Series

Q.

Find the missing number in the series: $4,18,?,100,180,294,448$.

1. $48$

2. $50$

3. $58$

4. $60$

Q.

If a:b = 2:3 and b:c = 4:3, then find a:b:c

1. 2:3:9

2. 2:3:12

3. 2:3:8

4. 8:12:9

5. None of these

Q.

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

1. 1875

2. 1777

3. 1877

4. 1785

Q. If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)}$ are in the ratio 2:1, find the value of n.

1. 1
2. 2
3. 3
4. 0
5. None of these

Q.

Fill in the missing number:
12, 8, 14, 6, 16, ?

1. 32
2. 10
3. 18
4. 4
5. None of the above

Q.

The value of $\frac{{\left(243\right)}^{0.13}\times {\left(243\right)}^{0.07}}{{\left(7\right)}^{0.25}\times {\left(49\right)}^{0.075}\times {\left(343\right)}^{0.2}}$is :

1. 

2. 

3. 

4. 

5. 

Q. In each of these questions, one term in the given number series is wrong. Find out the wrong term.
3 5 13 43 176 891 5353

1. 43
2. 176
3. 891
4. 5
5. 13

Q.

Twenty times a positive integer is less than its square by 96. What is the integer?

1. 20

2. 24

3. 30

4. 41

5. 46

Q.

Find the value of 1-2-3+2-3-4+...+ upto 100 terms.

1. -694

2. -626

3. -624

4. -549

Q. A number sequence has 100 elements. Any of its elements (except for the first and last element) is equal to the product of its neighbours. The product of the first 50 elements, just as the product of all the elements is 27. What is the sum of the first and the second element?

1. 10
2. 7
3. 12
4. 6

Q. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs.300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total paid to them as salary during the period ?(CAT 2001)

1. Rs. 93, 300
2. Rs. 93, 200
3. Rs. 93, 100
4. None of these

Q.

5 9 25 91 414 2282.5
3 (a) (b) (c) (d) (e)
What will come in the place of (c)?

1. 63.25

2. 63.75

3. 64.25

4. 64.75

5. None of these

Q.

If $(33{)}^3$ is subtracted from the square of a number, the answer so obtained is 5272. What is the number?

1. 223

2. 213

3. 203

4. None of these

Q.

The sum of $24$ terms of the following series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+...$ is

1. $300$

2. $200\sqrt{2}$

3. $300\sqrt{2}$

4. $250\sqrt{2}$

Q.

The sum of four numbers is 64. If 3 is added, subtracted, multiplied and divided to the first, second, third and fourth number respectively, then all the results are equal. What is the difference between the largest and the smallest of the original numbers?

1. 27

2. 21

3. 32

4. 48

5. None of these

Q.

A and B invest some amount of money in a scheme for equal period of time. The profit earned by A is Rs.3200 and the investment of A is twice that of B.
What is the total profit earned by A and B?

1. Rs.6000

2. Rs.6400

3. Rs.4800

4. Rs.7200

5. Rs.8400

Q. 6, 7, 16, 51, 208, ?

1. 1036
2. None of these
3. 1042
4. 1056
5. 1048

Q. 120 320 ? 2070 5195 13007.5

1. 800
2. 920
3. 850
4. 900
5. None of these

Q.

What should come in place of the question mark (?) in the following number series?
12, 14, 17, 13, 8, 14, 21, 13, 4, ?

1. 14
2. 13
3. 15
4. None of the above
5. 2

Q. Let a = 111...1(55 digits),
$b=1+10+{10}^2+{10}^3+{10}^4$
$c=1+{10}^5+{10}^{10}+{10}^{15}+...+{10}^{50},then$

1. b = ac
2. c = ab
3. a = b + c
4. a = bc

Q.

A number added to its square gives 132. The twice of the number is

1. 11

2. 22

3. 24

4. 23

5. 16

Q.

The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is

1. 49

2. 33

3. 81

4. 25

5. 27

Q.

The sum of $n$ terms of the series $\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}.....$ is

1. $\sqrt{2n+1}$

2. $\sqrt{2n+1}-1$

3. $\frac{1}{2}\sqrt{2n+1}$

4. $\frac{1}{2}\sqrt{2n+1}-1$

Q. Directions : Study the following graph and answer the questions that follow.

The number of boys participating in the rally from school B is what per cent of the total number of children participating in the rally from the school? (rounded off to two digits after decimal)

1. 48.84
2. 47.37
3. 49.28
4. None of these
5. 46.46

Q.

The sum of four consecutive even integers is 1284. The greatest one of them is:

1. 322

2. 324

3. 349

4. 320

5. 326

Q.

In each of these questions, one term in the given number series is wrong. Find out the wrong term.
6 7 16 41 90 154 292

1. 7
2. 16
3. 90
4. 154
5. 41

Q. The infinite sum of $1+\frac{4}{7}+\frac{9}{7^2}+\frac{16}{7^3}+\frac{25}{7^4}+$ .......Is k. The Value of 27K is___

Q.

If from two -- third of a number 50 is subtracted, the result is equal to sum of 40 and one -- fourth of the same number. What is the number?

1. 246

2. 336

3. 216

4. 174

5. 416

Q. 9 4.5 4.5 6.75 13.5 33.75 ?

1. 101.25
2. 103.75
3. 99.75
4. None of these
5. 105.5

Q.

The value of $\left[{\left(10\right)}^{150}÷{\left(10\right)}^{146}\right]$is

1. 1000

2. 10000

3. 100000

4. 10⁶

5. None of these