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Functions and Graphs - Class XII

Covers function properties, continuity, limits, calculus, and graphing concepts for Class XII mathematics

12 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

If f is even function and g is an odd function, then $f _og$ is ............function.

  1. Even
  2. Odd
  3. Neither even nor odd
  4. Either even
Question 2 Multiple Choice (Single Answer)
State the whether given statement is true or false
If $f\left( x \right) = \dfrac{{x + 1}}{{x - 1}},$ then $f\left( x \right) + f\left( {\dfrac{1}{x}} \right) = 0$
  1. True
  2. False
Question 3 Multiple Choice (Single Answer)

The identity function on real numbers given by $f(x)=x$ is continuous at every real numbers.

  1. True
  2. False
Question 4 Multiple Choice (Single Answer)

The minimum value of $f\left( x \right) ={ x }^{ 2 }+2x+3 ,x\in R$ is equal to 

  1. $2$
  2. $3$
  3. $4$
  4. $1$
Question 5 Multiple Choice (Single Answer)
 Years Production of Car P  Production of Car Q Production of Car R 
2001  76  59  28
2002  82  62  36
2003  65  47 42 
2004  70  54  31
2005  85  57  49
2006  80  68  38
Direction (1-2) : Study the following table which shows the production of three different types of cars over the years.
The difference between the total production of three cars in the year $2004$ and $2006$ is _____.
  1. $11$
  2. $43$
  3. $31$
  4. $28$
Question 6 Multiple Choice (Single Answer)
 Years Production of Car P  Production of Car Q Production of Car R 
2001  76  59  28
2002  82  62  36
2003  65  47 42 
2004  70  54  31
2005  85  57  49
2006  80  68  38
Direction (1-2) : Study the following table which shows the production of three different types of cars over the years.
The average production of which of the following types of cars was maximum?
  1. $Q$
  2. $P$
  3. $R$
  4. All are equal
Question 7 Multiple Choice (Single Answer)

If $f:,\left( {3,6} \right) \to \left( {1,3} \right)$ is a function defined by $f\left( x \right) = x - \left[ {\frac{x}{3}} \right],,then,{f^{ - 1}}\left( x \right) = $

  1. $x-1$
  2. $x+1$
  3. $x$
  4. none of these
Question 8 Multiple Choice (Single Answer)

The tangents to the graph of the function  $y=f(x)$ at the point with abscissa $x=1$ forms an angle of $\pi/6$ and the point $x=2$ an angle of $\pi/3$ and at the point $x=3$ an angle of $\pi/4$. The value of 
$\displaystyle \int _{1}^{2}{f'(x)f''(x)dx}+\displaystyle \int _{2}^{3}{f''(x)dx}$

  1. $\dfrac{4\sqrt{3}-1}{3\sqrt{3}}$
  2. $\dfrac{3\sqrt{3}-1}{2}$
  3. $\dfrac{4-\sqrt{3}}{3}$
  4. $None\ of\ these$
Question 9 Multiple Choice (Single Answer)

The graph of the function $\cos x\cos x(x+2)-\cos^{2}(x+1)$ is  

  1. A straight line through $(0, -\sin^{2}1)$ with slope $2$.
  2. A straight line through $(0, 0)$
  3. A parabola with vertex $(1, -\sin^{2}1)$
  4. A straight line through $\left(\dfrac{\pi}{2},-\sin^{2}1\right)$ and parallel to the $x-axis$.
Question 10 Multiple Choice (Single Answer)

If $f(x)=\left | \sin x \right |$, then domain of $f$ for the existence of inverse is  

  1. $[0,\pi ]$
  2. $\left [ 0,\dfrac{\pi }{2} \right ]$
  3. $\left [ -\dfrac{\pi }{4},\dfrac{\pi }{4} \right ]$
  4. $\left [ -\dfrac{\pi }{2},\dfrac{\pi }{2} \right ]$
Question 11 Multiple Choice (Single Answer)

The solution set of the equation $(x+1)^2+[x-1]^2=(x-1)^2+[x+1]^2$ where $[x]$ and $(x)$ are the greatest integer and nearest integer to $x$, is 

  1. $ x\in R$
  2. $x\in N$
  3. $x\in I$
  4. $x\in Q$
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