Lakshya Education MCQs

Question: If (1x2n)+(1y2n)=a(xnyn), then (1x2n1y2n)dydx is equal to
Options:
A.xn−1yn−1
B.yn−1xn−1
C.xy
D.1
Answer: Option A
: A

Putxn=sinθandyn=sinϕthen,(cosθ+cosϕ)=a(sinθsinϕ)2cos(θ+ϕ2)cos(θϕ2)=2acos(θ+ϕ2)sin(θϕ2)cot(θϕ2)=a(θϕ2)=cot1aθϕ=2cot1aorsin1xnsin1yn=2cot1aDifferentiatingbothsides,wehavenxn1(1x2n)nyn1(1y2n)dydx=0(1x2n1y2n)dydx=xn1yn1

Submit Answer & Explaination

Earn Reward Points by submitting Detailed Explaination for this Question

More Questions on This Topic :

Question 1. If y=x+y+x+y+...., then dydx is equal to
  1.    12y−1
  2.    y2−x2y3−2xy−1
  3.    (2y−1)
  4.    None of these
Answer: Option B
: B

y=x+y+y
(y2x)=2y
or(y2x)2=2y
Differentiating both sides w.r.t. x, then
2(y2x)(2ydydx1)=2dydx
dydx=(y2x)2y32xy1
Question 2. Let f(x)=loge{u(x)v(x)},u(2)=4,v(2)=2,u(2)=2,v(2)=1, then f(2) is equal to
Answer: Option B
: A

f(x)=loge{u(x)v(x)}
=logeu(x)logev(x)
f(x)=u(x)u(x)v(x)v(x)
f(2)=u(2)u(2)v(2)v(2)
=4221
=22=0
Question 3. The derivative of sin1(2x1+x2) with respect to tan1(2x1x2) is
Answer: Option B
: B

Letu=sin1(2x1+x2)=2tan1x
dudx=21+x2
andv=tan1(2x1+x2)=2tan1x
dvdx=21+x2
dudv=(dudx)(dvdx)=1
Question 4. If x = a cos θ,y=b sin θ,then d3ydx3 is equal to
  1.    (−3ba3)cosec4θ cot4θ
  2.    (3ba3)cosec4θ cotθ
  3.    (−3ba3)cosec4θ cotθ
  4.    None of the above
Answer: Option C
: C

x=acosθdxdθ=asinθandy=bsinθdydθ=bcosθdydx=bacotθd2ydx2=bacosec2θdθdx=ba2cosec3θd3ydx3=3ba2cosec2θ(cosecθcotθ)dθdx=3ba2cosec3θcotθ(1asinθ)=3ba3cosec4θcotθ
Question 5. If sin (x+y)=loge(x+y),thendydx is equal to
  1.    2
  2.    - 2
  3.    1
  4.    - 1
Answer: Option D
: D

sin(x+y)=loge(x+y),
cos(x+y)(1+dydx)=1(x+y)(1+dydx)
(1+dydx)(cos(x+y)1x+y)=0
cos(x+y)1(x+y)0
1+dydx=0
dydx=1
Question 6. If xcos y+ycos x=5. Then
  1.    at x = 0, y = 0, y’ = 0
  2.    at x = 0, y = 1, y’ = 0
  3.    at x = y = 1, y’ = – 1
  4.    at x = 1, y = 0, y’ = 1
Answer: Option C
: C

xcosy+ycosx=5
ecosylogex+ecosxlogey=5
ecosylogex{cosyxlogex(siny)dydx}+ecosxlogey{cosxydydxsinxlogey}=0
Putx=y=1,(cos10)+(cos1dydx0)=0
dydx=1
ory=1

Check all Questions in this Topic : Click HERE