the last terms are 136, 4 and 31 respectively. find the value of n.
A) 8. B) 7. C) 6. D) 9
16) the sum of p terms of a series is 3p²+ 5p, the terms of the series form:
A) Geometric progression
B) arithmetic progression
C) harmonic progression
D) both B and C above
17) The sum of the n terms of an AP is 3n²+ 5n. Find the number of term which is equal to 152.
A) 52. B) 15. C) 25. D) 21
18) If each term of a series in AP be multiplied by 5,would the series so obtained be again in AP
A) yes B) no it will change to HP
C) no, it will change to GP. D) N
19) If all the terms of the series 72+70+68+...+40, are increased by 12.5%, what is the sum of the new series so forme ?
A) 1000. B) 952
C) 1071. D) 1254
20) If the 3rd and the 6th term of an AP are 7 and 13 respectively, work out the sum of the first 20th term of the series.
A) 340. B)540 . C)550. D) 440
21) The ratio of the 7th to the 3rd term the 3rd term of an AP is 12:5; find the ratio of the 13th term to the fourth term.
A) 3:10. B) 9:4. C) 10:3. D) 4:1
22) Find the sum of the first hundred hundred even natural numbers divisible by 5.
A) 50500. B) 50050
C) 50005. D) 50000
23) Find the sum of 32 terms of an AP, whose third term is 1 and the sixth term is -11.
A) -1600. B) -1696
C) -1796. D) -1785
24) What is the common difference of an AP, whose first term is 1, last term is 50 and the sum of all terms is 204?
A) 5. B) 6. C) 7. D) 9
25) The sum of n terms of an AP, whose first term is 22 & common difference -4 is 64.find n.
A) 4 B) 8 C) both A and B
D) neither A nor above.
26) The sum of n terms of an AP is n². Find its common difference.
A) 1. B) -1. C) 3. D) 2
27) The sum of certain number of terms of terms in AP is 5500. The first and the last terms are 100 and 1000. Find the number of terms.
A) 10. B) 9. C) 15. D) 12
28) A person ₹975 in monthly installments, each installment being less than the former by ₹5. The amount of first installment is ₹100. in what time will the entire amount be paid?
A) 14 months. B) 17 months
C) 15 months. D) 20 months
29) If the first term of an AP is 2 and the sum of the first five terms is equals to one-fourth of the sum of the next 5 terms, then what is the 20th term?
A) 110. B) -110. C) -125. D) -112
30) Find the sum of all odd numbers of four digits which are divisible by 9.
A) 2754000. B) 2574000
C) 24750000. D) 2548000
31) Find the sum of all numbers lying between 100 and 1000 which are divisible by 13.
A) 37600. B) 37674
C) 36457. C) 45875
32) The sum of the first 50 terms of an AP is 200, and the sum of the next 50 terms is 2700. Find the common difference.
A) -1. B) 2. C) 1. D) -2
33) divide 20 into 4 parts which are in AP and such that the product of the first and fourth is to the product of the 2nd and 3rd in the ratio 2:3.
A) 2,4,6,8. B) 2,3,7,9
C) 8,6,5,3. D) 1,4,6,9
34) Find the four terms in AP whose is 20 and the sum of whose squares is 120.
A) 2,4,6,8. B) 8,6,4,2
C) 2,5,7,8. D) none
35) The first term of an AP is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. Find the third third term of the progression.
A) 70/17. B) 70/11
C) 7/11. D) 70/19
36) The sum of the first 21 terms of an AP is 28, and the sum of the first 28 terms is 21. Then which of the following is true?
A) one of the term of the progression is zero.
B) there is no terms which value is 0.
C) The first term of the progression is 3.
D) both A and C above.
37) Mr X. borrows ₹1000 and agrees to repay without interest in 10 installments. each installment being less than preceding by ₹8. Find the first installment.
A) ₹100 B)₹136 C)₹125 D)₹134
38) Mr. Y borroows ₹2000 and agrees to repay with a total interest of ₹340 in 12 monthly installments, each installment being less than the preceding one by ₹10. Find the amount of the last installment.
A)₹250. B)₹180. C)₹140. D)₹100
39) A farmer undertakes to pay off a dept of ₹6240 by monthly installments. he pays ₹300 at the first installment and increases every subsequent installment by ₹40 over the the immediate previous installment. in how many installment it Debt will be cleared up?
A) 10. B) 16. C) 14. D) 12
40) A man arranges to pay off a debt of ₹7200 in 20 installments which are arithmetic progression. After 15 installments being paid one-third of the debt still remain unpaid. How much will he pay in the sixteenth installment ?
A) ₹450. B)₹500. C)₹548. D)448
41) Ram arranges to pay off a debt of ₹9600 in 48 installments which form and AP. When 40 of these installments are paid. He becomes insolvent and the creditor find that ₹2400 still remain unpaid. Find the value of the second installment paid by him. Ignore interest.
A)₹87.5 B)₹82 5 C)₹92.5 D) none
42) The rate of monthly salary of an office assistant increases annually in AP. if he was drawing ₹200 a month during the 11th year and ₹380 a month during 29t year, find out his initial salary and the rate of annual increment. Find also his salary at the time of retirement on completion of 32 years of service.
A) ₹100,₹10,₹310
B) ₹90,₹10,₹410
C) ₹100,₹10,₹410
D) ₹100,₹20,₹410
43) The cost of a boring a tube-well, 600 metres deepp, is as follows: 25 paise for the first metre and an additional 4 paise for every subsequent metre. Find the total cost of boring.
A) ₹7000 B) ₹7300
C) ₹7330 D) ₹7338
44) A person lends ₹1000 to a friend agreeing to charge no interest and also recover the amount by monthly installments decreasing successively by ₹2. In how many months will the loan be paid up, if the first installment of ₹64 be paid one month after the sum is lent?
A) 24 months. B) 25 months
C) 27 months. D) 21 months.
45) A club consists of members whose ages are in arithmetic progression, the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 years. Find the number of members in the club.
A) 24. B) 26. C) 25. D) 29
46) Two posts are offered to Mr. X. In the one, the starting salary is ₹1200 and increases annually by ₹80; in the other, the salary commences at ₹850 and increases annually by ₹120. The man decides to accept the post that will give him better total income in the past 16 years. Which post will he accept ?
A) First post B) second post
C) either of A or B D) none
47) A man saved ₹16500 in ten years. In each year after the first he saved ₹100 more than he did in the preceding year. How much did he save in the first year?
A)₹1100 B)₹1650
C)₹450 D)₹1200
48) A man agrees to accept certain wages for the first month on the understanding that his pay is to be raised 1 Rupee every subsequent month until the maximum (namely ₹300 per month) is reached. At the end of the month for which receives ₹300 for the first time he resigns and finds that his wages during his period of service have averaged ₹288 a month. How long did he served.
A) 25 months. B) 27 months.
C) 30 months. D) none
49) The cost of constructing a 500 feet road is as follows: ₹22 for the first foot and an additional of ₹2 for every subsequent foot. Find the cost of constructing the last foot of the road.
A)₹920 B)₹1000
C)₹1020 D)₹1100
50) A set out from a certain place and travels 1 mile the first day, 2 Mile the second day, 3 miles the 3rd so on. B sets out from the same place, 5 days after A and travels the same road at the rate of 12 miles a day. How far will A travel before he is overtaken by B.
A) 36 miles. B) 46 miles
C) 35 miles. D) 24 miles
51) A man 50 years old has 8 sons born at equal intervals. The sum of ages of the father and the sons is 186 years. What is the age of the eldest son, the youngest son being 2 years old?
A)41yrs B)44yrs. C)42yrs D)43yrs E) 32
52) If 100 stones be placed in a straight line, exactly a metre apart, the first being one metre from the basket, what distance will a person go, who gathers them simply, returning with each to the basket?
A) 10000m. B) 10100m
C) 11000m D) none
53) Find the sum of the following series till n terms: 1+5+12+22+35+..... n terms.
A) (n+1)/2 B) n(n+1)/2
C) n²(n+1)/2. D) n³(n+1)/2
54) A person deposits ₹50 at the beginning of every month into a savings account in which interest is allowed at 5% per annum, on the minimum monthly balances. Find the balance of the account at the end of 3rd year, calculating the simple interest.
A) ₹2038.75 B) ₹1938.75
C) ₹2538.75. D) ₹1838.75
55) The Cricket Board of India decides to raise to cricketer's beneficiary fund of ₹5 crore. A start is made with 10 lakh and every year an addition of ₹3 lakh is made. In how many years will the the fund reach the desired value?
A)15 yrs B)17yrs.C)16yrs D)18yrs
56) Taking data from the previous question, what should be the last year's contribution to make up the desired fund?
A)₹33 lakh. B)₹33.5 lakh
C)₹34 lakh. D)₹35 lakh
57) the first term of an AP is 5, the common difference is 3 and the last term is 80, find the numbers of terms.
A) 24. B) 25. C) 26. D) 27
58) The 6th and 17th term of an AP are 19 and 41 respectively, find the 40th term.
A) 78. B) 98. C) 102. D) 87
59) if 10 times the 10th term of an AP is equals to 15 times the 15th term, then 25th term of an AP is....
A) 1. B) 25. C) 0. D)-25
60) The 10th and 18th terms of an AP are are 41 and 73 respectively. Find 26th term.
A) 50. B) 100. C) 123. D) 105
61) If the nth term of an AP 9,7,5,... is the same as the nth term of an AP. 15,12,9,.. find n
A) 7. B) -7. C) 5. D) 17
62) The 4th term of an AP is three times the first times and the 7th term exceeds twice the third term by 1. The sum of the first term and common difference is:
A) 3. B) 2. C) 5. D) 7
63) Find the second term of an AP. Whose 6th term is 12 and the 8th term is 22.
A) 8. B) - 8. C) 4. D) -4
64) How many numbers of two digits are divisible by 3?
A) 25. B) 31. C) 29. D) 30
65) An AP consists of 60 terms. if the first and the last term be 7 and 125 respectively. Find 32nd terms.
A) 96. B) 36. C) 69. D) 63
66) The sum of 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th term is 34. What is the common difference of the AP
A) 5.5. B) 2.5. C) 3.5. D) 1.5
67) The first and the last terms of an AP are a and 1 respectively. The sum of nth term from the beginning and nth term from the end is ..
A) a+21 B)a+31 C) a+1 D) 2a+1
68) The sum of the three terms of an AP is 21 and the product of the first and the third term exceeds the second term by 6, find three terms.
A) 1,7,13. B) 7,13,19
C) 1,5,9. D) none
69) three numbers are in AP, if the sum of these numbers be 27 and the product 648, find the numbers.
A) 6,9,15. B) 6,9,12
C) 6,10,13. D) 5,8,11
70) Find the four numbers in AP, whose sum is 50 and in which the greatest number 4 times the least.
A) 5,10,15,25. B) 5,10,15,30
C) 5,10,15,20. D) none
71) The angles of a quadrilateral are in AP. Whose common difference is 10°. Find the angle (in degrees)
A)65,75,85,95. B) 75,85,95,115
C) 55,75,95,115. D) 75,85,95,105
72) The sum of three numbers in AP is 12 and the sum of their cubes is 288 Find the numbers.
A) 2,4,6. B) 6,4,2
D) both of the above. D) none
73) Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
A) 1863.B)1683 C)1386 D)1368
74) Find the sum of first n odd natural numbers.
A) 2n. B) n²+n. C) n². D) n²- n
75) Find the sum of all odd numbers between 100 and 200.
A)8500. B)7500. C)5500 D)6500
76) The sum of all odd integers between 1 and 1000 which are divisible by 3 is..
A) 86337 B)83667
C) 76638 D)73569
77) Find the sum of all integers between 84 and 719, which are multiple of 5.
A)80500 B) 50780
C) 50800. D) 84580
78) Find the sum of all integers between 50 and 500 which are divisible by 7 ?
A) 17696. B) 69671
C) 17966. D) 17699
79) Find the sum of all even integers between 101 and 999.
A) 246955. B) 246950
C) 256490. D) 246590
80) Find the sum of all integers between 100 and 550, which are divisible by 9.
A) 16545. B) 16958
C) 16425. D) 16895
81) The sum of the first n terms of two AP's are in the ratio (7n+2):(n+4). Find the ratio of their 5th terms.
A) 1:5 B)2:3. C)5:1. D) 3:2
82) How many terms are there in the AP. Whose first and the 5th term are -14 and 2 respectively and the sum of the terms is 40.
A) 8. B) 9. C) 11. D) 10
83) The sum of first 7 terms of an AP is 10 and that of next 7 terms is 17. Find the first term of the progression.
A) 2. B) 1. C) - 1. D) 3
84) The third term of an AP is 7 and the 7th term exceeds three times the third term by 2. What is the sum of the the first term, the common difference and the sum of first 20 terms.
A) 740 B) 742. C) 741. D) 743
85) The first term of an AP is 2 and the last term is 50. The sum of all these terms is 442. what is the common difference?
A) 3. B) 2. C) 1. D) 5
86) The number of terms of an AP is even; the sum of odd terms is 24 , of the even terms is 30, and the last term exceeds the first by 21/2, find the number of terms.
A) 7. B) 8. C) 9. D) 6
87) If 12th term of an AP is -13 and the sum of the first 4 terms is 24, what is the sum of first 10 terms ?
A) 100. B) 10. C) 0. D) -10
88) If the fifth and the twelfth terms of an AP are 30 and 65 respectively, what is the sum of first 20 terms ?
A) 150. B)1150 C) 115. D) 50
89) The digits of a positive integers, having three digits, are in AP and their sum is 15. The number obtained by reversing the digits 594 less than the original number. Find the number.
A) 258. B) 852. C) 582. D) 659
90) Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 km/h. The second goes at a speed of 8 km/h in the first hour and increases the speed by 1/2 km each succeeding hour. After how many hours will the second car overtake the first car if both car goes non stop ?
A) 8hrs B)7hrs. C) 9hrs. D)11hrs
91) A man repays a loan of ₹ 3250 by paying Rs20 in the first month and then increases the payment by ₹15 every month. How long will it take him to clear the loan loan ?
A) 20. B) 19. C) 18 D) 21 months.
92) 150 workers were engaged to finish a piece of work in a certain number of days. four workers dropped the second day, 4 more workers dropped the third day and so on. it takes 8 more days to finish the work now. Find the number of days in which the work was completed.
A)24. B) 23. C) 20. D) 25 days
93) Along a road lie an odd number of stones placed at interval of 10 metres. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried the job with one of the end stones by carrying them in succession. In carrying all the stones he covered a distance of 3 km. Find the number of stones.
A) 15. B) 20. C) 25. . D) 29
94) A man saved ₹16500 in ten years. In each year after the first he saved ₹100 more than he did in the receding year. How much did you save in the first year?
A)₹1100 B)₹1000 C)₹900 D)₹1200
95) A man saves ₹32 during the 1st year, ₹36 in the second year and in this way he increases his savings account by ₹4 every year. Find in what time his saving will be ₹200
A) 4yrs. B) 5yrs. C) 3yrs. D) 6yrs
96) A man arranges to pay a debt of ₹3600 by 40 annual instalments which form an AP. When 30 of the installments are paid, he dies leaving one-third of the debt unpaid, find the value of the first installment.
A) ₹15. B)₹31. C) ₹45. D) ₹51
-> A manufacturer of radio sets produced 600 units in the third year and 700 units in the future seventh year. Assuming that the product increases uniformly by a fixed number every year, Find:
97) The production in the 1st yr.
A) 450. B) 350. . C) 550. D) 658
98) The total Product in 7 years
A)4375 B)4735 C)3745. D)6574
99) The production in the 10th yr
A)577. B) 775. C) 684. D) 575
100) There are 25 trees at equal distance of 5m in a line with a well, the distance of the well from the nearest tree being 10m. A gardener waters all in the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
A)3300m. B)3360m
C) 3344 m. D) 4000 m
101) A man saved is employed to count ₹10710. He counts at the rate of ₹180 per minute for half an hour. After this he counts at the rate of ₹3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
A) 89. B)98. C) 80. D) 84 min
102) A piece of equipment cost a certain Factory ₹600000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third shot year, and so on. What will be its value at the end of 10 years, all percentage applying to the original cost ?
A) 100000. B) 50000
C) 110000. D) 105000
Mg. A. R -2
1) The first and the common difference an AP are 4 and 3 respectively. Find the 11th term.
a) 32 b) 33 c) 34 d) 35 e) none
2) Find the number of terms in an AP in which the first and last terms are 7 and 45 respectively and the common difference is 2.
a) 10 b) 20 c) 30 d) 40 e) none
3) The 6th and the 10th terms of an AP are 22 and 38 respectively. Find the first term and common difference.
a) 2,4 b) 4,6 c) 6,8 d) 8,10 e) 10
4) The 12th and 14th term and the Last term of an AP are 25,31 and 37 respectively. Find the first term , common difference, number of terms.
a) -8,3,16 b) 8,3,16 c) -6,4,20 d) none
5) Find the sum of the first 20 terms of an AP in which the first term is 6 and the common difference is 2.
a) 300 b) 400 c) 500 d) 600 e) none
6) Find the AM of the first 31 terms of an AP in which the first term is 3 and the common difference is 5.
a) 78 b) 79 c) 80 d) 81 e) 92
7) Divide 100 into four parts which are in AP such that the product of the second part and third part is 72 more than the product of the other two parts.
a) 16,22,28,34 b) 15,21,27,33 c) 16, 23,30,37 d) none
8) Three terms in AP have a sum of 45 and product of 3240. Find them
a) 12,15,18 b) 18,15,12 c) both a and b d) only a e) only b
9) The first term and the Last term of an AP are 9 and 69 respectively. If the sum of all terms is 468, find the number of terms and the common difference.
a) 10, 60/11 b) 12, 60/11 c) 10,12 d) 60, 60/11 e) none
10) The 17th term and the 28th term of an AP are 66 and 110 respectively. Find the 33th term.
a) 100 b) 110 c) 120 d) 130 e) none
11) The sum of three numbers which are in AP is 24. The sum of their square is 200. Find the numbers.
A) 6,8,10 b) 10,8,6 c) both a and b d) only a e) none
12) What is the arithmetic mean of the arithmetic progression 2,5,8,11,14,17,20 ?
a) 11 b) 12.5 c) 9.5 d) 15.5 e) none
13) What is the arithmetic mean of the arithmetic progression 3,7,11,15,19,23, 27,31 ?
a) 15 b) 17 c) 19 d) 15.5 e) none
14) Find the 10th term of the AP whose 4th term is 7 and whose 17th term is 72.
a) 32 b) 37 c) 42 d) 47 e) none
15) Find the sum of the first 31 terms of an AP whose first term is 6 and whose common difference is 8/3.
a) 1410 b) 1418 c) 1426 d)1434 e) none
16) Find the sum of the terms of an AP whose first term, last term and common difference are 3,101 and 7 respectively.
a) 750 b) 720 c) 780 d) 810 e) none
17) An arithmetic progression has 15 terms. Its 8 term is 8. Id S is the sum of its terms, which of the following true?
a) S> 100 b) S = 100 c) S < 100 d) S≥ 100 e) none
18) Find the sum of the terms of an AP whose first term, last term and number of terms are -9,51 and 21 respectively.
a) 420 b) 441 c) 462 d) 483 e) none
19) What is the 15th term of an AP whose first term is equal to its common difference and whose 3rd term is 9
a) 15 b) 30 c) 45 d) 60 e) none
20) An AP has 50 terms. The nth term from the beginning and the n-th term from the end are 5 and 45 respectively. Find the sum of all terms.
A) 2500 b) 1250 c) 625 d) 500 e) none
21) If x,y and z are three natural numbers in AP, then the x-th term, the y-th term and the z-th term of any arithmetic progression A are in
a) arithmetic progression
b) geometric progression
c) not necessarily in AP or GP
22) If x,y and z are three natural numbers in AP, then the x-th term, the y-th term and the z-th term of any geometric progression G are in
a) arithmetic progression
b) geometric progression
c) not necessarily in AP or GP
23) The sum of the first 71 terms of an AP is 0. Which of the following terms must be 0 ?
a) 18th b) 19th c) 36th d) 37th e) none
24) The sum of the first 30 terms of an AP is 40. The sum of its first 60 terms is also 40. Find the sum of its 31st and 60th terms.
a) 0 b) 600 c) 40 d) 1200 e) none
25) Find the sum of the cubes of the first 10 natural numbers.
a) 55 b) 385 c) 3025 d) 166375 e) none
Mg. A. R -3
1) The 67th term of an AP is 15 times the fourth term of the series. Find the 21st term, if the 11th term is 23.
a) 37 b) 43 c) 49 d) 55 e) 53
2) Find the smallest of the three numbers in AP, if the product of the first and the third numbers is 252 and the sum of the three numbers is 48.
a) 10 b) 12 c) 14 d) 16 e) 18
3) Find the expression for the sum of n terms of an AP, if the tenth term is 40 and 12th term is 44.
a) 10n+25n² b) 20+20n² c) 25+15n² d) n²+21n e) none
4) If the sum to 37 terms of an AP is 703, then find the middle term.
a) 34 b) 17 c) 38 d) 46 e) 19
5) Find the least value of the number of terms of the series 20,18,16,....for which the series has the maximum sum
a) 9 b) 10 c) 11 d) 12 e) 13
6) If the sum of the fifth, thirteenth and eighteenth terms of an AP 0, then find the 12th term.
a) -2 b) -1 c) 0 d) 1 e) none
7) How many numbers 450 and 950 are divisible by both 3 and 7 ?
a) 20 b) 24 c) 30 d) 35 e) 26
8) The first three terms of arithmetic progression are 3x, 5x + 8 and 10 x + 4. Find the sum of the first 10 terms of the series.
a) 780 b) 810 c) 750 d) 870 e) 840
9) The first term of an AP consisting of 30 terms is 10 and the common difference is 5. Find the ratio of the sum of the 30 terms of the AP to the sum of the last 20 terms of AP.
a) 99:13 b) 96 :17 c) 93 :19 c) 99 :68 d) n
10) Find the sum of the first 10 terms of the series : 3.2²+4.3²+ 5.4²+.....
a) 3009 b) 4860 c) 3408 d) 3608 e) 3806
11) Find the sum of all two digit numbers which leave a reminder of 3 when divided by 7.
a) 576 b) 624 c) 676 d) 686 e) none
12) Find the number of terms common to the progression and 7,11, 15,....497 and 1, 6, 11, 16,.... 501.
a) 26 b) 22 c) 20 d) 25 e) 27
13) Find the values of (50x1)+(49×2)+ (48× 3)+....(1 ×50).
a) 21050 b) 22100 c) 23100 d) 24200 e) 21300
14) Find the sum of all the integers from 1 to 300 that are divisible either by 3 or 5.
a) 21150 b) 36250 c) 35150 d) 37350 e) 37530
15) The sum of n terms of two series in AP are in the ratio (7n -17):(4n +16). Find the ratio of their 21st terms.
a) 3:2 b) 4: 3 c) 5:4 d) 4: 5 e) none
16) The terms of an AP are all positive. The square of 4th term equals the sum of the square of the previous two terms. The sum of the first four terms is 14. Find the common difference.
a) 1 b) 2 c) -1 d) -2 e) 0
17) There are 30 terms in an AP. The second and the third terms are distinct integers. The ratio of the sum of first 20 terms and the sum of the first 10 terms equals twice the ratio of the second and the first terms. Which of the following can be the sum of all its terms?
a) 1120 b) 1560 c) 2020 d) 3750 e) 7750
18) The first of AP is 6 and the common difference is 4. The n-th term of the series is 250. Find the value of n
a) 60 b) 62 c) 66 d) 64 e) none
19) The sum of the three numbers in an arithmetic progression is 39 and the sum of the squares of the three numbers is 515. Find the smallest of the three numbers.
a) 9 b) 10 c) 11 d) 12 e) 13
20) Find the sum of the squares of the first 10 even numbers.
a) 840 b) 1540 c) 1260 d) 1370 e) none
21) The common difference of an AP is 3. If the product of the first and the last term of the AP having the seven terms is 595, what could be the sum of all the terms of the arithmetic progression ?
a) 108 b) 216 c) 432 d) 128 e) 182
22) If the sum of the 37 terms of an AP is 703. Then Find the sum of the first 10 terms of the arithmetic progression, given the first term of the AP is one.
a) 55 b) 65 c) 75 d) 85 e) none
23) The sum of the four numbers in an ascending AP is 160 and the product of the extreme is 1564. Find the smallest of the numbers.
a) 28 b) 34 c) 42 d) 43 e) none
24) (1²+2²+......n²)/{(n+1)²+(n +2)²+....(2m)²} = 385)2485. Find the value of m.
a) 10 b) 20 c) 25 d) 30 e) 35
25) Find the value of -1²+2²-3²+4²-5²+6²+ .....-19²+20²
a) 210 b) 420 c) 630 d) 720 e) none
26) The sum of the first n terms of an AP is given by 2n²+6n. Find the common difference.
a) 1 b) 2 c) 4 d) 3 e) none
Mg. A. R-4
1) A person gets a starting salary of ₹5000 per month. During the first year of his job, he receives a monthly increment of ₹200 starting from the second month. During the second year, he receives a monthly increment of ₹400, a monthly increment of ₹600 for the third year and so on. Find the total amount received by him at the end of 4 years. (Assuming that the salary he gets during the last month of a year is same as that during the first month of the next year(
a) ₹5864 lakh b) ₹5914 Lakh c) ₹5964 Lakh d) ₹6.36 lakh e) ₹6.15 lakh
2) The price of a car is ₹150000. A person purchases the car in installments. In the first month the person pays an installment of ₹ 2000 in the next month, the person pays an installment of ₹2500. In the following month, the person pays an installment of ₹ 3000 and so on The person pays the installments for a total Period of the 2 years. Find the extra amount paid by the person over the price of the car.
a) 6000 b) 6500 c) 37000 d) 36000 e) 6700
3) 1³+2³+3³+....m³= 3025. Find the value of m.
a) 8 b) 9 c) 10 d) 11 e) none
4) Find the sum of all the three digit numbers which leave a remainder of 1 when divided by 8.
a) 61472 b) 61480 c) 61488 d) 61496 e) 61508
5) How many 3 digit numbers less than 500 are neither divisible by 4 nor by 6?
a) 232 b) 244 c) 254 d) 266 d) 264
6) In a three digit number, the hundreds digit, the tens digit and the units digit are in descending order in AP. Each digit of the number is multiplied by the sum of the other two digits. The sum of all such results is A. B is the product of the tens digit and the sum of all the digits and A = 4B/3. Find the number of such numbers.
a) 4 b) 3 c) 2 d) 1 e) more than 4
7) The sum of the first n terms of two arithmetic progression X and Y are in the ratio 11n -17 : 5n -21. Find the ratio of the 16th terms of X and Y.
a) 3:2 b) 2: 3 c) 9: 4 d) 27: 8 e) 162 :67
8) Find the number of terms common to the progression 2, 8, 14, 20,...98 and 6, 10, 14, 18,.....102.
a) 7 b) 6 c) 8 d) 9 e) 10
9) Find the sum of the terms of the series : 1 x20, 2 x 19, 3x18, .....20x 1.
a) 1750 b) 1645 c) 1540 d) 1435 e) 1840
10) if X is the sum of the first n terms of the series 40+ 38 +36+.... then find the maximum value of X.
a) 450 b) 420 c) 390 d) 480 e) 410
11) The sum of the squares of the three terms in AP is 365. The product of the first and the third terms is 120. Find the sum of the squares of the second term and the common difference.
a) 145 b) 170 c) 122 d) 197 e) 144
12) A. M between (x+ y)² and (x- y)² is
A) 0 B) 1 C) x² D) y² E) x²+ y²
13) 4 A. M between 17 and 52.
A) 7, 14, 21, 28 B) 14, 21, 28, 35 C) 24, 31, 38,45 D) 31, 35,45, 52 E) none
14) two numbers whose product is 91 and whose A. M is 10.
A) 13,7 B) 7,13 C) 23, 17 D) 17, 23 E) none
15) First three terms of the sequence, whose nth term is (-1)ⁿ ⁻¹. 5ⁿ⁺¹.
A) 25, -125, 625 B) -25, 125, -625 C) 25, 125, 625 D) -25, -125, -625 E) n
16) If the 3rd and the 6th terms of an AP are 7 and 13 respectively, then first term is
A) 3 B) 4 C) 5 D) -3 E) -4
17) The natural numbers between 100 to 1000 which are multiple of 5
A) 179 B) 180 C) 181 D) 182 E) n
19) The sum of three decreasing numbers in AP is 27. If 3 is multiplied by each number then the series become in
A) AP B) increasing AP C) decreasing AP D) none
20) The sum of all odd numbers between 1 and 100 which are divisibile by 3, is
A) 83667 B) 90000 C) 83660 D) 87690 E) none
21) Find the first three terms of the sequence whose nth term (uₙ) is given by uₙ= nth prime number
A) 2,3,5 B) 3,5,7 C) 5,7,9 D) 7,9,11 E) 9,11,15
22) The 6th term of the sequence {1, 4, 9, 16,. ....} is
A) 25 B) 36 C) 32 D) 64 E) 86
23) The 5th term of the sequence {1/3, 1/9,......} is
A) 1/27 B) 1/15 C) 1/81 D) 1/12 E) 1/45
24) The nth term of the sequence {1, 1/8, 1/27,......} is
A) 1/n B) 1/n² C) 1/n³ D) 1/(n²-1) E) 1/(n³ -1)
25) The sum of first r terms of a series is ar²+ br; then its 12th term is
A) a+ b B) 12a+ b C) 21a+ b D) 23a+ b E) a+ 12b
26) The 5th and 13th terms of an AP are 16 and 28 respectively. Then 1st term is
A) 10 B) 23/2 C) 13 D) 29/2 E) -4
Mg. A. R-5
1) The sum of 1+4+7+10+13+.... to 20terms
A)550 B) 570 C) 590 D) 600 E) 420
2) If each term of an AP be divided by a constant quantity, the resulting terms are also in __
3) The sum of n terms of an AP is 3n²+ 5n, which term is equal to 152
A) 20 B) 22 C) 25 D) 27 E) 40
4) Find the sum of all the odd numbers, which are perfect squares between 50 and 10000
A) 166666 B) 166665 C) 166566 D) 166656 E) 165666
5) x, 2x+1 and 14 are in AP, then the value of x is
A) 2 B) 4 C) 6 D) 8 E) 10
6) If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k is
A) n B) 1/n C) (n-1)/n D) (n+1)/2n E) (n + 1)/n
7) If four numbers in AP are such that their sum is 50 and greatest number is 4 times the least, then the numbers are
A) 5,10,15,20 B) 4,8,10,16 C) 3,7,11,15 D) 5, 10, 15, 25 E) n
8) The AM of two numbers is 10, if one number is 7 then the other number will be
A) 15 B) 14 C) 13 D) 9 E) 12
9) The pth term of an AP is 2p - 7, which of the following will be its 4th term
A) 1 B) -1 C) 3 D) -3 E) 5
10) Insert a number of arithmetic means between 4 and 34 such that the sum of the resulting AP is 133.
A) 9 B) 9, 14 C) 9, 24, 19, D) 9, 14, 19, 24, 29 E) 9, 14, 19, 29, 43
11) Which of the following is the 12th term of the series n+ (n -1)+ (n -2)+...?
A) n-10 B) n-11 C) n-12 D) n-13 E) n
12) If the pth term of an AP is q and the qth term is p, then p+ q th term is
1) p B) q C) pq + d) pq+1 E) 0
13) given a²+ 2a+2, 3a²+ 6a+ 6 and 4a²+ 5a+ 4 are in AP. Find the value of a
A) 2 B) 3 C) -2 D) -3 E) 1
14) Find the middle term/s of 2+ 5+ 8+ ....+ 152.
A) 77 B) 66 C) 55 D) 44 E) 33
15) find the sum up to middle term of 2+2.4+ 2.8+....+10.4
A) 6 B) 6.4 C) 136.4 D) 186.5 E) n
16) The sum of n terms of an AP is n. Then common difference is
A) 2 B) 4 C) 6 D) 8 E) 10
17) 3rd term of an AP is 1/5 and the 5th term is 1)3. Then sum of the 15th term is
A) 5 B) 8 C) 12 D) 15 E) 21
18) How many even numbers are there between 91 and 259
A) 78 B) 80 C) 84 D) 90 E) 96
19) Find the sum of all the numbers of the form n³ lying between 100 and 10000.
A) 6800 B) 6831 C) 6871 D) 6891 E) 7000
20) The sum of first 21 terms of an AP is 28 and the sum of the 1st 28 terms is 21. One of the term is zero. TRUE/FALSE
21) 1²+ 2²+ 3²+ .....45² = ?
A) 5950 B) 6560 C) 9768 D) 8790 E) n
22) In the sequence of an AP is n/(n²+1) then third term is
A) 1/2 B) 2/5 C) 3/10 D) 4/17 E) 5/26
23) Which term of the sequence 20, 77/4, 37/2, .... is the first negative term
A) 27 B) 28 C) 29 D) 30 E) 32
24) Find the 20th term of an AP from the end 3, 7, 11, ....407
A) 83 B) 331 C) 86 D) 441 E) 91
25) How many numbers of two digits are divisibile by 7
A) 12 B) 13 C) 14 D) 10 E) 15
26) In the AP 2, 5, 8,... upto 50 terms and 3, 5, 7, 9,... upto 60 terms, find how many terms are identical.
A) 15 B) 20 C) 25 D) 30 E) 1
Mg. A. R-6
1) Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
A) 1234 B) 19786 C) 19668 D) 12456 E) n
2) sum of all two digit numbers which when divided by 4 yield unity as remainder is
A) 1200 B) 1210 C) 1250 D) 1265 E) 1300
3) The 1st and last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be
A) 5 B) 6 C) 7 D) 8 E) 9
4) The number of terms of the AP 3, 7, 11, 15,... to be taken so that the sum is 406 is
A) 5 B) 10 C) 12 D) 14 E) 20
5) Find the sum of first n natural numbers.
A) n B) (n+1) C) n(n+1) D) n(n+1)/2 E) n³
6) Find the sum of all odd numbers between 100 and 200.
A) 7000 B) 7200 C) 7400 D) 7500 E) 8000
7) Suppose Tₙ represents the nth term, a the first number of the sequence and d the difference between two consecutive numbers. What will be the nth term of an AP
A) Tₙ= a+(n+1) d B) Tₙ= a+(n-1) d
C) Tₙ= a - (n+1) d D) Tₙ= a-(n+1) d
8) Find the sum of the series 20, 50, 80, to 25 terms
A) 9500 B) 5900 C) 5800 D) 7500 E) n
9) The sum of 20 members in AP is 650. If the first term of the series is 4. What is the common difference between the terms?
A) 1 B) 2 C) 3 D) 4 E) 5
