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:- Find the equations of the diagonals of the parallelogram PQRS whose vertices are P(4, 2, -6), Q(5, -3, 1), R(12, 4, 5) and S(11, 9, -2). Use these equations to find the point of intersection of diagonals. Solution:- Vertices of parallelogram PQRS are P(4, 2, -6), Q(5, -3, 1), R(12, 4, 5) and S(11, … 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 – – – (i) – – – (ii) Let dr’s of the line l are … Read more
Question: A function f:[-4,4] → [0,4] is given by f(x) = √16 – x². show that f is an onto function but not a one-one function. Further, find all possible values of ‘a’ for which f(a) = √7. Solution:- A function f:[-4, 4] → [0, 4] is given that One-one :- Let are lies in … 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
Question: If 20 m of wire is available for fencing off a flower-bed in the form of a circular sector, then the maximum area(In sq m) of the flower bed is (a) 12.5 (b) 10 (c) 25 … Read more
Question: Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere. Solution: Consider be the centre and be the radius of the given sphere, In ΔOBM, using pythagoras theorem BM is the radius of cone Volume of cone Differentiating … Read more
Question: A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum? Solution: Let … Read more
Question: Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base. Solution: Let be the radius of the circular base and be the height of closed right circular cylinder. Formula for Total surface area –(i) Volume of cylinder Differentiating with respect … Read more