Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2018MathematicsProbability

If P(n): 1+3+5+ +(2 n-1)=n^2 is

Options

  1. Atrue for all n N
  2. Btrue for n 1
  3. Ctrue for no n
  4. DNone of these

Correct answer

A. true for all n N

Step-by-step solution

Since, P(1): 1=1 (true) aligned & Let P(k) & 1+3+5+ +(2 k-1)=k^2 & P(k+1) & 1+3+5+ +(2 k-1)+2 k+1 & & & =k^2+2 k+1=(k+1)^2 aligned So, it holds for all n .

Practice Probability on Quantrex Academy →

More from Probability

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is 1 4 and the probability that the second student g 2025For three events A, B and C of a sample space, P(exactly one of A or B occurs)= P ( exactly one of B or C occurs )= P ( exactly one of C or A occurs )= 1 4 . If probability of all 2025A bag P contains 4 red and 5 black balls, another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag P and two balls are drawn from bag Q, then the pro 2025On every evening, a student either watches TV or reads a book. The probability of watching TV is 4 5 . If he watches TV, the probability that he will fall asleep is 3 4 and it is 1 2025Let X be the random variable taking values 1,2, , n for a fixed positive integer n. If P ( X = k )= 1 n for 1 k n , then the variance of X is 2025A radar system can detect an enemy plane in one out of ten consecutive scans. The probability that it can detect an enemy plane atleast twice in four consecutive scans is 2025Three numbers are chosen from 1 to 30. The probability that they are not three consecutive numbers is 2025If two events A and B are such that P ( A )=0.3, P ( B )=0.4 and P ( A B )=0.5 , then P ( B /( A B ))= 2025 Full Probability list All Manipal MET PYQs