Progression
Exam Duration: 45 Mins Total Questions : 30
If five times term of an AP is equal to seven times. The seventh term of the AP, ten what is the twelth term?
- (a)
-1
- (b)
0
- (c)
1
- (d)
-2
Determine k=, so that (k+2), (4k-6) and (3k-2) are three consective terms what is the twelth term?
- (a)
3
- (b)
2
- (c)
4
- (d)
6
The sum of four terms in an AP is 64. The product of the extreme terms is 220. Find the first and fourth term.
- (a)
14,28
- (b)
10,22
- (c)
28,14
- (d)
6,30
Find the sum of all the two-digit numbers which leave a remainder of 3 when divided by 7
- (a)
676
- (b)
467
- (c)
567
- (d)
476
The sum to n terms of AP is \({ 3n }^{ 2 }\). Find the nth term of the series.
- (a)
6n-3
- (b)
3n-3
- (c)
3n+3
- (d)
6n+3
The sum of all integers between 50 and 300 which end in 2 is
- (a)
4500
- (b)
4100
- (c)
4300
- (d)
4200
If 20 is divided into four parts which are in AP such that the product of the first and fourth is to the product of the second and third is in tha ratio 2:3.
- (a)
1,3,7,9
- (b)
2,4,6,8
- (c)
3,5,5,7
- (d)
4,6,3,7
Find the tenth term of the GP \(\frac { 1 }{ \sqrt { 2 } } ,-1,\sqrt { 2 } ,.....\)
- (a)
-16
- (b)
16
- (c)
\(16\sqrt { 2 } \)
- (d)
\(-16\sqrt { 2 } \)
The third term and sixth term of a GP are 1 and 1/8 respectively. Find the fifteenth term.
- (a)
\(\frac { 1 }{ { 2 }^{ 10 } } \)
- (b)
\(\frac { 1 }{ { 2 }^{ 6 } } \)
- (c)
\(\frac { 1 }{ { 2 }^{ 12 } } \)
- (d)
\(\frac { 1 }{ { 2 }^{ 8 } } \)
The first three terms of a GP are 2x,3x+8 and 5x+24. Find the eighth term of the progression if x>0.
- (a)
2048
- (b)
1024
- (c)
512
- (d)
256
Which term of the GP \(\sqrt { 3 } ,\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ 3\sqrt { 3 } } ,.....is\quad \frac { 1 }{ 243\sqrt { 3 } } \)
- (a)
5th
- (b)
7th
- (c)
8th
- (d)
6th
How many terms of a GP 1,416, ...... must be taken to have their sum equal to 341?
- (a)
5
- (b)
6
- (c)
7
- (d)
8
In a GP, the sum of infinite series is 2 and the sum of the squares of the infinite series is \(\frac { 4 }{ 3 } \). Find the first term of the series.
- (a)
1
- (b)
\(\frac { 1 }{ 2 } \)
- (c)
2
- (d)
\(\frac { 1 }{ 4 } \)
Anil proposes to save Rs.1 on the first day, Rs,2 on the second day, Rs.4 on the third day, Rs. 8 on the fourth day and so on. How much does he save in the mouth of july?
- (a)
\(Rs.{ 2 }^{ 31 }\)
- (b)
\(Rs.{ (2 }^{ 31 }-1)\\ \\ \\ \)
- (c)
\(Rs.\frac { 1 }{ { 2 }^{ 31 } } \)
- (d)
\(Rs.\frac { 1 }{ { 2 }^{ 31 }-1 } \)
The number of bacteria in a certain culture doubles every hour. If there were 50 bacteria present in the culture originally, how many bacteria will born in 12th hour?
- (a)
102460
- (b)
120450
- (c)
102400
- (d)
120400
If the first and fourth terms of a GP are 1 and 27 the common ratio is
- (a)
1
- (b)
\(\frac { 1 }{ 3 } \)
- (c)
3
- (d)
\(\frac { 1 }{ 27 } \)
If \(-\frac { 2 }{ 7 } ,x,-\frac { 7 }{ 2 } \)are in GP,then x is
- (a)
1
- (b)
-1
- (c)
\(\frac { 2 }{ 7 } \)
- (d)
-\(\frac { 7 }{ 2 } \)
If the Arithmetic Mean (AM) and Geometric Mean (GM) of two numbers are 13 and 12 respectively, find the numbers.
- (a)
16,9
- (b)
12,12
- (c)
8,18
- (d)
36,4
A man has to pay Rs.2000 in yearly instalments, each instalment being less than the earlier one by Rs.10. The amount of first instalment is Rs.200. In what time the entire amount will be paid?
- (a)
14 yr
- (b)
10 yr
- (c)
12 yr
- (d)
16 yr
A display of canned soup in a supermarket is such that the top layer contains one can and each lower layer has one more can than the layer above. If there are 12 layers, the total number of cans will be
- (a)
72 cans
- (b)
78 cans
- (c)
81 cans
- (d)
86 cans
For doing a certain job, a boy is offered Rs. 5 on the first day, Rs.15 on the second day, Rs.90 on the third day and so on. How much will the boy earn at the and of 7 days?
- (a)
Rs.5486
- (b)
Rs.5484
- (c)
Rs.5465
- (d)
Rs.5450
Shyam's rich uncle gave him Rs.100 on his first birthday. On each birthday after that he doubled his previous gift.By the day after Sham's eighth birthday, what was the total amount that his uncle had given him?
- (a)
Rs.25500
- (b)
Rs.25400
- (c)
Rs.25450
- (d)
Rs.25600
The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the two children is \(4\sqrt { 3 } \) and their harmonic mean is 6, then what is the father's age?
- (a)
48 yr
- (b)
32 yr
- (c)
40 yr
- (d)
56 yr
The geometric mean of 4 and x is10, then x is equal is
- (a)
5/2
- (b)
5
- (c)
25
- (d)
50
If m,n,r are in arithmetic progression and a,b,c are in geometric progression, then \({ a }^{ n-r }{ b }^{ r-m }{ c }^{ m-n }\)is eqal to
- (a)
0
- (b)
1
- (c)
\(\sqrt { 2 } \)
- (d)
2
If \({ a }_{ k }=(\sqrt { 3 } { ) }^{ k }\)for k=1,2,3,...and \(\sum _{ k=1 }^{ n }{ { a }_{ k } } =39+13\sqrt { 3 } \) then n is equal to
- (a)
6
- (b)
8
- (c)
10
- (d)
12
If \({ a }_{ k }\)=\((\sqrt { 3 } { ) }^{ k }\) for k=1,2,3,...and \(\sum _{ k=1 }^{ n }{ { a }_{ k } } \)=39+\(3\sqrt { 3 } \) then n is equal to
- (a)
6
- (b)
8
- (c)
10
- (d)
12
The least value of n such that
\(1+3+{ 3 }^{ 2 }+...+{ 3 }^{ n }>2007\) is
- (a)
7
- (b)
8
- (c)
9
- (d)
10
If \({ a }_{ 1 }=7,{ a }_{ 2 }=11,{ a }_{ 3 }=15,...and\quad { a }_{ n }=403,\quad then\quad is\quad equal\quad to\quad \)
- (a)
97
- (b)
98
- (c)
99
- (d)
100
\({ 16 }^{ 1/3 }\times { 16 }^{ 1/9 }\times { 16 }^{ 1/27 }\times ...\infty \quad is\quad equal\quad to\)
- (a)
1
- (b)
4
- (c)
6
- (d)
16