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CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 14 - MCQExams.com

If y=x(xx), then dydx is
  • y[xx(logex)logx+xx]
  • y[xx(logex)logx+x]
  • y[xx(logex)logx+xx1]
  • y[xx(logex)logx+xx1]
If y=x(logx)log(logx), then dydx is
  • yx((lnxx1)+2lnxln(lnx))
  • yx(logx)log(logx)(2log(logx)+1)
  • yxlnx[(lnx)2+2ln(lnx)]
  • yxlogylogx[2log(logx)+1]
The derivative of x(x+4)32(4x3)43 w.r.t x is
  • x(x+4)32(4x3)43{12x+32(x+4)163(4x3)}
  • x(x+4)43(4x3)32{12x+32(x+4)163(4x3)}
  • x(x+4)54(4x3)34{12x+32(x+4)163(4x3)}
  • None of these
fn(x)=efn1(x) for all nϵN and f0(x)=x, then ddx{fn(x)} is
  • fn(x)ddx{fn1(x)}
  • fn(x)fn1(x)
  • fn(x)fn1(x)f2(x).f1(x)
  • none of these
If f(x)=Π100n=1(xn)n(101n), then find f(101)f(101)
  • 14950
  • 1025050
  • 1014950
  • 15050
If y=x+y+x+y+, then  dydx=
  • y2x2y32xy1
  • x2x2x32xy1
  • x2x2x32xy21
  • None of these
The value of f(3) is
  • 8
  • 10
  • 12
  • 18
If for all x,y the function f is defined by; f(x)+f(y)+f(x)f(y)=1 and f(x)>0.When f(x) is differentiable f(x)=,
  • 1
  • 1
  • 0
  • cannot be determined
The function f(x)=ex+x being differentiable and one to one, has a differentiable inverse f1(x), then find ddx(f1(x)) at the point f(loge2).
  • 13
  • 1
  • 3
  • 0
The value of f(9) is
  • 240
  • 356
  • 252
  • 730
Given, f(x)=x33+x2sin1.5axsinasin2a5arcsin(a28a+17), then
  • f(x) is not defined at x=sin8
  • f(sin8)>0
  • f(x) is not defined at x=sin8
  • f(sin8)<0
Let f be a twice differentiable such that f(x)=f(x) and f(x)=g(x). If h(x)={f(x)}2+{g(x)}2, where h(5)=11. Find h(10)
  • 1
  • 10
  • 11
  • 100
Derivative of (xcosx)x with respect to x is
  • (xcosx)x[(logx+1){logcosx+xcosx.(sinx)}]
  • (xcosx)x[(logx+1)+{logcosx+xcosx.(sinx)}]
  • (xcosx)x[(logx+1)+{logsinx+xcosx.(cosx)}]
  • None of these
Find the derivative of |x|+a0xn+a1xn1+a2xn2+....+an1x+an
  • x|x|+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an1
  • 1+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an1
  • x|x|+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an
  • None of these
Equation xn1=0,n>1,nϵN, has roots 1,a2,....an.
The value of nr=212ar, is
  • 2n1(n2)+12n1
  • 2n(n2)+12n1
  • 2n1(n1)12n1
  • none of these
Let f(x)=x1+x+2410x1,1x26 be a real valued function, then f(x) for 1<x<26 is
  • 0
  • 1x1
  • 2x1
  • 1
f:RR and f(x)=2ax+sin2x, then the set of values of a for which f(x) is one-one and onto is
  • a(12,12)
  • a(1,1)
  • aR(12,12)
  • aR(1,1)
If y and z are the functions of x and if y2+z2=λ2, then yddx(yλ)+ddx(z2λ) is equal to
  • zλdzdx
  • zλdxdz
  • λzdzdx
  • None of these
Let h(x) be differentiable for all x and let f(x)=(kx+ex)h(x) where k is some constant. If h(0)=5,h(0)=2 and f(0)=18, then the value of k  is equal to
  • 3
  • 4
  • 5
  • 1
Let f be a differentiable function satisfying f(x)+f(y)+f(z)+f(x)f(y)f(z)=14 for all x, y, zR
Then,
  • f(x)<0 for all xR
  • f(x)=0 for all xR
  • f(x)>0 for all xR
  • none of these
Let f(x)=x2+xg(1)+g"(2) and g(x)=f(1).x2+xf(x)+f"(x) then
  • f(1)+f(2)=0
  • g(2)=g(1)
  • g(2)+f(3)=6
  • none of these
If y+x+yx=c (where c0), then dydx has the value equal to
  • 2xc2
  • xy+y2x2
  • yy2x2x
  • c22y
Equation xn1=0,n>1,nϵN, has roots 1,a2,....an.
The value of nr=211ar, is
  • n4
  • n(n1)2
  • n12
  • none of these
Suppose, A=dydx of x2+y2=4 at (2,2),B=dydx of siny+sinx=sinxsiny at (π,π) and C=dydx of 2exy+exeyex=exy+1 at (1,1), then (ABC) has the value equal to .....
  • 12
  • 13
  • 1
  • 2
If f(x)=x+22x4+x22x4, then the value of 10f(102+) is
  • 1
  • 0
  • 1
  • Does not exist
Let f(x) be a polynomial function of second degree.If f(1)=f(1) and  a,b,c are in A.P f(a),f(b),f(c) are in 
  • G.P.
  • H.P.
  • A.G.P
  • A.P.
For the curve represented implicitly as 3x2y=1, the value of limx(dydx) is 
  • equal to 1
  • equal to 0
  • equal to log23
  • non existent
If x2+y2=R2 (R>0) then k=y(1+y2)3 where k in terms of R alone is equal to
  • 1R2
  • 1R
  • 2R
  • 2R2
If cos4θx+sin4θy=1x+y then dydx=
  • xy
  • tan2θ
  • 0
  • (x2+y2)sec2θ
Two functions f and g have first and second derivatives at x=0 and satisfy the relations, f(0)=2g(0), f(0)=2g(0)=4g(0), g(0)=5f(0)=6f(0)=3 then
  • If h(x)=f(x)g(x) then h(0)=154
  • If k(x)=f(x).g(x)sinx then k(0)=2
  • limx0g(x)f(x)=12
  • None of these
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers