161 - Mathematics Questions Answers

Mathematics >> Algebra >> Equations and Inequalities Olympiad

$I f \frac{9}{a} + \frac{24}{b} = 1, a, b, \in ℝ^{+}, p r o v e t h a t a^{2} + b^{2} \geq 9 {(4 + \sqrt[3]{9})}^{3} .$

Asked By: JAMES GHOSH

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Joshi sir comment

Mathematics >> Calculus >> Applications of integrations IIT JEE

Plzz solve for even and odd values both during intermediate of answer steps 🙏🙏🙏

Asked By: ASHLOK

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Mathematics >> Algebra >> Sequence and Series IIT JEE

The expression ax2 + 2bx + b has same sign as that of b for every real x, then the roots of equation bx2 + (b – c) x + b – c – a = 0 are (A) real and equal (B) real and unequal (C) imaginary (D) None of these

Asked By: PREM

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Mathematics >> Algebra >> Equations and Inequalities IIT JEE

If a,b and c are positive real numbers, show that

$\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} \geq \frac{3}{2}$

Asked By: MROY

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Mathematics >> Algebra >> Equations and Inequalities IIT JEE

How to do it without using cauchy schwartz inequality?

Asked By: LUFFY

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Mathematics >> Co ordinate Geometry >> Straight Lines IIT JEE

Asked By: LUFFY

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Joshi sir comment

$L e t t h e l i n e s i n t h e p a i r a r e m_{1} x - y = 0 a n d m_{2} x - y = 0 F i n d p e r p e n d i c u l a r s f r o m (x^{,}, y^{,}) o n l i n e s a n d c a l c u l a t e t h e i r s u m U s e f o r m u l a e m_{1} + m_{2} = - \frac{2 h}{b} a n d m_{1} m_{2} = \frac{a}{b}$ Inform for any issue

Mathematics >> Calculus >> Area bounded region, volume, surface area and arc length IIT JEE

Asked By: LUFFY

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Joshi sir comment

length for one turn = 3

Draw diagonal of a rectangle then turn it as a cylinder, you will get the construction given in the question.

$I n t r i a n g l e l = \sqrt{3^{2} + n^{2}} S o t o t a l l e n g t h o f w i r e h a v i n g n t u r n = n \sqrt{3^{2} + n^{2}} C o m p a r e w i t h 20 a n d s o l v e$

Mathematics >> Calculus >> Integrations IIT JEE

Asked By: LUFFY

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Mathematics >> Calculus >> Applications of differentiation IIT JEE

Asked By: KANDUKURI ASHISH

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$T h e g e n e r a l s o l u t i o n o f t h i s k i n d o f d i f f e r e n t i a l e q . i s y = e^{a x} L e t a f u n c t i o n g (x) = e^{a x} f (x) (1) d i f f e r e n t i a t e e q . (1) t h r i c e f o r g e t t i n g g^{,,,} (x) n o w f o r g e t t i n g t h e s a m e f u n c t i o n a s g i v e n f i n d a . y o u g e t t h e s a m e f u n c t i o n f o r a = 1 / 2 . c l e a r l y, f o r m i n 5 z e r o s o f g (x), t h e r e a r e m i n 2 z e r o s f o r g^{,,,} (x) . s o l v e a n d i n f o r m i f f a c e a n y p r o b l e m .$