TCS Questions on Series and Progressions with Answers -1

1.How many odd and even numbers are there between 42 and 400?? Find the sum of odd numbers and the sum of even numbers!
a.39338
b.33214
c.45321
d.12321
Answer: a
Explaination:
Odd numbers are from 43 to 399. Number of odd numbers = (l−a)/d+1= 399−43/2+1=179
Their sum =n/2(l+a)= 39559
Even numbers are from 44 to 398. Number of even numbers =(l−a)/d+1=(398−44)/2+1=178
Their sum =178/2(398+44)=39338

2.In a staircase, there ar 10 steps. A child is attempting to climb the staircase. Each time she can either make 1 step or 2 steps. In how many different ways can she climb the staricase?
a.10
b.21
c.36
d.None of these
Answer: d
Explaination: Use fibonnacci series, with starting two terms as 1, 2. So next terms are 3, 5, 8, 13, 21, 34, 55, 89

3. Find the average of the terms in the series 1-2+3-4+5….+199-200
a.-0.1
b.-0.2
c.-0.5
d.-0.3
Answer:c
Explaination:(1-2) +(3-4) + (5-6) +……..(199-200) = -100
Average = 100 / 200 = -0.5

4.A series 1234123441234441234444…..n what is the value on 200th position..??
a.1
b.2
c.3
d.4
Answer:d
Explanation:
1234 => 4 times 12344 => 5 times 123444 => 6 times . . . 4 + 5 + 6 + …n < 200 n(n+1)/2 - 6 = 200 So n = 19 i.e. 4+5+6+...19 = 184 After the 184th term,the sequence has 20 terms 12344444444444444444 = 20 terms => 200th term = 4

5.On a 26 question test, 5 points were deducted for each wrong answer and 8 points were added for right answers. If all the questions were answered how many were correct if the score was zero?
a.10
b.11
c.12
d.13
Answer:a
Explanation:
Let x ques were correct. Therefore, (26- x) were wrong 8x−5(26−x)=08x−5(26−x)=0 Solving we get x=10