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[mathjax] Question 1 निम्नलिखित फलनों को x के सापेक्ष अवकलित करें। [Differentiate the following functions w.r.t x] (i) $e^{x^{3}}$ Sol : $y=e^{x^{3}}$ Taking log both sides $logy=loge^{x^{3}}$...
[mathjax] Question 1 $\frac{d y}{d x}$ ज्ञात करें यदि [Find $\frac{d y}{d x}$ if ,] (i) $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ Sol : Differentiating with respect to x $\frac{2}{3}...
[mathjax] Question 1 निम्नलिखित फलनों को x के सापेक्ष अवकलित करें। [Differentiate the following w.r.t x] (i) sin -1 3x Sol : Let y=sin -1 3x Differentiating with respect to x $\frac{d...
[mathjax] Question 1 x के सापेक्ष के फलन अर्थात् संयुक्त फलनों के अवकलन पर आधारित प्रश्नः [Differentiate the following functions with respect to x] (i) sin(ax+b) Sol : Let y= sin(ax+b)...
[mathjax] Question 1 यदि (If) $f(x)=\frac{x-2}{x^{2}-3 x+2}$ , when x≠2 =1 , when x=2 तो (then find) $f^{\prime}(2)$ Sol : When x≠2 , $f(x)=\frac{x-2}{x^{2}-3 x+2}$ $=\frac{x...
[mathjax] Question 1 निम्नलिखित फलनों के सांतत्य (संतता) की जाँच दुए हुए बिन्दुओं पर कीजिए । [Examine the continuity of the following functions at indicated points] [Note : f (x), x=a f (a)𝜖R $\lim...
[mathjax] Question 1 आव्यूह का प्रयोग कर निम्नलिखित समीकरण निकाय को हल करे. [Using matrices solve the following system of equations:] (i) 2 x+5 y=1 3 x+2 y=7 Sol : The system of equation is...
[mathjax] Question 1 निम्नलिखित आव्यूहों के परिवर्त तथा सहखण्डज निकालें छ [Find the transpose and adjoint of the following matrices] (i) $\left[\begin{array}{ll}2 & 3 \\ 5 & 1\end{array}\right]$ Sol...
[mathjax] Question 1 त्रिभुज का क्षेत्रफल निकालें जिसके शीर्ष निम्नलिखित हैं : [Find the area of the triangle whose vertices are :] (i) (-2,4),(2,-6),(5,4) Sol : <to be added> Diagram...
[mathjax] निम्नलिखित का मान निकालें (Evaluate the following): (i) $\begin{vmatrix} 7 &5 \\ -2 & 3 \end{vmatrix}$ Sol : = 21-(-10) = 21+10 = 31 (ii) $\begin{vmatrix} cos \alpha &sin \alpha \\ sin...
[mathjax] Question 1 If Z + is the set of all non-negative integers , determine whether or not each of the operation * given below gives a binary operation. In case * is not a binary operation, given...
[mathjax] Question 1 (i) माना कि A={1,9} , B={5,13} तथा R={(a,b):a∈A,b∈B तथा a-b}से विभाज्य है । दिखाएँ कि R,A से B मे सार्वत्रिक सम्बन्ध है । Sol : 1-5=-4, 4 से विभाजय है । 1-13=-12, 4 से विभाजय है...