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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 3 - MCQExams.com

If f(x)=|log10x| then at x=1
  • f is not continuous
  • f is continuous but not differentiable
  • f is differentiable
  • the derivative is 1
If x+y+yx=c, then d2xdy2 is equal to
  • 2c
  • 2c2
  • 2c2
  • none of these
If f(x)={ax2b,if|x|<11|x|if|x|1 is differential at x=1. Find the values of a and b
  • a=1/2; b=3/2
  • a=1/2; b=3/2
  • a=1/2; b=3/2
  • a=1/2; b=3/2
Find dydx if y=xx
  • xx(lnx+1)
  • xx(lnx1)
  • x.xx1
  • xx1(lnx+1)

 Find dydx at t=π4 if y=cos4t  & x=sin4t.


  • 1
  • 0
  • -1
  • 4

Differentiate xlnx with respect to lnx.


  • 2(xlnx)(lnx)
  • (lnxlnx)(lnx)
  • (xlnx)(lnx)/x
  • (lnxlnx)(lnx)/x
ddx(xlogx) is equal to
  • 2xlogx1logx
  • xlogx1
  • 23(logx)
  • xlogx1.logx
If y=31+3x41+4x51+5x71+7x81+8x, then y(0) is equal to
  • 1
  • 1
  • 2
  • Non existant
If f(x) and g(x) are both continuous at x=c then which of the following is/are always continuous at x=c?
  • f(x)+g(x)
  • (f(x)g(x))×f(x)
  • g(x)×f(x)
  • f(x)g(x)g(x)
Derivative of sin x w.r.t. cos x is
  • cos x
  • cot x
  • - cot x
  • tan x
If y=tan11sinx1+sinx, then the value of dydx at x=π6 is
  • 12
  • 12
  • 1
  • 1
If x=acos3θ and y=asin3θ, then 1+(dydx)2 is equal to
  • |secθ|
  • sec2θ
  • secθ
  • |tanθ|
If x=cos3θ and y=sin3θ, then 1+(dydx)2 is equal to:
  • tan2θ
  • cot2θ
  • sec2θ
  • cosec2θ
If y=1cosθ,x=1sinθ, then dydx at θ=π4 is
  • 1
  • 1
  • 12
  • 12
If y=(1+x)(1+x2)(1+x4)......(1+x2n) then the value of (dydx) at x=0 is
  • 0
  • 1
  • 1
  • 2
The differential coefficient of log10x with respect to logx10 is
  • 1
  • (log10x)2
  • (logx10)2
  • x2100
The function represented by  the following graph is.

572668_db4e79fb2abd478fa7332735dca6ad0f.png
  • Differentiable but not continuous x=1
  • Neither continuous nor Differentiable at x=1
  • Continuous but not Differentiable at x=1
  • Continuous but Differentiable at x=1
If x=acos3θ,y=asin3θ, then 1+(dydx)2 is _____
  • tanθ
  • tan2θ
  • sec2θ
  • 1
If xy=exy then dydx is equal to
  • logxlog(xy)
  • exxxy
  • logx(1+logx)2
  • 1y1xy
  • y(xy)x2
If x=ct and y=ct, find dydx at t=2
  • 14
  • 4
  • 14
  • 0
Given a function f(x)={1ifx0ax+bif0<x<11ifx1 where a,b are constants. The function is continuous everywhere.
What is the value of a?
  • 1
  • 0
  • 1
  • 2
Consider the parametric equation x=a(1t2)1+t2,y=2at1+t2.
What is dydx equal to?
  • yx
  • yx
  • xy
  • xy
Consider the function f(x)={αcosxπ2xifxπ23ifx=π2
which is continuous at x=π2, where α is a constant.
What is the value of α?
  • 6
  • 3
  • 2
  • 1
If y = cos t and x = sin t, then what is \dfrac{dy}{dx} equal to ?
  • xy
  • \dfrac{x}{y}
  • -\dfrac{y}{x}
  • -\dfrac{x}{y}
Consider the function
f(x)=\begin{cases}ax-2 & for & -2 < x < -1 \\ -1 & for & -1\le x\le 1 \\ a+2(x-1)^2 & for & 1 < x < 2\end{cases}
What is the value of a for which f(x) is continuous at x=-1 and x=1?
  • -1
  • 1
  • 0
  • 2
Consider the function f(x)=\left\{\begin{matrix} x^2-5, & x\leq 3\\ \sqrt{x+13}, & x > 3\end{matrix}\right..

Consider the following statements.
1. The function is discontinuous at x=3.
2. The function is not differentiable at x=0.
Which of the statements is/ are correct?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
If y={\cot}^{-1}\begin{bmatrix}\dfrac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\end{bmatrix}, where 0 < x < \dfrac{\pi}{2}, then \dfrac{dy}{dx} is equal to
  • -\dfrac{1}{2}
  • 2
  • \sin x + \cos x
  • \sin x - \cos x
If x^ay^b=(x-y)^{a+b}, then the value of \dfrac{dy}{dx}-\dfrac{y}{x} is equal to
  • \dfrac{a}{b}
  • \dfrac{b}{a}
  • 1
  • 0
Consider the following in respect of the function f(x) = | x- 3 | :
f(x) is continuous at x = 3
f(x) is differentiable at x = 0.
Which of the above statements is/are correct ?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
If f(x)=\sqrt{25-x^2}, then what is \displaystyle \lim_{ x\rightarrow 1 } \dfrac{f(x)-f(1)}{x-1} equal to?
  • \dfrac{1}{5}
  • \dfrac{1}{24}
  • \sqrt{24}
  • -\dfrac{1}{\sqrt{24}}
0:0:2


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