## TCS Sample Problems On Odd & Even Integers

Below are three questions on numbers on concepts dealing with odd and even and a new class called "even-odd" numbers.
Question 1
If n is an even-odd number then which of the following must be false?
(A number is called "even-odd" if it is halfway between an even integer and an odd integer.)
a) n/2 is not an integer
b)(2n)2 is an integer
c)4n is an odd integer
d)none of these
Answer : c)4n is an odd integer
Solution:
A number is called "even-odd" if it is halfway between an even integer and an odd integer. For example, consider an even integer 10 and an odd integer -5. Number halfway between them will be (10 - (-5)) / 2 = 7.5. Here 7.5 is an "even-odd" number.
i.e., an even-odd number will be in the form x + 1/2 = x.5 where x is any integer.
Let us see with each option:
Consider option a :
Since n is a fraction number then n/2 is also a fraction.
i.e., n/2 is not an integer.
Hence option a is true.
Consider option b :
(2n)2 = 4n2
since n is an even-odd number then n^2 is not an integer.
Also n2 will have 1/4 = .25 in its decimal place. (For example, consider n = 7/2. Then n2 will be 7/2 x 7/2 = 49/4. 49/4 can be written as 49 + 1/4. Here 1/4 will contribute to the decimal part.)
When we multiply n2 by 4 we have an integer, since .25 x 4 = 1.
Hence option b is true
Consider option c:
We can express 4n as 2 x 2n.
Since n is X.5 then 2n must be an integer and any multiple of 2 gives an even integer.
But the statement says that 4n is an odd integer.
Hence option c is false.
Question 2
If p is an odd number and q is an even number, which of the following must be an even?
I. 2p+3q
II. p2 - q2
III.(pq)2
IV. (1+pq)2
Options:
a) I only b)II&IV only c)I&III only d)I,II&III only
Answer : c)I&III only
Solution:
We know that any multiple of 2 is even and 3 times of an even number is also even.
Then 2p and 3q both are even.
Since the addition of two even numbers is again an even, then 2p+3q is even.
i.e., I is even.
Now, the square of any even number is even and the square of an odd is odd. Then p2 is odd and q2 is even
And difference between even number and odd number is an odd number.
Then p2 - q2 is an odd.
Hence II is odd.
The multiplication of an odd and even number will be an even number, then pq is even,
And the square of an even is even, so (pq)2 is also even.
Hence III is even.
since pq is even, then 1 + pq will be odd.
And the square of odd is odd. Therefore (1 + pq)2 is odd.
Hence IV is odd.
Therefore only I and III are even. Thus the answer is I & III only.
Question 3
If n is an odd integer, then which of the options will be even.
a)(n2)/2 + n b)nn + n + 1 c)(n2 + 3)2 d)none of these
Answer : c)(n2 + 3)2
Solution :
Consider option a,
since n is an odd number then n2 is also an odd
We can express (n2)/2 + n as ( n2 + 2n)/ 2.
And n2 is odd and 2n is even, then n2 + 2n will be odd
Then ( n2 + 2n)/ 2 is not an even integer.
Consider option b,
since n is odd, then n power anything is odd and nn is odd.
The addition of 3 odd numbers is odd, then nn + n + 1 is an odd integer.
Consider option c,
Here n2 is odd and then n2 + 3 is also odd.
Now, the square of an odd integer is odd, then (n2 + 3)2 is an even integer.
Hence the option c)(n2 + 3)2 is the answer.

## 3 Common Resume Mistakes To Avoid

You need to be aware of some of the common resume mistakes that freshers often commit that could play spoilsport to a magnitude you can't imagine. Yes, you could miss golden opportunities due to any of the below discussed mistakes.

### Mistake 1 : Not Updating Resumes Periodically

Our life changes everyday and resume is not an exception. Every day, every week and every month you are new person with your skill sets getting upgraded. You should take care that your resume closely resembles your current skill set.
For example, you could be strong in C basics during last week. But during the current week you could had completed reading C pointers and data structures to gain a little mastery over C. Now just think the dampening role that your resume could play if it still reads "C Basics". Employers don't have magic mirrors that could reveal your exact skill set. Hence updating resumes on a weekly basis is very important.

### Mistake 2 : Not Having Resume Saved On Desktop

Having resumes saved on Desktop is a very simple technique that could help you to evaluate your Resumes periodically. More importantly, this simple practice also constantly reminds you of your current skill set and the urgency to upgrade your skills to stand ahead of competition.
For example, if you are strong in C language and you are really satisfied with it, the chances are that you are not going to learn OOPS unless otherwise an employer clearly requires that. Instead if you are having your resume saved on Desktop, the chances are that you evaluate your resume now and then, and you are sure to get a feeling that "Wont my resume look far good if I had OOPS in my skill set as well?". And yes, you could best appreciate questions of this kind by imagining the long term benefits they can bring.

### Mistake 3 : Not Cross Comparing Your Resume With Other Resumes

If you are in a particular batch, and say there are at least 30 students in your batch, you increase your chances of being picked up by an employer if your resume has some unique skills which are not found in other resumes. For example, "C Basics", "Windows OS" etc are some of the common skills found in most resumes. Say if your resume has an extra qualification like "Sun JAVA Certified" and if the employer is recruiting for JAVA based projects, your aptitude or placement test score becomes secondary and chances are that your employer is going to give you an easy Pass to enter his organization.

## Wipro DBMS Sample Interview Questions

Question 1
(In DBMS like Oracle) Which of the following allow null values ? A Unique Key or Primary Key ?
Primary Key constraint does not allow null values to be inserted while it is legal in case of Unique key.
Question 2
Considering an Oracle database as an example, can NULL values be used in arithmetic operations ? Explain your answer ?
No, NULL value cannot be used in arithmetic operation. This is because a NULL just denotes an 'absence' of information rather than 'empty' or 'zero' value.
Question 3
How you can delete a duplicate row from Unique key column?
This necessity does not arise. First of all Unique key column will not allow duplicate rows to be inserted.
Question 4
Tell any one advantage of using stored procedures in applications?
Stored Procedures abstract complex SQL queries from application code. For example, a task involving multiple lines of complex SQL queries can be simplified to a single stored procedure call.

## Wipro Sample Questions On Roots Of An Equation

Question 1
What is the sum of the irrational roots of the equation (x-1)(x-3)(x-5)(x-7)=9 ?
a)10 b)8 c)6 d)4
Solution:
Given that
(x - 1) (x - 3) (x - 5) (x - 7) = 9
Let x - 4 = p
Then the given eqn becomes
(p + 3) (p + 1) (p - 1) (p - 3) = 9
(p2 - 1) (p2 - 9) = 9
p4 - 10p2 + 9 = 9
p2 (p2 - 10) = 0
p2 =0 or p2-10 =0
p = 0 or p = sqrt(10) or p = - sqrt(10)
then x - 4 = 0, x - 4 = sqrt(10) or x - 4 = - sqrt(10)
Now the roots of the given eqn are 4,4 + sqrt(10) and 4 - sqrt(10)
The irrational roots are 4+sqrt(10) and 4 - sqrt(10)
The sum of the irrational roots = 4 + sqrt(10) + 4 - sqrt(10) = 8.
Hence the answer is 8.
Question 2
The product of the distinct roots of the equation (3x)(3x+2)(3x-4)(3x-6)= 64 is:
a)-32/27 b)-61/5 c)63/16 d)69/12
Solution:
Given that
(3x)(3x+2)(3x-4)(3x-6)= 64
Let 3x - 2 = p
Then the given eqn becomes
(p + 2) (p + 4) (p - 2) (p - 4) = 64
(p2 - 4) (p2 - 16) = 64
p4 - 20p2 + 64 = 64
p4 - 20p2 = 0
p2(p2 - 20) = 0
p2 = 0 or p2-20 = 0
p = 0 or p = sqrt(20) or p = - sqrt(20)
then 3x - 2 = 0, 3x - 2 = sqrt(20) or 3x - 2 = - sqrt(20)
and x=2/3, x=[2 + sqrt(20)] / 3 or x = [2 - sqrt(20)] / 3
Now the distinct roots of the given eqn are 2/3, [2 + sqrt(20)] / 3 and [2 - sqrt(20)] / 3
The product of the distinct roots = 2/3 x [2 + sqrt(20)] / 3 x [2 - sqrt(20)] / 3 = 2[(22)-(sqrt(20))2] / 27 = -32/27
Hence the answer is -32/27.
Question 3
Find the product of the roots of x3-7x2+13x-7 = 0
a)1 b)3 c)5 d)7
Solution:
Let f(x)= x3 - 7x2 + 13x - 7
Obviously a rational root is 1 , as f(1) = 1-7+13-7= 0. (i.e x = 1 satisfies the equation perfectly)
So x3-7x2+13x-7 can be written as(x-1)Q(x). We shall find Q(x) by dividing x3-7x2+13x-7 by (x - 1) as follows :
```x-1) x3-7x2+13x-7 (x2-6x+7 is Q(x) by division.
x3-x2
-------------
-6x2+13x
-6x2+ 6x
------------
7x-7
7x-7
------------
0```
So Q(x) = x2 - 6x + 7.
Therefore f(x) = (x-1) (x2 - 6x + 7) .
So the other two roots can be determined from the quadratic x2 - 6x + 7= 0.
(Note : Roots x1 and x2 of any equation of the form ax2+bx+c = 0 are given by the formula. x1 = (-b + sqrt(b2 - 4ac))/2a and x2 = (-b - sqrt(b2 - 4ac))/2a. Refer http://www.teacherschoice.com.au/maths_library/algebra/alg_6.htm for more information.)
So, for our equation, x1 = {-(-6)+sqrt((-6)2-4*7)} / 2 = (3+sqrt(2))is the positive irrational root.
x2 = (3-sqrt(2)) is another positive irrational root.
x = 1 is the positive rational root.
Now the product of the roots = 1(3+sqrt(2))(3-sqrt(2))= (9 - 2)= 7
Hence the answer is 7.

## Infosys delays 17,000 campus recruitment offers

Bangalore: With a challenging environment, and low visibility into client spend, Infosys has said that it will be deferring joining dates, and the management is also putting some cost saving measures in place, reports Shreya Roy of CNBC-TV18.
Infy had decided that with its current business needs in mind it will defer its campus recruitment process. The company had initially made 27,000 campus offers, but now the company says that 17,000 of these will be deferred by up to three months.
However, the firm has reiterated that it plans to honour each of these offers in due course of time. In fact the company which prided itself on a six-month long extensive training programme for fresh intakes has also decided to cut the period short by two months, four months of this training programme will be conducted at its sprawling Mysore campus, while two months will be an online programme.
With a challenging environment, and low visibility into client spend, Infy said it will delay its campus recruitment.
The company is also taking a few more cost-cutting measures, such as the senior management has decided to forgo privilege travel. Until recently, Infosys has also deferred increments for its employees, but last quarter it had eventually gave its employees a hike of six percent.
Rajiv Bansal, CFO, Infosys Bangalore, says that it is going to be challenging, but a very exciting role. The company is going through some tough times. The first important thing will be to reassure all the stakeholders whether it is investors, customers or employees that Infosys is a great company has a right strategy. We are all working on the new strategy Infosys 3.0, which will change the business model of Infosys.

## Categories

Receive Quality Tutorials Straight in your Inbox by submitting your Email ID below.