If √1-x2+√1-y2=a(x-y) then dy/dx=
A. √(1+y2)/√(1+x2)
B. √(1+x2)/√(1+y2)
C. √(1-y2)/√(1+x2)
D. √(1-y2)/√(1-x2)
If f(x)=x2sin(1/x) for x≠0, f(0)=0 then
A. f and f1are continuous at x=0
B. f is derivative at x=0 and f1is not continuous at x=0
C. f is derivable at x=0 and f1 is continuous at x=0
D. noneof these
If x= et(cos t +sin t), y= et(cos t-sin t) then dy/dx=
A. tan t
B. –tan t
C. tan (3t/2)
D. –cot (3θ/2)
If x-y=Sin-1 x-Sin-1 y then dy/dx=
A. √y(4x√x-√y)/√x(2√y+√x)
B. √y(1-2√xy-y)/√x(1+2√xy+x)
C. 2x+3/2y+5
D. √1-y2-√(1-x2)(1-y2)/√(1-x2)-√(1-x2)(1-y2)
d/dx{(√(a2+x2)+ √(a2-x2))/ (√(a2+x2)- √(a2-x2))}
A. (2a2/x2){1+a2/√(a4-x4)}
B. (2a2/x3){1+a2/√(a4-x4)}
C. 1+a2/√(a4-x4)
D. 1-a2/√(a4+x4)
If 3x2+4xy+2y2+x-8=0 and dy/dx at (1,1),(1,2),(2,-1),(-1,3) are respectively A,B,C,D then the descending order of A,B,C,D is
A. A,B,C,D
B. B,C,A,D
C. C,A,B,D
D. B,A,C,D
The derivative of (sin x)x w.r.to x is
A. (sin x)x[x cot x+ log sin x]
B. (sin x)x[x cot x-log sin x]
C. -(sin x)x[x cot x+ log sin x]
D. -(sin x)x[x cot x-log sin x]
Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then
A. a=-1/2,b=3/2
B. a=-1/2,b=1/2
C. a=1,b=-1
D. a=1/2,b=1/2
The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is
A. 1
B. 1/2
C. 1/4
D. 1/8
If cos x/2 . cos x/22. Cos x/23.... cos x/2n= sin x/2nsin (x/2n) then (1/22)sec2x/2+(1/24) sec2x/22...(1/22n)sec2x/2n=
A. (1/22n)cosec2x/2n+cosec2x
B. –(1/22n)cosec2x/2n+cosec2x
C. cosec2x/2n+cosec2 x
D. none
If sin2 mx+cos2 ny=a2 then dy/dx=
A. m sin (2mx)/nsin(2ny)
B. m cos(2mx)/nsin(2ny)
C. mcos(2mx)/n cos(2ny)
D. m sin(2mx)/n cos (2ny)
The derivative of cos hx/2w.r.to x is
A. 2 sech2 2x
B. 3 cosh 3x
C. 1/2 sin hx/2
D. -5 cosech25x
If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=
A. 0
B. 6
C. -6
D. none
Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then
A. f is differentiable everywhere
B. f is not differentiable everywhere
C. f is not differentiable at x=1
D. f is not differentiable everywhere
The derivative of (log x)xw.r.to x is
A. (log x)x-1[1+log x log (log x)]
B. (log x)x-1[1-log x log(log x)]
C. –(log x)x-1[1+log x log (log x)]
D. –(log x)x-1[1-log x log(log x)]