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[mathjax] Question 1 निम्नलिखित के माध्य तथा प्रसरण निकालें [Find the mean and variance of the following] (i) 6 ,7 ,10 ,12 ,13 ,4 ,8 ,12 (ii) 65, 58 ,68 ,44 ,48 ,45 ,60 ,62 ,60 ,50 Sol : (i) 6 ,7 ,10...
[mathjax] Question 1 निम्नलिखित आंकड़ो के लिए माध्य के सापेक्ष माध्य विचलन ज्ञात कीजिए : (i) 30,40,70,60,20,10,50 Sol : 10,20,30,40,50,60,70 माध्य$(\overline{{x}})=\frac{10+20+30+40+50+60+70}{7}$...
[mathjax] Question 1 निम्नलिखित कधनों के संयोंजन तधा वियोजन लिखें : [Write down the conjunctioon and disjunction of the following statements.] (i) p : जैक पहाड़ी पर ऊपर गया। [Jack went up the hill.]...
[mathjax] Question 1 जाँच कीजिए कि निम्नलिखित वाक्यों में से कौन कथन है ? अपने उत्तर के लिए कारण भी बतलाइए । [Check whether the following sentences are statements. Give reasons for your answer.] (i)...
[mathjax] निम्नलिखित फलनों का x के सापेक्ष अवकलन करें : [Differentiate the following functions w.r.t. to x]: Question 1 (i) $x^{3} \cos x$ Sol : माना $y=x^{3} \cdot \cos x$ Differentiating w.r.t x...
[mathjax] Question 1 x के सापेक्ष निम्नलिखित का अवकल गुणांक निकाले। [Find the derivatives (differential coefficient) of the following functions w.r.t x] (i) 10x 5 Sol : माना y=10x 5 Differentiating...
[mathjax] निम्नलिखित का प्रथम सिद्धान्त से अवकल गुर्णांक (अवकलन) निकाले [Find the differential coefficient (derivative) of the following from first principles] Question 1 (i) 10x Sol : Let f (x)=10x...
[mathjax] Question 1 यदि(If) f x=x 2 , find f ' (2) निकाले । Sol : $\left[f^{\prime}(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\right]$ $f^{\prime}(2)=\lim _{h \rightarrow 0}...
[mathjax] Question 1 यदि (If) f (x)=x 2 +x+2, जब(when) x<1 =x 4 +3,जब(when)x>1 तो क्या $\lim _{x \rightarrow 1} f(x)$ का अस्तित्व है।(then does $\lim _{x \rightarrow 1} f(x)$ exist?) Sol :...
[mathjax] Question 18 निकाले (Find) $\lim_{x\rightarrow 0}\frac{3\sin x-\sin x}{x(\cos 2x-\cos 4x)}$ Sol : [sin3x=3sinx-4sin 3 x 4sin 3 x=3sinx-sin3x cosC-cosD=2sin$\frac{C+D}{2}\sin \frac{D-C}{2}$]...
[mathjax] Question 2 निकाले (Evaluate) $\lim_{x\rightarrow 1}\frac{x^3-1}{x-1}$ Sol : $=\lim_{x\rightarrow 1}\frac{x^3-1^3}{x-1}$ =3.(1) 3-1 =3(1) 2 =3 Question 3 निकाले (Evaluate)...
[mathjax] Question 1 यदि A(3,1,-2) तथा B(1,-3,-1) दो बिन्दु हैं, तो उन बिन्दुओं के नियामक निकालें जो रेखा खण्ड AB को (i) 1 : 3 के अनुपात मे अन्तर्विभाजित करता है। (ii) 3 : 1 के अनुपात मे बहिर्विभाजित...