Archives

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 t = tan θ x =... 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 + dy/dx) = [1/(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 = cos xo We know 1o = π/180 radian So y = cos... 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 = 2t/(1 + t2) y = (1 - t2)/(1 + t2) Put t =... View Article

If x^y.y^x = 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) (3) -y/x (4) -x/y Solution: Given xy.yx = 100 Take log on... 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 of these Solution: Given x3 + y3 - 3axy = 0... View Article

If x²e^y + 2xye^x + 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 + x))/x(xey-x + 2) (4) none of these... 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) = 5 Differentiate w.r.t.x 3 cos xy (d/dx)(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 = t8 + 1 Differentiate w.r.t.t dy/dt = 10t9... 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 Take log on both sides log y = tan x log (tan x)tan x = tan2 x log tan... 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 (3) sin xcosx. sec2x log sinx (4) tanx .(sinx)tanx– 1... 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 Take log on both sides log y = (1/logx 4) log 2 logx 4 = log 2/log y... 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 log x } (3) (sin x)log x { [log(sin x)/x] + log 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 = a sin 2θ(1 + cos 2θ) We know sin 2θ = 2 sin θ... 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 Differentiate w.r.t.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 lone pair of electrons that... 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 pair of electrons which is shared... 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 concentration. The constant of... View Article

Is silica a silicon dioxide

Silica is also called silicon dioxide. Silica is a natural compound made of silicon and oxygen. It is found in earth’s crust, plants, animals,... View Article

Does phenol react with NaHCO3?

Phenol is a weak acid due to the presence of the polar O-H group. Therefore phenol does not react with bases like sodium hydrogen carbonate (NaHCO3)... View Article

M	T	W	T	F	S	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28