MCQOPTIONS
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MCQOPTIONS
This section includes 657 Mcqs, each offering curated multiple-choice questions to sharpen your Testing Subject knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The function \[{{x}^{x}}\] is increasing, when [MP PET 2003] |
| A. | \[x>\frac{1}{e}\] |
| B. | \[x<\frac{1}{e}\] |
| C. | \[x<0\] |
| D. | For all real x |
| Answer» B. \[x<\frac{1}{e}\] | |
| 2. |
The function \[f(x)={{x}^{1/x}}\] is [AMU 2002] |
| A. | Increasing in \[(1,\,\,\infty )\] |
| B. | Decreasing in \[(1,\,\,\infty )\] |
| C. | Increasing in \[(1,\,e),\] decreasing in \[(e,\infty )\] |
| D. | Decreasing in \[(1,\,e),\] increasing in \[(e,\infty )\] |
| Answer» D. Decreasing in \[(1,\,e),\] increasing in \[(e,\infty )\] | |
| 3. |
The function \[f(x)=x\,+\,\cos x\] is [DCE 2002] |
| A. | Always increasing |
| B. | Always decreasing |
| C. | Increasing for certain range of x |
| D. | None of these |
| Answer» B. Always decreasing | |
| 4. |
If \[f(x)=\frac{1}{x+1}-\log \,(1+x),\,x>0,\]then \[f\]is [RPET 2002] |
| A. | An increasing function |
| B. | A decreasing function |
| C. | Both increasing and decreasing function |
| D. | None of these |
| Answer» C. Both increasing and decreasing function | |
| 5. |
If \[f(x)={{x}^{3}}-6{{x}^{2}}+9x+3\] be a decreasing function, then x lies in [RPET 2002] |
| A. | \[(-\infty ,-1)\cap (3,\,\infty )\] |
| B. | \[(1,\,\,3)\] |
| C. | \[(3,\,\,\infty )\] |
| D. | None of these |
| Answer» C. \[(3,\,\,\infty )\] | |
| 6. |
If \[f(x)=x{{e}^{x(1-x)}}\], then \[f(x)\] is [IIT Screening 2001] |
| A. | Increasing on \[\left[ -\frac{1}{2},\,1 \right]\] |
| B. | Decreasing on R |
| C. | Increasing on R |
| D. | Decreasing on \[\left[ -\frac{1}{2},1 \right]\] |
| Answer» B. Decreasing on R | |
| 7. |
The function \[f(x)=\frac{\log x}{x}\] is increasing in the interval [UPSEAT 2001] |
| A. | \[(1,\,2e)\] |
| B. | (0,e) |
| C. | (2, 2e) |
| D. | (1/e, 2e) |
| Answer» C. (2, 2e) | |
| 8. |
If \[f(x)=\sin x-\cos x,\] the function decreasing in \[0\le x\le 2\pi \] is [UPSEAT 2001] |
| A. | \[[5\pi /6,\,3\pi /4]\] |
| B. | \[[\pi /4,\,\pi /2]\] |
| C. | \[[3\pi /2,\,5\pi /2]\] |
| D. | None of these |
| Answer» E. | |
| 9. |
In the interval [0, 1], the function \[{{x}^{2}}-x+1\]is |
| A. | Increasing |
| B. | Decreasing |
| C. | Neither increasing nor decreasing |
| D. | None of these |
| Answer» D. None of these | |
| 10. |
Function \[f(x)=\frac{\lambda \sin x+6\cos x}{2\sin x+3\cos x}\] is monotonic increasing, if [MP PET 2001] |
| A. | \[\lambda >1\] |
| B. | \[\lambda <1\] |
| C. | \[\lambda <4\] |
| D. | \[\lambda >4\] |
| Answer» E. | |
| 11. |
On the interval (1,3), the function \[f(x)=3x+\frac{2}{x}\]is [AMU 1999] |
| A. | Strictly decreasing |
| B. | Strictly increasing |
| C. | Decreasing in (2, 3) only |
| D. | Neither increasing nor decreasing |
| Answer» C. Decreasing in (2, 3) only | |
| 12. |
The function which is neither decreasing nor increasing in \[\left( \frac{\pi }{2},\frac{3\pi }{2} \right)\] is [MP PET 2000] |
| A. | cosec x |
| B. | \[\tan x\] |
| C. | \[{{x}^{2}}\] |
| D. | \[|x-1|\] |
| Answer» B. \[\tan x\] | |
| 13. |
Consider the following statements S and R S : Both \[\sin x\] and cosx are decreasing functions in \[\left( \frac{\pi }{2},\pi \right)\] R : If a differentiable function decreases in (a, b) then its derivative also decreases in (a, b). Which of the following is true [IIT Screening 2000] |
| A. | Both S and R are wrong |
| B. | Both S and R are correct but R is not the correct explanation for S |
| C. | S is correct and R is the correct explanation for S |
| D. | S is correct and R is wrong |
| Answer» E. | |
| 14. |
The function \[f(x)=1-{{e}^{-{{x}^{2}}/2}}\] is [AMU 1999] |
| A. | Decreasing for all x |
| B. | Increasing for all x |
| C. | Decreasing for \[x<0\] and increasing for \[x>0\] |
| D. | Increasing for \[x<0\] and decreasing for \[x>0\] |
| Answer» D. Increasing for \[x<0\] and decreasing for \[x>0\] | |
| 15. |
The function \[\frac{a\sin x+b\cos x}{c\sin x+d\,\cos x}\] is decreasing, if [RPET 1999] |
| A. | \[ad-bc>0\] |
| B. | \[ad-bc<0\] |
| C. | \[ab-cd>0\] |
| D. | \[ab-cd<0\] |
| Answer» C. \[ab-cd>0\] | |
| 16. |
\[2{{x}^{3}}+18{{x}^{2}}-96x+45=0\]is an increasing function when [RPET 1997] |
| A. | \[x\le -8,\,x\ge 2\] |
| B. | \[x<-2,x\ge 8\] |
| C. | \[x\le -2,x\ge 8\] |
| D. | \[0\le x\le -2\] |
| Answer» B. \[x<-2,x\ge 8\] | |
| 17. |
Function \[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+29\] is monotonically decreasing, when [RPET 1996] |
| A. | \[x<2\] |
| B. | x > 2 |
| C. | x >1 |
| D. | 1< x < 2 |
| Answer» E. | |
| 18. |
If \[f(x)=\frac{x}{\sin x}\]and \[g(x)=\frac{x}{\tan x}\], where \[0 |
| A. | Both \[f(x)\] and \[g(x)\] are increasing functions |
| B. | Both \[f(x)\] and \[g(x)\] are decreasing functions |
| C. | \[f(x)\]is an increasing function |
| D. | \[g(x)\] is an increasing function |
| Answer» D. \[g(x)\] is an increasing function | |
| 19. |
If \[f(x)={{x}^{3}}-10{{x}^{2}}+200x-10\], then [Kurukshetra CEE 1998] |
| A. | \[f(x)\]is decreasing in \[]-\infty ,10]\] and increasing in \[[10,\,\infty [\] |
| B. | \[f(x)\]is increasing in \[]-\infty ,10]\] and decreasing in \[[10,\,\infty [\] |
| C. | \[f(x)\]is increasing throughout real line |
| D. | \[f(x)\]is decreasing throughout real line |
| Answer» D. \[f(x)\]is decreasing throughout real line | |
| 20. |
The function \[\frac{x-2}{x+1},(x\ne -1)\]is increasing on the interval |
| A. | \[(-\infty ,\,\,\,0]\] |
| B. | [0, \[\infty \]) |
| C. | R |
| D. | None of these |
| Answer» D. None of these | |
| 21. |
The function f defined by \[f(x)=(x+2){{e}^{-x}}\] is [IIT Screening 1994] |
| A. | Decreasing for all x |
| B. | Decreasing in \[(-\infty ,\,-1)\] and increasing in \[(-1,\infty )\] |
| C. | Increasing for all x |
| D. | Decreasing in \[(-1,\,\infty )\] and increasing in \[(-\infty ,\,-1)\] |
| Answer» E. | |
| 22. |
Which one is the correct statement about the function \[f(x)=\sin 2x\] |
| A. | \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{2} \right)\] and decreasing in \[\left( \frac{\pi }{2},\pi \right)\] |
| B. | \[f(x)\] is decreasing in \[\left( 0,\frac{\pi }{2} \right)\] and increasing in \[\left( \frac{\pi }{2},\pi \right)\] |
| C. | \[f(x)\] is increasing in \[\left( 0,\frac{\pi }{4} \right)\] and decreasing in \[\left( \frac{\pi }{4},\frac{\pi }{2} \right)\] |
| D. | The statements , and are all correct |
| Answer» D. The statements , and are all correct | |
| 23. |
The interval of the decreasing function \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\]is |
| A. | \[\left( \frac{1}{3},\,1 \right)\] |
| B. | \[\left( -\frac{1}{3},1 \right)\] |
| C. | \[\left( -\frac{1}{3},\,\frac{1}{3} \right)\] |
| D. | \[\left( -1,-\frac{1}{3} \right)\] |
| Answer» C. \[\left( -\frac{1}{3},\,\frac{1}{3} \right)\] | |
| 24. |
The function \[f(x)={{x}^{3}}-3{{x}^{2}}-24x+5\] is an increasing function in the interval given below [MP PET 1998] |
| A. | \[(-\infty ,\,-2)\cup (4,\infty )\] |
| B. | \[(-2,\infty )\] |
| C. | (?2, 4) |
| D. | \[(-\infty ,\,4)\] |
| Answer» B. \[(-2,\infty )\] | |
| 25. |
The least value of k for which the function \[{{x}^{2}}+kx+1\]is an increasing function in the interval \[1 |
| A. | ? 4 |
| B. | ? 3 |
| C. | ? 1 |
| D. | ? 2 |
| Answer» E. | |
| 26. |
For all real values of x, increasing function f(x) is [MP PET 1996] |
| A. | \[{{x}^{-1}}\] |
| B. | \[{{x}^{2}}\] |
| C. | \[{{x}^{3}}\] |
| D. | \[{{x}^{4}}\] |
| Answer» D. \[{{x}^{4}}\] | |
| 27. |
If \[f(x)=2x+{{\cot }^{-1}}x+\log (\sqrt{1+{{x}^{2}}}-x)\], then \[f(x)\] |
| A. | Increases in [0 ,\[\infty \]) |
| B. | Decreases in [0 ,\[\infty \]) |
| C. | Neither increases nor decreases in (0, \[\infty \]) |
| D. | Increases in (?\[\infty \],\[\infty \]) |
| Answer» B. Decreases in [0 ,\[\infty \]) | |
| 28. |
The interval in which the function \[{{x}^{3}}\]increases less rapidly than\[6{{x}^{2}}+15x+5\], is |
| A. | \[(-\infty ,\,-1)\] |
| B. | (?5 , 1) |
| C. | (?1 ,5) |
| D. | (5 , \[\infty \]) |
| Answer» D. (5 , \[\infty \]) | |
| 29. |
Which of the following is not a decreasing function on the interval \[\left( 0,\frac{\pi }{2} \right)\] |
| A. | \[\cos x\] |
| B. | \[\cos 2x\] |
| C. | \[\cos 3x\] |
| D. | \[\cot x\] |
| Answer» D. \[\cot x\] | |
| 30. |
The value of ?a? in order that \[f(x)=\sqrt{3}\] \[\sin x-\cos x-2ax+b\] decreases for all real values of x, is given by |
| A. | \[a<1\] |
| B. | \[a\ge 1\] |
| C. | \[a\ge \sqrt{2}\] |
| D. | \[a<\sqrt{2}\] |
| Answer» C. \[a\ge \sqrt{2}\] | |
| 31. |
If the function \[f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}\]is increasing for all values of x, then |
| A. | \[K<1\] |
| B. | \[K>1\] |
| C. | \[K<2\] |
| D. | \[K>2\] |
| Answer» E. | |
| 32. |
The function \[f(x)=\tan x-x\] [MNR 1995; Pb. CET 2000; Karnataka CET 2002] |
| A. | Always increases |
| B. | Always decreases |
| C. | Never decreases |
| D. | Sometimes increases and sometimes decreases |
| Answer» B. Always decreases | |
| 33. |
In which interval is the given function \[f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+1\] is monotonically decreasing [RPET 1995] |
| A. | [2, 3] |
| B. | (2, 3) |
| C. | \[(-\infty ,\,2)\] |
| D. | \[(3,\,\infty )\] |
| Answer» C. \[(-\infty ,\,2)\] | |
| 34. |
The function \[f(x)=\cos x-2px\] is monotonically decreasing for [RPET 1987; MP PET 2002] |
| A. | \[p<\frac{1}{2}\] |
| B. | \[p>\frac{1}{2}\] |
| C. | \[p<2\] |
| D. | \[p>2\] |
| Answer» C. \[p<2\] | |
| 35. |
If \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\]is monotonically increasing in each interval, then [RPET 1992; Kurukshetra CEE 2002] |
| A. | \[k<3\] |
| B. | \[k\le 3\] |
| C. | \[k>3\] |
| D. | None of these |
| Answer» D. None of these | |
| 36. |
The function \[y=2{{x}^{3}}-9{{x}^{2}}+12x-6\] is monotonic decreasing, when [MP PET 1994] |
| A. | \[1<x<2\] |
| B. | \[x>2\] |
| C. | \[x<1\] |
| D. | None of these |
| Answer» B. \[x>2\] | |
| 37. |
Let \[y={{x}^{2}}{{e}^{-x}}\], then the interval in which y increases with respect to x is [MNR 1994; Kurukshetra CEE 1998] |
| A. | \[(-\infty ,\infty )\] |
| B. | \[(-2,\,0)\] |
| C. | \[(2,\infty )\] |
| D. | \[(0,\,2)\] |
| Answer» E. | |
| 38. |
If x tends 0 to \[\pi \], then the given function \[f(x)=x\sin x+\cos x+{{\cos }^{2}}x\] is |
| A. | Increasing |
| B. | Decreasing |
| C. | Neither increasing nor decreasing |
| D. | None of these |
| Answer» C. Neither increasing nor decreasing | |
| 39. |
The function \[\frac{1}{1+{{x}^{2}}}\]is decreasing in the interval |
| A. | \[(-\infty ,\,-1]\] |
| B. | \[(-\infty ,\,0]\] |
| C. | \[[1,\infty )\] |
| D. | \[(0,\infty )\] |
| Answer» E. | |
| 40. |
If \[f(x)=\sin x-\frac{x}{2}\] is increasing function, then [MP PET 1987] |
| A. | \[0<x<\frac{\pi }{3}\] |
| B. | \[-\frac{\pi }{3}<x<0\] |
| C. | \[-\frac{\pi }{3}<x<\frac{\pi }{3}\] |
| D. | \[x=\frac{\pi }{2}\] |
| Answer» D. \[x=\frac{\pi }{2}\] | |
| 41. |
The interval for which the given function \[f(x)=2{{x}^{3}}-3{{x}^{2}}-36x+7\] is decreasing, is |
| A. | (? 2, 3) |
| B. | (2, 3) |
| C. | (2,? 3) |
| D. | None of these |
| Answer» B. (2, 3) | |
| 42. |
For the every value of x the function \[f(x)=\frac{1}{{{5}^{x}}}\]is |
| A. | Decreasing |
| B. | Increasing |
| C. | Neither increasing nor decreasing |
| D. | Increasing for x > 0 and decreasing for x < 0 |
| Answer» B. Increasing | |
| 43. |
If \[f'(x)\]is zero in the interval (a, b) then in this interval it is |
| A. | Increasing function |
| B. | Decreasing function |
| C. | Only for a > 0 and b>0 is increasing function |
| D. | None of these |
| Answer» E. | |
| 44. |
Function \[f(x)={{x}^{4}}-\frac{{{x}^{3}}}{3}\]is |
| A. | Increasing for \[x>\,\frac{1}{4}\]and decreasing for \[x<\frac{1}{4}\] |
| B. | Increasing for every value of x |
| C. | Decreasing for every value of x |
| D. | None of these |
| Answer» B. Increasing for every value of x | |
| 45. |
The function \[f(x)={{x}^{2}}\]is increasing in the interval |
| A. | \[(-1,\,1)\] |
| B. | \[(-\infty ,\,\infty )\] |
| C. | \[(0,\,\infty )\] |
| D. | \[(-\infty ,\,0)\] |
| Answer» D. \[(-\infty ,\,0)\] | |
| 46. |
\[f(x)={{x}^{3}}-27x+5\]is an increasing function, when [MP PET 1995] |
| A. | \[x<-3\] |
| B. | \[|x|\,>3\] |
| C. | \[x\le -3\] |
| D. | \[|x|\,<3\] |
| Answer» C. \[x\le -3\] | |
| 47. |
For which interval the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\] is decreasing [MP PET 1993] |
| A. | \[(-2,\,\infty )\] |
| B. | \[(-2,\,-1)\] |
| C. | \[(-\infty ,\,-1)\] |
| D. | \[(-\infty ,\,\,-2)\]and \[(-1,\,\infty )\] |
| Answer» E. | |
| 48. |
The function \[x+\frac{1}{x},(x\ne 0)\]is a non-increasing function in the interval |
| A. | [? 1, 1] |
| B. | [0, 1] |
| C. | [?1, 0] |
| D. | [?1,2] |
| Answer» B. [0, 1] | |
| 49. |
Eccentricity of the curve \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\] is [UPSEAT 2002] |
| A. | 2 |
| B. | \[\sqrt{2}\] |
| C. | 4 |
| D. | None of these |
| Answer» C. 4 | |
| 50. |
The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is [MP PET 2002] |
| A. | \[10\sqrt{2}\] |
| B. | 5 |
| C. | \[5\sqrt{2}\] |
| D. | 20 |
| Answer» E. | |