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Q. If y=\frac{1}{1+x^{n-m}+x^{p-m}}+\frac{1}{1+x^{m-n}+x^{p-n}}+\frac{1}{1+x^{m-p}+x^{n-p}} , then \frac{dy}{dx} at e^{m^{n^{p}}} \text{(a) }e^{mnp} \text{(b) }e^{\frac{mn}{p}} \text{(c) }e^{\frac{np}{m}} \text{(d) } none ...
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1. In the isosceles triangle ABC, \left|\vec{AB} \right|=\left|\vec{BC} \right|=8 , a point E divides AB internally in the ratio 1:3, then the cosine of the angle between \vec{CE} & \vec{CA} is ( where \left| \vec{CA}\right|= ...
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Q. Use the fact that e^x>1+x to prove that e^\pi>\pi^e . ...
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*Image* P.S. : It is a doubt. ...
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Q. Use the fact that e^x>1+x to prove that e^\pi>\pi^e . ...
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a rigid body rotates with constant angular velocity w about the line whose vector equation is r=lambda(i+2j+2k). the speed of the particle at the instant it passes through the point with p.v. 2i+3j=5k is a) w√2 b) 2w c)w/∠...
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If a1<a2<a3<a4<a5<a6, then equation (x-a1) (x-a3) (x-a5) + 3(x-a2) (x-a4) (x-a6)=0 has: A) three real roots B) a root in (-∞,a1) C) no real root in (a1,a2) D) no real root in (a5,a6) There may be more than on ...
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If a1<a2<a3<a4<a5<a6, then equation (x-a1) (x-a3) (x-a5) + 3(x-a2) (x-a4) (x-a6)=0 has: A) three real roots B) a root in (-∞,a1) C) no real root in (a1,a2) D) no real root in (a5,a6) There may be more than on ...
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1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...
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1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...
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1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...
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1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...
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1. A small 10W source of ultraviolet light of wavelength 99nm is held at a distance 0.1m from a metal surface. The radius of an atom of the metal is approximately 0.05nm. Find a) the average number of photons striking an atom ...
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Q: The potential drop V0 (in VOLTS) across a resistor varies as V0 = 2 i3/2 where ' i ' is the current in mA. Find the resistance of above device when V0 = 16 V. Q: A conducting sphere of radius ' a ' has charge Q on it. It i ...
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find x such that 1+ 1/1+ 1/1+ =x . . 1+ 1/x ...
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find x such that 1+ 1/1+ 1/1+ =x . . 1+ 1/x ...
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1. Let f be defined on [0,1] be a twice differentiable function such that, \left|f''(x) \right|\leq 1 for all x \in \left[0,1 \right] . If f(0)=f(1) , then show that, \left|f'(x)\right|<1 for all x \in \left[0,1 \right] . ...
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1. Let f be defined on [0,1] be a twice differentiable function such that, \left|f''(x) \right|\leq 1 for all x \in \left[0,1 \right] . If f(0)=f(1) , then show that, \left|f'(x)\right|<1 for all x \in \left[0,1 \right] . ...
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\hspace{-16}$Calculate value of \\\\\\ $\mathbf{(1)::I_{1}=\int_{0}^{\pi}\frac{\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\\\ $\mathbf{(2)::I_{2}=\int_{0}^{\pi}\frac{x.\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\ \hspace{-16}$Ans\; :: $I_{ ...
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\hspace{-16}\int\frac{x^2}{\left(1+\sin 2x\right)}dx ...
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the argument of (1- i 3 ) is (1+ i 3 ) A) 60° B) 120° C) 210° D) 240° i got the answer as 240° but the book ans says it is 60°.... 'am baffled!! ...
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the argument of (1- i 3 ) is (1+ i 3 ) A) 60° B) 120° C) 210° D) 240° i got the answer as 240° but the book ans says it is 60°.... 'am baffled!! ...
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PROVE: n!/r! (n-r)! + n!/(r-1)!(n-r+1)! = (n+1)!/r! (n-r+1)! ...
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1. Prove that (n!)! is divisible by (n!)^{(n-1)!} . 2. Show that 1!+2!+3!+ \dots + n! cannot be a perfect square for any n \in \mathbb{N}, \: n\geq 4 . ...
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1. Prove that (n!)! is divisible by (n!)^{(n-1)!} . 2. Show that 1!+2!+3!+ \dots + n! cannot be a perfect square for any n \in \mathbb{N}, \: n\geq 4 . ...
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1. Prove that (n!)! is divisible by (n!)^{(n-1)!} . 2. Show that 1!+2!+3!+ \dots + n! cannot be a perfect square for any n \in \mathbb{N}, \: n\geq 4 . ...
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Q. Find the hydration product: *Image* ...
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Q. Find the hydration product: *Image* ...
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Q. An electron in the ground state of the He atom joins the Helium nucleus to form He+ ion. Assuming that electron had zero kinetic energy after the transition, find the wavelength of the photon emitted. ...
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Q1. Light is incident from glass to water.Find the range of the angle of deviation for which there are two angles of incidence. n(water) =4/3 . n(glass)=3/2 . Q2. An object P is focussed by a microscope M. A glass slab of thi ...
