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CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 15 - MCQExams.com

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
  • 5
  • 4
  • 3
  • 2
If sin(xy)+cos(xy)=0 then dydx=
  • yx
  • yx
  • xy
  • xy
Given  f(x)=x33+x2sin1.5axsina.sin2a5arcsin(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
The equation (xn)m+(xn2)m+(xn3)m+...+(xnm)m=0 (m is odd positive integer), has
  • all real roots
  • one real and (n1) imaginary roots
  • one real and (m1) imaginary roots
  • No real roots
Suppose A=dydx when x2+y2=4 at (2,2),B=dydx when siny+sinx=sinxsiny at (π,π) and C=dydx when 2exy+exeyexey=exy+1 at (1,1), then (A+B+C) has the value equal to 
  • 1
  • e
  • 3
  • 0
If y=xlnxln(lnx), then dydx is equal to:
  • yx(lnxlnx1+2lnxln(lnx))
  • yxlnxln(lnx)(2ln(lnx)+1)
  • yxlnxlnx2+2ln(lnx)
  • ylnxxlnx(2ln(lnx)+1)
If for a continuous function f,f(0)=f(1)=0,f(1)=2 and g(x)=f(ex)ef(x), then g(0) is equal to 
  • 1
  • 2
  • 0
  • None of these
Let f(x) be a polynomial function of degree 2 and f(x)>0 for all xR. If g(x)=f(x)+f^{'}(x)+f^{"}(x), then for any x
  • g(x)<0
  • g(x)>0
  • g(x)=0
  • g(x)\geq 0
If \displaystyle f(x-y), f(x).f(y) and f(x+y) are in AP for all x, y and f(0)\neq 0, then
  • f(2)=f(-2)
  • f(3)+f(-3)=0
  • f^{'}(2)+f^{'}(-2)=0
  • f^{'}(3)=f^{'}(-3)
Consider the functions defined implicitly by the equation \displaystyle y^{3}-3y+x=0 on various intervals in the real line. If \displaystyle x\epsilon \left ( -\infty , -2 \right )\cup \left ( 2, \infty  \right ), the equation implicitly defines a unique real valued differentiable function \displaystyle y= f\left ( x \right ). If \displaystyle x\epsilon \left ( -2 , -2 \right ) the equation implicitly defines a unique real valued differentiable function \displaystyle y= g\left ( x \right ) satisfying \displaystyle g= g\left ( 0\right )= 0.
If \displaystyle f\left ( -10\sqrt{2} \right )= 2\sqrt{2} then \displaystyle f''\left ( -10\sqrt{2} \right )=
  • \displaystyle \frac{4\sqrt{2}}{7^{3}\cdot 3^{2}}
  • \displaystyle -\frac{4\sqrt{2}}{7^{3}\cdot 3^{2}}
  • \displaystyle \frac{4\sqrt{2}}{7^{3}\cdot 3^{3}}
  • \displaystyle \frac{4\sqrt{2}}{7^{}\cdot 3^{}}
If the prime sign (') represents differentiation w.r.t. x and f^{'}=\sin x+\sin 4x.\cos x, then f^{'}\left ( 2x^{2}+\cfrac{\pi }{2} \right ) at x=\sqrt{\dfrac{\pi }{2}} is equal to
  • 0
  • -1
  • -2\sqrt{2\pi }
  • none of these
If f(x)=x.\left | x \right |, then its derivative is:
  • 2x
  • -2x
  • 2|x|
  • {2}{x} sgn x
If \sqrt{y+x}+\sqrt{y-x}=c (where c\neq 0), then \displaystyle \frac{dy}{dx} has the value equal to
  • \displaystyle \frac{2x}{c^{2}}
  • \displaystyle \frac{x}{y+\sqrt{y^{2}-x^{2}}}
  • \displaystyle \frac{y-\sqrt{y^{2}-x^{2}}}{x}
  • \displaystyle \frac{c^{2}}{2y}
If y=\left | \cos x \right |+\left | \sin x \right | then \frac{dy}{dx} at x=\frac{2\pi }{3} is
  • \frac{1-\sqrt{3}}{2}
  • 0
  • \frac{1}{2}\left ( \sqrt{3}-1 \right )
  • none of these
\displaystyle y=\left ( 1+\frac{1}{x} \right )^{x}+x^{1+\frac{1}{x}}.
Differentiate
  • \displaystyle \left ( 1+\frac{1}{x} \right )^{x}\left [ \log \left ( 1+\frac{1}{x} \right )-\frac{1}{x+1} \right ]+x^{1+1/x}\left [ \frac{x+1-\log x}{x^{2}} \right ].
  • \displaystyle \left ( -1+\frac{1}{x} \right )^{x}\left [ \log \left ( 1+\frac{1}{x} \right )-\frac{1}{x+1} \right ]+x^{1+1/x}\left [ \frac{x+1+\log x}{x^{2}} \right ].
  • \displaystyle \left ( 1+\frac{1}{x} \right )^{x}\left [ \log \left ( 1+\frac{1}{x} \right )-\frac{1}{x+1} \right ]+x^{1-1/x}\left [ \frac{x+1-\log x}{x^{2}} \right ].
  • \displaystyle \left ( -1+\frac{1}{x} \right )^{x}\left [ \log \left ( 1+\frac{1}{x} \right )-\frac{1}{x+1} \right ]+x^{1-1/x}\left [ \frac{x+1+\log x}{x^{2}} \right ].
If \displaystyle f\left ( a \right )=a^{2},\phi \left ( a \right )=b^{2} and \displaystyle {f}'\left ( a \right )=3{\phi }'\left ( a \right ) then \displaystyle \lim_{x\rightarrow 0}\frac{\sqrt{f\left ( x \right )}-a}{\sqrt{\phi \left ( x \right )}-b} is
  • \displaystyle b^{2}/a^{2}
  • \displaystyle b/a
  • \displaystyle 2b/a
  • None of these
Using the ahove approximation, the value \displaystyle \sqrt{104} is
  • 10.18
  • 10.49
  • 10.2
  • 10.28
If \displaystyle y=\sum _{ r=1 }^{ x }{ \tan ^{ -1 }{ \frac { 1 }{ 1+r+{ r }^{ 2 } }  }  } then \displaystyle \frac { dy }{ dx } is equal to
  • \displaystyle \frac { 1 }{ 1+{ x }^{ 2 } }
  • \displaystyle \frac { 1 }{ 1+{ \left( 1+x \right)  }^{ 2 } }
  • 0
  • None of these
Using the above approximation, the value of \displaystyle \cos 40^{\circ} is
  • \displaystyle \frac{1}{\sqrt{2}}-\frac{\pi }{\sqrt{2}36}
  • \displaystyle \frac{1}{\sqrt{2}}+\frac{\pi }{36\sqrt{2}}
  • 0.747
  • 0.7267
If \displaystyle y=x^{2}\cos x then \displaystyle y_{8}\left ( 0 \right ) is
  • 72
  • 56
  • 0
  • -56
Let f(x) = \begin{cases} \overset{x}{\underset{0}{\int}} \{1 + |1 - t|\}dt & if \,x > 2\\ 5x - 7 & if \,x \le 2\end{cases} then
  • \displaystyle f is not continuous at \displaystyle x=2
  • \displaystyle f is continuous but not differentiable at \displaystyle x=2
  • \displaystyle f is differentiable everywhere
  • \displaystyle {f}'\left ( 2+ \right ) doesn't exist
Let y be an implicit function of  x defined by x^{2x}-2x^{x}\cot y-1=0. Then {y}'\left ( 1 \right ) equals:
  • 1
  • \log 2
  • -\log 2
  • -1
If f\left( x \right) = {\left| x \right|^{\left| {\sin x} \right|}}, then {f'}\left( { - \dfrac{\pi }{4}} \right) is equals
  • {\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( { - \dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{4}{\pi } - \dfrac{{2\sqrt 2 }}{\pi }} \right)
  • {\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( {\dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{4}{\pi } + \dfrac{{2\sqrt 2 }}{\pi }} \right)
  • {\left( {\dfrac{\pi }{4}} \right)^{1/\sqrt 2 }}\left( {\dfrac{{\sqrt 2 }}{2}{\text{ln}}\dfrac{\pi }{4} + \dfrac{{2\sqrt 2 }}{\pi }} \right)
  • None of these.
\phi (x)=f\left( x \right) g\left( x \right) \quad and\quad f^{ ' }\left( x \right) g^{ ' }\left( x \right) =k,\dfrac { 2k }{ f\left( x \right) g\left( x \right)  } =
  • \frac { \phi "(x) }{ \phi (x) } -\frac { f"(x) }{ f(x) } -\frac { g"(x) }{ g(x) }
  • \frac { \phi "(x) }{ \phi (x) } +\frac { f"(x) }{ f(x) } +\frac { g"(x) }{ g(x) }
  • \frac { \phi "(x) }{ \phi (x) } +\frac { f"(x) }{ f(x) } -\frac { g"(x) }{ g(x) }
  • \frac { \phi "(x) }{ \phi (x) } -\frac { f"(x) }{ f(x) } +\frac { g"(x) }{ g(x) }
If \displaystyle y=x^{4}e^{2x} then \displaystyle y_{10}\left ( 0 \right ) is equal to
  • \displaystyle 2^{10}
  • \displaystyle 315 \times 2^{10}
  • \displaystyle 195 \times 2^{10}
  • \displaystyle 315 \times 2^{8}
A metal sphere with radius of 10\ cm is to be covered with a 0.02\ cm coating of silver approximately silver required is (in cm^3)
  • \displaystyle 2\pi
  • \displaystyle 10\pi
  • \displaystyle 6\pi
  • \displaystyle 8\pi
Let f and g be differentiable function such that {f}'\left ( x \right )=2g\left ( x \right ) and {g}'\left ( x \right )=-f\left ( x \right ), and let T\left ( x \right )=\left ( f\left ( x \right ) \right )^{2}-\left ( g\left ( x \right ) \right )^{2}. Then {T}'\left ( x \right ) is equal to
  • T(x)
  • 0
  • 2f(x)g(x)
  • 6f(x)g(x)
If y\left ( n \right )=e^{x}e^{x^{2}}...e^{x^{n}}, 0< x< 1. Then \displaystyle \lim_{n\rightarrow \infty }\frac{dy\left ( n \right )}{dx} at x=\dfrac12 is
  • e
  • 4e
  • 2e
  • 3e
If \displaystyle \int f(x) dx = \frac {3}{55}  \sqrt[3]{\tan^5 x} (5  \tan^2 x + 11) + C then f(x) is equal to
  • \displaystyle \sqrt[3] {\sin^2 x  \cos^{-14} x}
  • \displaystyle \sqrt[3] {\tan^2 x(1 + \tan^2 x)^6}
  • \displaystyle \sqrt[3] {\cos^2  x  \sin^{-14} x}
  • \displaystyle \frac {7}{3} \sqrt[3] {\sin^2  x \cos^{-14} x}
Consider the function: f(-\infty,\infty)\rightarrow (-\infty,\infty) defined by \displaystyle f(x)=\frac{x^{2}-ax+1}{x^{2}+ax+1},0<a<2

Which of the following is true?
  • f(x) is decreasing on (-1,1) and has a local minimum at x=1
  • f(x) is increasing on (-1,1) and has a local maximum at x=1
  • f(x) is increasing on (-1,1) and has neither a local maximum nor a local minimum at x=-1
  • f(x) is decreasing on (-1,1) and has neither a local maximum nor a local minimum at x=1
0:0:2


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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers