Question-Answer

Question 2: Check whether the relation R in R defined as R={(a, b): a ≤  b³} is reflexive, symmetric or transitive. Solution:- R defined as R={(a, b): a ≤  b³} is reflexive, symmetric or transitive.   Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric.  Transitive:- is not transitive. is neither reflexive nor symmetric … Read more

Question 1:- Show that the relation R on the set R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. Solution:  R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. where a, b ∈ R Reflexivity:- Obiviously, … Read more

Question:-        A and B throw a die alternatively till one of them gets ‘6’ and win the game. Find their respective probabilities of winning, If A starts first Solution:       Let S denote the success(getting a ‘6’) and F denote the failure(Not getting a ‘6’). Thus, P(A wins in the … Read more

Question:- Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable. Solution:- Let X represent the number of red balls Possible value of X = … Read more

 Question: A line l passes through point (-1,3,-2) and is perpendicular to both the lines and . Find the vector equation of the line l. Hence, obtain its distance from origin. Solution: Point (-1, 3, -2) Equation of lines Let dr’s of the line l are (a, b, c) Equation of line passes through the … Read more

Question : Show that right circular cone of least curve surface and given volume has an altitude equal to √2 time the radius of the base Solution: Let ‘r’ be the radius of cone and ‘h’ be the height of cone Volume of cone –(i) Curve surface area of cone Squaring both side Differentiating with … Read more