Applicartions Of Derivatives Test

Applicartions Of Derivatives

This is Applicartions of Derivatives Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The instantaneous rate of change at t = 1 for the function f (t) = \(t\;{e^{ - t}} + 9\) is
  • A
    2
  • B
    0
    Correct
  • C
    9
  • D
    – 1
2
If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph
  • A
    meets the line y = 0 at least once
    Correct
  • B
    meets the line y = 0 at least twice
  • C
    meets the line y = 0 at least thrice
  • D
    does not meet the line y = 0.
3
Let f be a real valued function defined on (0, 1) \( \cup \)(2, 4) such that f ‘ (x) = 0 for every x, then
  • A
    f is a constant function if f \(\left( {\frac{1}{2}} \right)\) = 0.
  • B
    f is constant function if f \(\left( {\frac{1}{2}} \right)\)= f (3)
    Correct
  • C
    f is a constant function
  • D
    f is not a constant function
4
In case of strict decreasing functions, slope of tangent and hence derivative is
  • A
    Zero
  • B
    either negative or zero.
    Correct
  • C
    Positive
  • D
    Negative
5
The function f (x) = 2 – 3 x is
  • A
    decreasing
    Correct
  • B
    increasing
  • C
    neither decreasing nor increasing
  • D
    none of these
6
The function f (x) = \({x^2}\) – 2 x is increasing in the interval
  • A
    \(x \geqslant - 1\)
  • B
    \(x \geqslant 1\)
    Correct
  • C
    \(x \ne 1\)
  • D
    \(x \ne - 1\)
7
The function f (x) = \({x^2}\), for all real x, is
  • A
    none of these
  • B
    Increasing
  • C
    neither decreasing nor increasing
    Correct
  • D
    Decreasing
8
The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all \(x \in {\mathbf{R}}\)if
  • A
    \(m \geqslant 0\)
  • B
    m< 0
    Correct
  • C
    m = 0
  • D
    m> 0
9
The function f(x) = \({\tan ^{ - 1}}x\) is
  • A
    strict decreasing
  • B
    strict increasing
    Correct
  • C
    differentiable nowhere.
  • D
    neither increasing nor decreasing
10
Let f (x) = \({x^3} - 6{x^2} + 9x + 8,\) then f (x) is decreasing in
  • A
    \(\left( { - \;\infty ,1} \right) \cup (3,\infty )\)
  • B
    \([3,\infty ]\)
  • C
    \(( - \infty ,1)\)
  • D
    [1, 3]
    Correct
11
The function f (x) = \({x^2}{e^{ - x}}\) strictly increases on
  • A
    \([{\text{ }}--\infty ,{\text{ }}0]\) \( \cup \)\([2,\infty )\)
  • B
    [0, 2]
    Correct
  • C
    none of these.
  • D
    \((0,\infty )\)
12
At (0, 0) the curve \({y^2} = {x^3} + {x^2}\)
  • A
    bisects the angle between the axes
    Correct
  • B
    makes an angle of \({60^o}\) with OX
  • C
    touches X – axis
  • D
    none of these.
13
Let f (x) = x – cos x, \(x \in {\mathbf{R,}}\) then f is
  • A
    an odd function
  • B
    none of these
  • C
    an increasing function
    Correct
  • D
    a decreasing function
14
In \(\left( {0,\frac{\pi }{2}} \right)\), the function f (x) = \(\frac{x}{{\sin x}}\)is
  • A
    a constant function
  • B
    none of these
  • C
    an increasing function
    Correct
  • D
    a decreasing function
15
Let f (x) = tan x – 4x, then in the interval \(\left[ { - \frac{\pi }{3},\frac{\pi }{3}} \right],f(x)\;\)is
  • A
    none of these
  • B
    a constant function
  • C
    a decreasing function
    Correct
  • D
    an increasing function