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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 4951. |
Range of \[f(x)=\ [x]\ -x\] is |
| A. | [0, 1] |
| B. | (?1, 0] |
| C. | R |
| D. | (?1, 1) |
| Answer» C. R | |
| 4952. |
If \[f(x)=a\cos (bx+c)+d\], then range of \[f(x)\] is [UPSEAT 2001] |
| A. | \[[d+a,\ d+2a]\] |
| B. | \[[a-d,\ a+d]\] |
| C. | \[[d+a,\ a-d]\] |
| D. | \[[d-a,\ d+a]\] |
| Answer» E. | |
| 4953. |
If \[f(x)=\log \left[ \frac{1+x}{1-x} \right]\], then \[f\left[ \frac{2x}{1+{{x}^{2}}} \right]\] is equal to [MP PET 1999; RPET 1999; UPSEAT 2003] |
| A. | \[{{[f(x)]}^{2}}\] |
| B. | \[{{[f(x)]}^{3}}\] |
| C. | \[2f(x)\] |
| D. | \[3f(x)\] |
| Answer» D. \[3f(x)\] | |
| 4954. |
The range of \[f(x)=\sec \left( \frac{\pi }{4}{{\cos }^{2}}x \right)\,,\ -\infty |
| A. | \[[1,\ \sqrt{2}]\] |
| B. | \[[1,\ \infty )\] |
| C. | \[[-\sqrt{2},\ -1]\cup [1,\ \sqrt{2}]\] |
| D. | \[(-\infty ,\ -1]\cup [1,\ \infty )\] |
| Answer» B. \[[1,\ \infty )\] | |
| 4955. |
The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(x-3)}{\sqrt{9-{{x}^{2}}}}\] is [AIEEE 2004] |
| A. | [1, 2) |
| B. | [2, 3) |
| C. | [1, 2] |
| D. | [2, 3] |
| Answer» C. [1, 2] | |
| 4956. |
The domain of the function \[f(x)=\exp (\sqrt{5x-3-2{{x}^{2}}})\] is [MP PET 2004] |
| A. | \[\left[ 1,\ -\frac{3}{2} \right]\] |
| B. | \[\left[ \frac{3}{2},\ \infty \right]\] |
| C. | \[[-\infty ,\ 1]\] |
| D. | \[\left[ 1,\ \frac{3}{2} \right]\] |
| Answer» E. | |
| 4957. |
The natural domain of the real valued function defined by \[f(x)=\sqrt{{{x}^{2}}-1}+\sqrt{{{x}^{2}}+1}\] is [SCRA 1996] |
| A. | \[1<x<\infty \] |
| B. | \[-\infty <x<\infty \] |
| C. | \[-\infty <x<-1\] |
| D. | \[(-\infty ,\ \infty )-(-1,\ 1)\] |
| Answer» E. | |
| 4958. |
Domain of \[f(x)={{({{x}^{2}}-1)}^{-1/2}}\] is [Roorkee 1987] |
| A. | \[(-\infty ,\ -1)\cup (1,\ \infty )\] |
| B. | \[(-\infty ,\ -1]\cup (1,\ \infty )\] |
| C. | \[(-\infty ,\ -1]\cup [1,\ \infty )\] |
| D. | None of these |
| Answer» B. \[(-\infty ,\ -1]\cup (1,\ \infty )\] | |
| 4959. |
Domain of the function \[f(x)=\frac{{{x}^{2}}-3x+2}{{{x}^{2}}+x-6}\] is |
| A. | \[\{x:x\in R,\ \ x\ne 3\}\] |
| B. | \[\{x:x\in R,\ \ x\ne 2\}\] |
| C. | \[\{x:x\in R\}\] |
| D. | \[\{x:x\in R,\ \ x\ne 2,\ x\ne -3\}\] |
| Answer» E. | |
| 4960. |
Domain of the function \[f(x)={{\sin }^{-1}}(1+3x+2{{x}^{2}})\] is [Roorkee 2000] |
| A. | \[(-\infty ,\ \infty )\] |
| B. | \[(-1,\ 1)\] |
| C. | \[\left[ -\frac{3}{2},\ 0 \right]\] |
| D. | \[\left( -\infty ,\ \frac{-1}{2} \right)\cup (2,\ \infty )\] |
| Answer» D. \[\left( -\infty ,\ \frac{-1}{2} \right)\cup (2,\ \infty )\] | |
| 4961. |
The largest possible set of real numbers which can be the domain of \[f(x)=\sqrt{1-\frac{1}{x}}\] is [AMU 2000] |
| A. | \[(0,\ 1)\cup (0,\ \infty )\] |
| B. | \[(-1,\ 0)\cup (1,\ \infty )\] |
| C. | \[(-\infty ,\ -1)\cup (0,\ \infty )\] |
| D. | \[(-\infty ,\ 0)\cup (1,\ \infty )\] |
| Answer» E. | |
| 4962. |
The domain of the function \[\sqrt{\log ({{x}^{2}}-6x+6)}\] is [Roorkee 1999; MP PET 2002] |
| A. | \[(-\infty ,\ \infty )\] |
| B. | \[(-\infty ,\ 3-\sqrt{3})\cup (3+\sqrt{3},\ \infty )\] |
| C. | \[(-\infty ,\ 1]\cup [5,\ \infty )\] |
| D. | \[[0,\ \infty )\] |
| Answer» D. \[[0,\ \infty )\] | |
| 4963. |
The equivalent function of \[\log {{x}^{2}}\] is [MP PET 1997] |
| A. | \[2\log x\] |
| B. | \[2\log |x|\] |
| C. | \[|\log {{x}^{2}}|\] |
| D. | \[{{(\log x)}^{2}}\] |
| Answer» C. \[|\log {{x}^{2}}|\] | |
| 4964. |
The domain of the function \[f(x)={{\sin }^{-1}}\{{{(1+{{e}^{x}})}^{-1}}\}\] is [AMU 1999] |
| A. | \[\left( \frac{1}{4},\ \frac{1}{3} \right)\] |
| B. | [?1, 0] |
| C. | [0, 1] |
| D. | [?1, 1] |
| Answer» B. [?1, 0] | |
| 4965. |
The domain of the function \[f(x)=\sqrt{x-{{x}^{2}}}+\sqrt{4+x}+\sqrt{4-x}\] is [AMU 1999] |
| A. | \[[-4,\ \infty )\] |
| B. | [?4, 4] |
| C. | [0, 4] |
| D. | [0, 1] |
| Answer» E. | |
| 4966. |
Domain of the function \[\frac{\sqrt{1+x}-\sqrt{1-x}}{x}\] is |
| A. | (?1, 1) |
| B. | (?1, 1)?{0} |
| C. | [?1, 1] |
| D. | [?1, 1]?{0} |
| Answer» E. | |
| 4967. |
Domain of the function \[\sqrt{2-x}-\frac{1}{\sqrt{9-{{x}^{2}}}}\] is |
| A. | (?3, 1) |
| B. | [?3, 1] |
| C. | (?3, 2] |
| D. | [?3, 1) |
| Answer» D. [?3, 1) | |
| 4968. |
Domain of the function \[\sqrt{\log \left\{ (5x-{{x}^{2}})/6 \right\}}\] is |
| A. | (2, 3) |
| B. | [2, 3] |
| C. | [1, 2] |
| D. | [1, 3] |
| Answer» C. [1, 2] | |
| 4969. |
Domain of the function \[f(x)=\frac{x-3}{(x-1)\sqrt{{{x}^{2}}-4}}\] is [BIT Ranchi 1991] |
| A. | (1, 2) |
| B. | \[(-\infty ,\ -2)\cup (2,\ \infty )\] |
| C. | \[(-\infty ,\ -2)\cup (1,\ \infty )\] |
| D. | \[(-\infty ,\ \infty )-\{1,\ \pm 2\}\] |
| Answer» C. \[(-\infty ,\ -2)\cup (1,\ \infty )\] | |
| 4970. |
Domain of the function \[f(x)=\sqrt{2-2x-{{x}^{2}}}\] is [BIT Ranchi 1992] |
| A. | \[-\sqrt{3}\le x\le \sqrt{3}\] |
| B. | \[-1-\sqrt{3}\le x\le -1+\sqrt{3}\] |
| C. | \[-2\le x\le 2\] |
| D. | \[-2+\sqrt{3}\le x\le -2-\sqrt{3}\] |
| Answer» C. \[-2\le x\le 2\] | |
| 4971. |
If ?n? is an integer, the domain of the function \[\sqrt{\sin 2x}\] is [MP PET 2003] |
| A. | \[\left[ n\pi -\frac{\pi }{2},\ n\pi \right]\] |
| B. | \[\left[ n\pi ,\ n\pi +\frac{\pi }{2} \right]\] |
| C. | \[[(2n-1)\pi ,\ 2n\pi ]\] |
| D. | \[[2n\pi ,\ (2n+1)\pi ]\] |
| Answer» C. \[[(2n-1)\pi ,\ 2n\pi ]\] | |
| 4972. |
If \[f(x)=\cos (\log x)\], then \[f({{x}^{2}})f({{y}^{2}})-\frac{1}{2}\left[ f\,\left( \frac{{{x}^{2}}}{2} \right)+f\left( \frac{{{x}^{2}}}{{{y}^{2}}} \right) \right]\] has the value [MNR 1992] |
| A. | ?2 |
| B. | ?1 |
| C. | ½ |
| D. | None of these |
| Answer» E. | |
| 4973. |
The domain of the function \[f(x)={{\log }_{3+x}}({{x}^{2}}-1)\] is [Orissa JEE 2003] |
| A. | \[(-3,\ -1)\cup (1,\ \infty )\] |
| B. | \[[-3,\ -1)\cup [1,\ \infty )\] |
| C. | \[(-3,\ -2)\cup (-2,\ -1)\cup (1,\ \infty )\] |
| D. | \[[-3,\ -2)\cup (-2,\ -1)\cup [1,\ \infty )\] |
| Answer» D. \[[-3,\ -2)\cup (-2,\ -1)\cup [1,\ \infty )\] | |
| 4974. |
. Domain of the function \[f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}\] is [UPSEAT 2001] |
| A. | \[-\infty <x<\infty \] |
| B. | \[1\le x\le 4\] |
| C. | \[4\le x\le 16\] |
| D. | \[-1\le x\le 1\] |
| Answer» C. \[4\le x\le 16\] | |
| 4975. |
The domain of the function \[f(x)=\log (\sqrt{x-4}+\sqrt{6-x})\] is [RPET 2001] |
| A. | \[[4,\infty )\] |
| B. | \[(-\infty ,\ 6]\] |
| C. | \[[4,\ 6]\] |
| D. | None of these |
| Answer» D. None of these | |
| 4976. |
The domain of the function \[f(x)=\sqrt{\log \frac{1}{|\sin x|}}\] is [RPET 2001] |
| A. | \[R-\{2n\pi ,\ n\in I\}\] |
| B. | \[R-\{n\pi ,\ n\in I\}\] |
| C. | \[R-\{-\pi ,\ \pi \}\] |
| D. | \[(-\infty ,\ \infty )\] |
| Answer» C. \[R-\{-\pi ,\ \pi \}\] | |
| 4977. |
If the domain of function \[f(x)={{x}^{2}}-6x+7\] is \[(-\infty ,\ \infty )\], then the range of function is [MP PET 1996] |
| A. | \[(-\infty ,\ \infty )\] |
| B. | \[[-2,\ \infty )\] |
| C. | \[(-2,\ 3)\] |
| D. | \[(-\infty ,\ -2)\] |
| Answer» C. \[(-2,\ 3)\] | |
| 4978. |
The domain of \[f(x)=\frac{{{\log }_{2}}(x+3)}{{{x}^{2}}+3x+2}\] is [IIT Screening 2001; UPSEAT 2001] |
| A. | \[R-\{-1,\ -2\}\] |
| B. | \[(-2,\ +\infty )\] |
| C. | \[R-\{-1,\ -2,\ -3\}\] |
| D. | \[(-3,\ +\infty )-\{-1,\ -2\}\] |
| Answer» E. | |
| 4979. |
The domain of the function \[f(x)={{\sin }^{-1}}[{{\log }_{2}}(x/2)]\] is [RPET 2002] |
| A. | [1, 4] |
| B. | [?4, 1] |
| C. | [?1, 4] |
| D. | None of these |
| Answer» B. [?4, 1] | |
| 4980. |
Domain of \[f(x)=\log |\log x|\] is [DCE 2002] |
| A. | \[(0,\ \infty )\] |
| B. | \[(1,\ \infty )\] |
| C. | \[(0,\ 1)\cup (1,\ \infty )\] |
| D. | \[(-\infty ,\ 1)\] |
| Answer» D. \[(-\infty ,\ 1)\] | |
| 4981. |
If \[f(x)=\frac{x}{x-1}\], then \[\frac{f(a)}{f(a+1)}=\] [MP PET 1996] |
| A. | \[f(-a)\] |
| B. | \[f\left( \frac{1}{a} \right)\] |
| C. | \[f({{a}^{2}})\] |
| D. | \[f\left( \frac{-a}{a-1} \right)\] |
| Answer» D. \[f\left( \frac{-a}{a-1} \right)\] | |
| 4982. |
Domain of the function \[\log |{{x}^{2}}-9|\] is |
| A. | R |
| B. | \[R-[-3,\ 3]\] |
| C. | \[R-\{-3,\ 3\}\] |
| D. | None of these |
| Answer» D. None of these | |
| 4983. |
The domain of \[{{\sin }^{-1}}\left[ {{\log }_{3}}\left( \frac{x}{3} \right) \right]\] is [AIEEE 2002] |
| A. | [1, 9] |
| B. | [?1, 9] |
| C. | [?9, 1] |
| D. | [?9, ?1] |
| Answer» B. [?1, 9] | |
| 4984. |
The domain of the function \[f(x)=\frac{{{\sin }^{-1}}(3-x)}{\ln (|x|\ -2)}\] is [Orissa JEE 2002] |
| A. | [2, 4] |
| B. | (2, 3) È (3, 4] |
| C. | [2,\[\infty \]) |
| D. | \[(-\infty ,\ -3)\cup [2,\ \infty )\] |
| Answer» C. [2,\[\infty \]) | |
| 4985. |
Domain of function \[f(x)={{\sin }^{-1}}5x\] is |
| A. | \[\left( -\frac{1}{5},\ \frac{1}{5} \right)\] |
| B. | \[\left[ -\frac{1}{5},\ \frac{1}{5} \right]\] |
| C. | R |
| D. | \[\left( 0,\ \frac{1}{5} \right)\] |
| Answer» C. R | |
| 4986. |
Domain and range of \[f(x)=\frac{|x-3|}{x-3}\] are respectively |
| A. | \[R,\ [-1,\ 1]\] |
| B. | \[R-\{3\},\ \left\{ 1,\ -1 \right\}\] |
| C. | \[{{R}^{+}},\ R\] |
| D. | None of these |
| Answer» C. \[{{R}^{+}},\ R\] | |
| 4987. |
If \[f(x)=ax+b\] and \[g(x)=cx+d\], then \[f(g(x))=g(f(x))\] is equivalent to [UPSEAT 2001] |
| A. | \[f(a)=g(c)\] |
| B. | \[f(b)=g(b)\] |
| C. | \[f(d)=g(b)\] |
| D. | \[f(c)=g(a)\] |
| Answer» D. \[f(c)=g(a)\] | |
| 4988. |
If \[f(x)\] is periodic function with period T then the function \[f(ax+b)\] where \[a>0\], is periodic with period [AMU 2000] |
| A. | \[T/b\] |
| B. | aT |
| C. | bT |
| D. | \[T/a\] |
| Answer» E. | |
| 4989. |
The period of \[f(x)=x-[x]\], if it is periodic, is [AMU 2000] |
| A. | \[f(x)\] is not periodic |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 4990. |
If \[(x,\,y)\in R\] and \[x,\ y\ne 0\]; \[f(x,\ y)\to \frac{x}{y}\], then this function is a/an [Orissa JEE 2004] |
| A. | Surjection |
| B. | Bijection |
| C. | One-one |
| D. | None of these |
| Answer» B. Bijection | |
| 4991. |
Given the function \[f(x)=\frac{{{a}^{x}}+{{a}^{-x}}}{2},\ (a>2)\]. Then \[f(x+y)+f(x-y)=\] |
| A. | \[2f(x).f(y)\] |
| B. | \[f(x).f(y)\] |
| C. | \[\frac{f(x)}{f(y)}\] |
| D. | None of these |
| Answer» B. \[f(x).f(y)\] | |
| 4992. |
\[f(x)=x+\sqrt{{{x}^{2}}}\] is a function from R\[\to \]R , then \[f(x)\] is [Orissa JEE 2004] |
| A. | Injective |
| B. | Surjective |
| C. | Bijective |
| D. | None of these |
| Answer» E. | |
| 4993. |
If R denotes the set of all real numbers then the function \[f:R\to R\] defined \[f(x)=\ [x]\] [Karnataka CET 2004] |
| A. | One-one only |
| B. | Onto only |
| C. | Both one-one and onto |
| D. | Neither one-one nor onto |
| Answer» E. | |
| 4994. |
If \[f:[0,\ \infty )\to [0,\ \infty )\] and \[f(x)=\frac{x}{1+x},\]then f is [IIT Screening 2003] |
| A. | One-one and onto |
| B. | One-one but not onto |
| C. | Onto but not one-one |
| D. | Neither one-one nor onto |
| Answer» C. Onto but not one-one | |
| 4995. |
A function f from the set of natural numbers to integers defined by \[f(n)=\left\{ \begin{align} & \frac{n-1}{2},\ \text{when}\ n\ \text{is}\ \text{odd} \\ & -\frac{n}{2},\ \text{when }n\text{ is even} \\ \end{align} \right.\], is [AIEEE 2003] |
| A. | One-one but not onto |
| B. | Onto but not one-one |
| C. | One-one and onto both |
| D. | Neither one-one nor onto |
| Answer» D. Neither one-one nor onto | |
| 4996. |
Let the function \[f:R\to R\] be defined by \[f(x)=2x+\sin x,\ x\in R\]. Then f is [IIT Screening 2002] |
| A. | One-to-one and onto |
| B. | One-to-one but not onto |
| C. | Onto but not one-to-one |
| D. | Neither one-to-one nor onto |
| Answer» B. One-to-one but not onto | |
| 4997. |
Let \[f(x)=\frac{{{x}^{2}}-4}{{{x}^{2}}+4}\] for \[|x|\ >2\], then the function \[f:(-\infty ,\ -2]\cup [2,\ \infty )\to (-1,\ 1)\] is [Orissa JEE 2002] |
| A. | One-one into |
| B. | One-one onto |
| C. | Many one into |
| D. | Many one onto |
| Answer» D. Many one onto | |
| 4998. |
Which one of the following is a objective function on the set of real numbers [Kerala (Engg.) 2002] |
| A. | \[2x-5\] |
| B. | \[|x|\] |
| C. | \[{{x}^{2}}\] |
| D. | \[{{x}^{2}}+1\] |
| Answer» B. \[|x|\] | |
| 4999. |
The function \[f:R\to R\] defined by \[f(x)={{e}^{x}}\] is [Karnataka CET 2002; UPSEAT 2002] |
| A. | Onto |
| B. | Many-one |
| C. | One-one and into |
| D. | Many one and onto |
| Answer» D. Many one and onto | |
| 5000. |
Let \[f:R\to R\] be a function defined by \[f(x)=\frac{x-m}{x-n}\], where \[m\ne n\]. Then [UPSEAT 2001] |
| A. | f is one-one onto |
| B. | f is one-one into |
| C. | f is many one onto |
| D. | f is many one into |
| Answer» C. f is many one onto | |