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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)\cdot f(y)=1 and f(x) > 0.When f(x) is differentiable f'(x)= ,
  • -1
  • 1
  • 0
  • cannot be determined
The function f(x)=e^x+x being differentiable and one to one, has a differentiable inverse f^{-1}(x), then find \dfrac {d}{dx} (f^{-1}(x)) at the point f(log_e 2).
  • \dfrac {1}{3}
  • 1
  • 3
  • 0
The value of f(9) is
  • 240
  • 356
  • 252
  • 730
Given, f(x)=-\displaystyle \frac {x^3}{3}+x^2 \sin 1.5 a-x \sin a\cdot \sin 2a-5 arc \sin (a^2-8a+17), then
  • f(x) is not defined at x=sin 8
  • f' (sin 8) > 0
  • f' (x) is not defined at x=sin 8
  • f'(sin 8) < 0
Let f be a twice differentiable such that f''(x)=-f(x) and f'(x)=g(x). If h(x)=\left \{f(x)\right \}^2+\left \{g(x)\right \}^2, where h(5)=11. Find h(10)
  • 1
  • 10
  • 11
  • 100
Derivative of {(x\cos{x})}^x with respect to x is
  • \displaystyle {(x\cos{x})}^x\left[(\log{x}+1)-\left\{\log{\cos{x}}+\frac{x}{\cos{x}}.(\sin{x})\right\}\right]
  • \displaystyle {(x\cos{x})}^x\left[(\log{x}+1)+\left\{\log{\cos{x}}+\frac{x}{\cos{x}}.(-\sin{x})\right\}\right]
  • \displaystyle {(x\cos{x})}^x\left[(\log{x}+1)+\left\{\log{\sin{x}}+\frac{x}{\cos{x}}.(\cos{x})\right\}\right]
  • None of these
Find the derivative of |x|+a_0x^n+a_1x^{n-1}+a_2x^{n-2}+....+a_{n-1}x+a_n
  • \frac {x}{|x|}+na_0x^{n-1}+(n-1)a_1x^{n-2}+(n-2)a_2x^{n-3}+....+a_{n-1}
  • 1+na_0x^{n-1}+(n-1)a_1x^{n-2}+(n-2)a_2x^{n-3}+....+a_{n-1}
  • \frac {x}{|x|}+na_0x^{n-1}+(n-1)a_1x^{n-2}+(n-2)a_2x^{n-3}+....+a_{n}
  • None of these
Equation x^n-1=0, n > 1, n\epsilon N, has roots 1, a_2, ....a_n.
The value of \displaystyle \sum_{r=2}^{n}\frac {1}{2-a_r}, is
  • \displaystyle \frac {2^{n-1}(n-2)+1}{2^n-1}
  • \displaystyle \frac {2^{n}(n-2)+1}{2^n-1}
  • \displaystyle \frac {2^{n-1}(n-1)-1}{2^n-1}
  • none of these
Let f(x) = \sqrt{x - 1} + \sqrt{x + 24 - 10\sqrt{x - 1}}, 1 \le x \le 26 be a real valued function, then f'(x) for 1 < x < 26 is
  • 0
  • \displaystyle\frac{1}{\sqrt{x - 1}}
  • 2\sqrt{x - 1}
  • 1
f:R\rightarrow R and f(x)=2ax+sin 2x, then the set of values of a for which f(x) is one-one and onto is
  • a\in \left (-\dfrac {1}{2}, \dfrac {1}{2}\right )
  • a\in (-1, 1)
  • a\in R-\left (-\dfrac {1}{2}, \dfrac {1}{2}\right )
  • a\in R-(-1, 1)
If y and z are the functions of x and if { y }^{ 2 }+{ z }^{ 2 }={ \lambda  }^{ 2 }, then \displaystyle y\frac { d }{ dx } \left( \frac { y }{ \lambda  }  \right) +\frac { d }{ dx } \left( \frac { { z }^{ 2 } }{ \lambda  }  \right) is equal to
  • \displaystyle \frac { z }{ \lambda  } \frac { dz }{ dx }
  • \displaystyle \frac { z }{ \lambda  } \frac { dx }{ dz }
  • \displaystyle \frac { \lambda  }{ z } \frac { dz }{ dx }
  • None of these
Let h(x) be differentiable for all x and let f(x)=(kx+e^x)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,\space y,\space z \in R
Then,
  • f'(x) < 0 for all x \in R
  • f'(x) = 0 for all x \in R
  • f'(x) > 0 for all x \in R
  • none of these
Let f(x)=x^{2}+xg^{'}(1)+g^{"}(2) and g(x)=f(1).x^{2}+xf^{'}(x)+f^"(x) then
  • f^{'}(1)+f^{'}(2)=0
  • g^{'}(2)=g^{'}(1)
  • g^{''}(2)+f^{''}(3)=6
  • none of these
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}
Equation x^n-1=0, n > 1, n\epsilon N, has roots 1, a_2, ....a_n.
The value of \displaystyle \sum_{r=2}^{n}\frac {1}{1-a_r}, is
  • \displaystyle \frac {n}{4}
  • \displaystyle \frac {n(n-1)}{2}
  • \displaystyle \frac {n-1}{2}
  • none of these
Suppose, A=\displaystyle \frac {dy}{dx} of x^2+y^2=4 at (\sqrt 2, \sqrt 2), B=\displaystyle \frac {dy}{dx} of sin y+sin x=sin x\cdot sin y at (\pi, \pi) and C=\displaystyle \frac {dy}{dx} of 2e^{xy}+e^xe^y-e^x=e^{xy+1} at (1, 1), then (A-B-C) has the value equal to .....
  • \displaystyle \frac { 1 }{ 2 }
  • \displaystyle \frac { 1 }{ 3 }
  • 1
  • 2
If f(x)=\sqrt {x+2\sqrt {2x-4}}+\sqrt {x-2\sqrt {2x-4}}, then the value of 10 f'(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 3^x-2^y=1, the value of \displaystyle\lim_{x\rightarrow \infty }\left ( \dfrac{dy}{dx} \right ) is 
  • equal to 1
  • equal to 0
  • equal to \log _2{3}
  • non existent
If \displaystyle x^2+y^2=R^2 (R>0) then \displaystyle k= \frac{{y}''}{\sqrt{(1+y'^{2})^3}} where k in terms of R alone is equal to
  • -\displaystyle \frac{1}{R^2}
  • -\displaystyle \frac{1}{R}
  • \displaystyle \frac{2}{R}
  • -\displaystyle \frac{2}{R^2}
If \displaystyle \frac { \cos ^{ 4 }{ \theta  }  }{ x } +\frac { \sin ^{ 4 }{ \theta  }  }{ y } =\frac { 1 }{ x+y } then \displaystyle \frac { dy }{ dx } =
  • xy
  • \tan ^{ 2 }{ \theta  }
  • 0
  • \left( { x }^{ 2 }+{ y }^{ 2 } \right) \sec ^{ 2 }{ \theta  }
Two functions f and g have first and second derivatives at x=0 and satisfy the relations, f(0)=\displaystyle \frac{2}{g(0)}, f'(0)=2g'(0)=4g(0), g''(0)=5f''(0)=6f(0)=3 then
  • If h(x)=\displaystyle \frac{f(x)}{g(x)} then h'(0)=\displaystyle \frac{15}{4}
  • If k(x)=f(x).g(x)\sin x then k'(0)=2
  • \displaystyle\lim _{x\rightarrow{0}}\displaystyle \frac{g'(x)}{f'(x)}=\displaystyle \frac{1}{2}
  • None of these
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers