Ncert Hero

Class 12 Ncert Solution Maths Differential Equations Previous Exercises Exercise 9.1 &9.2 Next Exercises Exercise 9.5 Exercise 9.6                                                                             Exercise 9.4 For each of the differential equations in Exercises 1 to 10, find the general solution: 1.\(\frac{dy}{dx}=\frac{1-\cos x}{1+ \cos x}\) Sol: We have \begin{aligned} \frac{dy}{dx}&=\frac{1-\cos x}{1+ \cos x}\\ &= \frac{\sin^2{x\over2} + \cos^2{x\over2} - \cos^2{x\over2} + \sin^2{x\over2}}{\sin^2{x\over2} + \cos^2{x\over2} +\cos^2{x\over2} - \sin^2{x\over2}}\\ &= \frac{\sin^2{x\over2}+ \sin^2{x\over2}}{ \cos^2{x\over2} +\cos^2{x\over2}}\\ &= \frac{2\sin^2{x\over2}}{ 2\cos^2{x\over2}}\\ &= \tan^2{x\over2}\\ \frac{dy}{dx}...

                                        Class 12 Ncert Solutions  Maths Differential Equations                                                                           Exercise 9.1 Next Exercises Exercise 9.1 &9.2 Exercise 9.4 Exercise 9.6 Determine order and degree(if defined) of differential equations given in Exercises 1 to 10. 1. \(\frac{d^4y}{dx^4}+ sin(y''')\) Ans: The order of the differential equation is 4 because the highest power of the highest derivative is 4.  The degree of the given equation is not defined since it is nota polynomial equation 2. \(y^{'} + 5y = 0\) Ans: The order of the equation is 1 and the degree of the equaion is also 1. 3. \(\left(\frac{d...

                                                                                    Class 12 Ncert Solutions Probability Maths                                                                Exercise 13.5 1. A die is thrown 6 times. If "getting an odd number' is a success, what is the probability of  (i) 5 successes ?  (ii) at least 5 successes?  (iii) at most 5 successes? Sol:  The repeated throwing of dice are Bernoulli trials. Let X denote no. of successes (getting an odd number) in an experiment of 6 trials. Clearly, X has the binomial distribution with n =6 and p=\(\frac{1}{2}\) \(\the...

                                                                                               Class 12 Ncert Solutions Probability Maths                                                                           Exercise 3.2   1. P(A) =\(\frac{3}{5}\) and P(B) = \(\frac{1}{5}\), find P(A\(\cap\)B) if A and B are independent events. Sol:  we have P(E\(\cap\)F) =P(E).P(E|F). But since A and B are independent so P(E\(\cap\)F) =P(E).P(F) = \(\frac{3}{5}\times\frac{1}{5}=\frac{3}{25}\) 2. Two cards are drawn at random and without replacement from...

                                                                                                     Class 12 Ncert Solutions Probability Maths                                                       Exercise 13.1 1. Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) = 0.2, find  P(E|F) and P(F|E). Sol: We have  P(E|F) =\(\frac{P(E∩F)}{P(F)}\) = \(\frac{0.2}{0.3}=\frac{2}{3}\) and P(F|E) = \(\frac{P(E∩F)}{P(E)}\) = \(\frac{0.2}{0.6}=\frac{2}{6}=\frac{1}{3}\) 2. Compute P(A|B), if P(B) = 0.5 and P(A∩B) = 0.32 Sol: We have P(A|B) = \(\frac{P(A∩B)}{P(B)}\) = ...