IAT-1(MATHEMATICS-I)(8.1.2021)(PART-A)

A curve in the plane is the graph of the function iff-------

• No horizontal line intersects the curve more than one times

• No vertical line intersects the curve more than one times

• At least a horizontal line intersects the curve more than one times

• At least a vertical line intersects the curve more than one times

Whether the function 

 $f(x)=2x-x^2$  is

• even

• odd

• neither even nor odd

• constant

A function f(x) is an increasing function on an interval I, if

• $f(x_1)<f(x_2)\ whenever\ x_1<x_2\ on\ an\ interval\ I$

• $f(x_1)<f(x_2)wheneverx_1>x_2on\ an\ interval\ I$

• $f(x_1)>f(x_2)\ whenever\ x_1<x_2\ on\ an\ interval\ I$

• $f(x_1)>f(x_2)\ whenever\ x_1>x_2\ on\ an\ interval\ I$

Determine whether the function shown in the graph is ………….

• even

• Odd

• neither even nor odd

• constant

The vertical line x=a is called vertical asymptote of the curve y=f(x), if

• $\lim_{x\rightarrow a}f\left(x\right)=\infty$

• $\lim_{x\rightarrow a^-}f\left(x\right)=-\infty$

• both (a) & (b)

• neither (a) nor (b)

 $If\ f(x)\ is\ continuous\ at\ ‘a’\ and\ g(x)\ is\ continuous\ at\ ‘g(a)’,\ then$  

•  $(g°f)(x)\ is\ continuous\ at\ ‘a’$  

•  $(f°g)(x)\ is\ continuous\ at\ ‘a’$  

• Either (a) or (b)

• None of these

Use the squeeze theorem, find the value of 

 $\lim_{x\rightarrow0}x^2\sin(1/x)$  

• -1

• 1

• 0

• 2

For what value of the constant ‘c’ is the function ‘f’ continuous on 

 $\left(-\infty,\infty\right)$  ,  $f\left(x\right)=cx^2+2x;x<2\ \ and\ f\left(x\right)=x^3-cx;x≥2$  

• 2/5

• 2/3

• 3/2

• 1/2

    The value of  $\lim_{x\rightarrow0}\left[x\right]\cos x\ ,\ \left[x\right]$ denotes the greatest integer function------------

• Lies between 0 and 1

• Lies between -1 and 0

• Lies between 0 and 2

• Lies between -2 and 0

  EVALUATE  $\lim_{x\rightarrow\pi}\frac{\sin x}{2+\cos x}$  

• 1/2

• -1

• 0

• 1