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[mathjax] Question 1 निम्नलिखित मापो को अदिश और सदिश के रूप मे वर्गीकरण करे । [Classify the following measures as scalars and vectors] (i) 5 सेकेण्ड(seconds) Sol : समय=अदिश (ii) 30 km/hr Sol :...
[mathjax] Question 1 किसी वक्र की ढाल किसी बिन्दु पर उस बिन्दु के कोटि की दुगुनी का प्रतिलोम है। वक्र बिन्दु (4,3) से गुजरती है। वक्र का समीकरण ज्ञात करे । Sol : माना वक्र की ढाल $\frac{dy}{dx}$ है,...
[mathjax] Question 1 $x \frac{d y}{d x}-3 y=x^{2}$ Sol : x से भाग देने पर $\frac{d y}{dx}-\frac{3 y}{x}=x$ $\frac{d y}{dx}+P y=Q$ $P=-\frac{3}{x}$, Q=x Integral factor $=e^{\int pd x}$ $=e^{-\int...
[mathjax] निम्नलिखित अवकल समीकरणो को हल करे। [Solve the following differential equations] Question 1 x(x-y)dy+y 2 dx=0 Sol : x(x-y)dy=-y 2 dx $\frac{dy}{dx}=\frac{-y^2}{x(x-y)}$...
[mathjax] Question 1 $(x-y)^2\frac{dy}{dx}=1$ Sol : Putting (x-y)=t Differentiating w.r.t x $1-\frac{dy}{dx}=\frac{dt}{dx}$ $1-\frac{dt}{dx}=\frac{dy}{dx}$ $t^2 \left(1-\frac{dt}{dx}\right)=1$...
[mathjax] Question 1 निम्नलिखित अवकल समीकरण को हल करे। [Solve the following differential equations] 1.$\frac{dy}{dx}=(e^x+1)y$ Sol : $\frac{dy}{dx}=(e^x+1)y$ $\frac{dy}{dx}=(e^x+1)dx$ दोनो तरफ समाकलन...
[mathjax] Question 1 सत्यापित कीजिए कि दिया हुआ फलन संगत अवकल समीकरण का हल है: [Verify that the given function is a solution of the corresponding differential equation] (i) $y=e^{-3x}:...
[mathjax] Question 1 यदि A,B,a,b स्वेच्छ अचर हो तो निम्नलिखित वक्रो के कुल का अवकल समीकरण ज्ञात कीजिए। [If A,B,a,b are arbitrary constant, find the D.E of the following family of curves] (i) Ax 2 +By...
[mathjax] Question 1 $\frac{d^{2} y}{d x^{2}}+4 x=0$ Sol : Order=2 Degree=1 Linear Differential Equation Question 2 $3 \frac{d^{2} y}{d x^{2}}-5\left(\frac{dy}{dx}\right)^{3}+2 y=0$ Sol : Order=2...
[mathjax] Question 1 वक्र y=x 2 ,रेखाओ x=1, x=2 तथा x-अक्ष से घिरे क्षेत्र का क्षेत्रफल ज्ञात कीजिए। [Find the area bounded by the curve y=x 2 , lines x=1, x=2 and x-axis] Sol :...
[mathjax] Question 1 (i) $\int_{0}^{2} x d x$ Sol : a=0, b=2 nh=2-0 nh=2 f(x)=x $\int_{0}^{2} x d x=\lim _{h \rightarrow 0} h \sum_{r=1}^{n} f(a+rh)$ $=\lim _{h \rightarrow 0} h \sum_{x=1}^{n}...
[mathjax] Question 1 Evaluate the following: (i) $\int_{-2}^{2}|x| d x$ Sol : Put x=0 $=\int_{-2}^{0} |x| d x+\int_{0}^{2}|x| d x$ $=-\int_{-2}^{0} x d x+\int_{0}^{2} x d x$...