If x = a cos4 θ, y = a sin4 θ, then dy/dx at θ = 3π/4 is
(1) -1 (2) 1 (3) -a2 (4) a2 Solution: Given x = a cos4 θ y = a sin4 θ... View Article
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If x = a(t cos t – sin t), y = a(t sin t + cos t). Then dy/dx is equal to
(1) -tan t (2) tan t (3) cot t (4) -cot t Solution: Given x = a(t cos t –... View Article
If cos x =(1/√(1+t2) and sin y = (t/√(1+t2)), then dy/dx =
(1) 1 (2) 0 (3) -1 (4) none of these Solution: Given cos x =(1/√(1+t2) So x = cos-1(1/√(1+t2) Put... View Article
If sin (x+y) = log (x+y), then dy/dx =
(1) 2 (2) -2 (3) 1 (4) -1 Solution: Given sin (x+y) = log (x+y) Differentiate w.r.t.x cos (x+y) (1... View Article
If x is measured in degrees, then d/dx (cos x) is equal to
(1) – sin x (2) – (180/π) sin x (3) – (π/180) sin x (4) sin x Solution: Let y... View Article
If x = 2t/(1 + t2), y = (1 – t2)/(1+ t2), then dy/dx equals
(1) 2t/(t2 + 1) (2) 2t/(t2 – 1) (3) 2t/(1 – t2) (4) none of these Solution: Given x =... View Article
If xy.yx = 100, then dy/dx is equal to
(1) -y(y + x log y)/x(y log x + x) (2) -y(x + y log x)/x(x log y + y)... View Article
If x3 + y3 – 3axy = 0, then dy/dx equals
(1) (ay – x2)/(y2 – ax) (2) (ay – x2)/(ay – y2) (3) (x2 + ay)/(y2 + ax) (4) none... View Article
If x2ey + 2xyex + 13 = 0, then dy/dx =
(1) (2xey-x + 2y(1 + x))/x(xey-x + 2) (2) -(2xey-x + 2y(1 + x))/x(xey-x + 2) (3) (2xex-y + 2y(1... View Article
If 3 sin (xy) + 4 cos (xy) = 5, then dy/dx =
(1) -y/x (2) y/x (3) x/y (4) none of these Solution: Given 3 sin (xy) + 4 cos (xy) =... View Article
Let y = t10 + 1 and x = t8 + 1, then d2y/dx2 is
(1) 5t/2 (2) 20 t8 (3) 5/16 t6 (4) None of these Solution: Given y = t10 + 1 x... View Article
[latex]y= (\tan x)^{(\tan x)^{\tan x}}[/latex], then at x = ?/4, the value of dy/dx =
(1) 0 (2) 1 (3) 2 (4) none of these Solution: Given \(\begin{array}{l}y= (\tan x)^{(\tan x)^{\tan x}}\end{array} \) Take log... View Article
If y = (sin x)tan x, then dy/dx is equal to
(1) sin x tan x (1 + sec2 x log sin x) (2) tan x (sinx) tanx–1 . cos x... View Article
If [latex]y=2^{\frac{1}{\log _{x}4}}[/latex], then x is equal to
(1) y (2) y2 (3) y3 (4) none of these Solution: Given \(\begin{array}{l}y=2^{\frac{1}{\log _{x}4}}\end{array} \) Take log on both sides... View Article
d/dx { (sin x)log x} =
(1) (sin x)log x { [log(sin x)/x] + cot x} (2) (sin x)log x { [log(sin x)/x] + cot x... View Article
If x = a sin 2?(1 + cos 2?), y = b cos 2?(1 – cos 2?), then dy/dx =
(1) (b tan θ)/a (2) (a tan θ)/b (3) a/(b tan θ) (4) b /a tan θ Solution: Given x... View Article
If x = a sin θ and y = b cos θ, then d2y/dx2 is
(1) (a/b2)sec2θ (2) -(b/a)sec2θ (3) -(b/a2)sec3θ (4) (b2/a2)sec3θ Solution: Given x = a sin θ y = b cos θ... View Article
Which is not an electrophile?
Answer: (a) NH3 Reason An electrophile is a compound that has a vacant orbital to attract electrons. Ammonia has a... View Article
Is ammonia a hydrogen bond
In Ammonia (NH3), the number of hydrogen bonds formed is limited since in each nitrogen there is only one lone... View Article
Is rate constant dependent on the concentration?
The rate law for a chemical reaction is the reaction between the rate of the chemical reaction and the reactant... View Article
