Question 6:- In a hotel four rooms are available Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons . Then the number of all possible ways in which this can be done is ______ Solution:- Let … Read more
Question 2:- How many ways 6 Boys & 6 Girls batch students can be seated around a circular table such that no two boys are together. Solution:- If one boys sit in the circle then the other student sit like a in linear then, Number of arrangement of 6 Boys in circle = (6-1)! = … Read more
Question 8:- Two dice are thrown Defined are the following two events A and B : A = {(x, y): x + y = 9}, B = {(x, y) : x ≠ 3}, Where (x, y) denote a point in the same sample space. Check if events A and B are independent or mutually exclusive. … Read more
Question 7:- If y = log(√x + 1/√x)², then show that . Solution:- Given, y = log(√x + 1/√x)² ⇒ y = 2log(√x + 1/√x) ⇒ ⇒ ⇒ ⇒ Again differentiate with respect to x ⇒ ⇒ ⇒ Question 1:- Using integration, find the area of the region bounded by the line y = 5x … Read more
Question 5:- Find the shortest distance between the lines : . Solution:- Shortest distance between two skew line Point on Ist line = (-1, 1, 9) and dr’s of Ist line = (2, 1, -3) Point on IInd line = (3, -15, 9) and dr’s of IInd line = (2, -7, 5) Since, ⇒ ⇒ … Read more
Question 4:- Find the image A‘ of the point A (2, 1, 2) in the line l : . Also, find the equation of the line joining AA’. Find the foot of perpendicular from point A on the line l. Solution:- Given point A(2, 1, 2) And line l : Cartesian equation of given line … Read more
Question 3:- Solve the differential equation ; given y(1) = 2. [CBSE 2025] Solution:- Given, ⇒ ⇒ ⇒ Integrate both side ⇒ ⇒ ⇒ ⇒ . . . (i) Given y(1) = 2 ⇒ ⇒ Hence, from equation (i) ⇒ ⇒ ⇒ ⇒ ⇒ Question 1:- Using integration, find the area of … Read more
Question 2:- Solve the following differential equation : . Solve:- Given, ⇒ . Compare, ⇒ Let, ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ Solution, ⇒ ⇒ ⇒ ⇒ Question 1:- Using integration, find the area of the region bounded by the line y = 5x + 2, the x- axis and the ordinates x = -2 … Read more
Evaluate int 0 to pi x cos x upon 1 plus cos square x Question 2: Evaluate: Solution: Let ………….(i) Using property ……….(ii) Put New limits, when x = 0, t ⇒ 1 and x = π ⇒ t = -1 Putting in eq (ii)
Question 1: Evaluate: Solution: Let I = . . . (i) Using property I = ⇒ I = ⇒ I = ⇒ Dividing by in numerator and denominator ⇒ ……..(ii) Let The limits are, when