Why Are Two Electric Bulbs Not Coherent
The light from two electric bulbs cannot be coherent. The time and direction of the emission of individual photons from... View Article
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Does Frozen Water Sink
We generally expect the solid to be heavier than the liquid form. It is not so with frozen water or... View Article
If Y Sinn X Cos Nx Then Dy Dx Is Equal To
1) n sinn–1 x sin (n + 1)x 2) n sinn-1 x cos (n – 1)x 3) n sinn–1 x... View Article
If Fx Log X2 Loge X Then F X At X E Is Equal To
1) 1 2) 1/e 3) 1/2e 4) 0 Solution: Given \(\begin{array}{l}f(x) =\log _{x^{2}}(\log _{e})x\end{array} \) = log (log x)/(log x)2... View Article
The Derivative Of Cos3 X With Respect To Sin3 X Is
1) – cot x 2) cot x 3) tanx 4) – tan x Solution: Let u = cos3x v =... View Article
If Xy Tan 1 Xy Cot 1 Xy Then Dy Dx Is Equal To
1) y/x 2) – y/x 3) x/y 4) -x/y Solution: xy = tan–1 (xy) + cot–1(xy) xy = π/2 (since... View Article
If Y Root X Loge X Then Dy Dx At X E Is
1) 1/e 2) 1/√e 3) √e 4) e2 Solution: y = √(x loge x) dy/dx = [1/2√(x loge x)] [... View Article
Find Dy Dx If X 2 Cos Theta Cos 2 Theta And Y 2 Sin Theta Sin 2 Theta
1) tan 3θ/2 2) – tan 3θ/2 3) cot 3θ/2 4) – cot 3θ/2 Solution: x = 2 cos θ... View Article
If Y X X2 Then The Derivatives Of Y2 With Respect To X2 Is
1) 2x2 + 3x – 1 2) 2x2 – 3x + 1 3) 2x2 + 3x + 1 4) 2x2... View Article
If Y Be An Implicit Function Of X Defined By X 2x 2x X Cot Y 1 0 Then Y 1 Is Equal To
1) –1 2) 1 3) log 2 4) – log 2 Solution: Given x2x – 2xx cot y – 1... View Article
If Y 1 X 1 X2 1 X4 1 X 2n Then The Value Of Dy Dx At X 0 Is
1) 0 2) -1 3) 1 4) 2 Solution: y = (1 + x) (1 + x2) (1 + x4)…(1... View Article
If Xy E2 X Y Then Dy Dx Is Equal To
(1) 2(1+log x)/(2+log x)2 (2) (1+log x)/(2+log x)2 (3) 2/(2+log x) (4) 2(1-log x)/(2+log x)2 Solution: xy = e2(x –... View Article
If Fx Mod X 2 X 1 X Then F 10 Is Equal To
1) –3 2) –2 3) –1 4) 0 Solution: f(x) = |x – 2| + |x + 1|- x (d/dx)|x|... View Article
If Y Sin X Sin 2x Sin 3x Sin Nx Then Dy Is
1) \(\begin{array}{l}\sum_{k=1}^{n}k \tan k \: xs\end{array} \) 2) \(\begin{array}{l}y.\sum_{k=1}^{n}k \cot k \: x\end{array} \) 3) \(\begin{array}{l}y.\sum_{k=1}^{n}k \tan k \: x\end{array}... View Article
If Pi Less Than X Less Than 2 Pi Then D Dx Tan 1 1 Cos X 1 Cos X 2 Is
(1) 0 (2) 1 (3) 1/2 (4) -1/2 Solution: (d/dx) [ tan-1((1-cos x)/(1+cos x))1/2] = (d/dx)((2 sin2x)/2)1/2/((2 cos2x)/2)½ (π <... View Article
D Dx Sin 1 X A Eq A Less Than 0 And Mod X A Less Than 1
(1) 1/√(a2-x2) (2) 1/√(x2-a2) (3) -1/√(a2-x2) (4) -1/√(x2-a2) Solution: \(\begin{array}{l}\frac{d}{dx}\left [ \sin^{-1}\frac{x}{a} \right ]=\end{array} \) \(\begin{array}{l}=\frac{1}{\sqrt{1-(\frac{x}{a}})^{2}}\frac{1}{a}\end{array} \) \(\begin{array}{l}=\frac{a}{\sqrt{a^{2}-x^{2}}}\frac{1}{a}\end{array} \) \(\begin{array}{l}=\frac{1}{\sqrt{a^{2}-x^{2}}}\\end{array}... View Article
If Fx Int Log T Dt X2 And X3 X 0 Then F X Is Equal To
1) (9x2 – 4x)log x 2) (4x – 9x2) log x 3) (9x2 + 4x)log x 4) (3x2 – 2x)log... View Article
If Fx Loge Loge X Then F E Is Equal To
1) e-1 2) e 3) 1 4) 0 Solution: f(x) = loge (loge x) f’(x) = (1/loge x)(1/x) Put x... View Article
If Y 3x 1 3x 1 Sin X Loge 1 X X 1 Then At X 0 Dy Dx Is Equal To
1) 1 2) 0 3) -1 4) -2 Solution: y = [(3x-1)/(3x+1)]sin x + loge (1+x) dy/dx = [(3x log... View Article
If Pi 2 Less Than X Less Than 3pi 2 Then The Value Of D Dx Tan 1 Cos X 1 Sin X Is Equal To
1) 1/2 2) -1/2 3) 1 4) -1 Solution: \(\begin{array}{l}\frac{d}{dx}\left \{ \tan^{-1}\left ( \frac{\cos x}{1+\sin x} \right ) \right \}=\end{array}... View Article
