MCQOPTIONS
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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.
| 5001. |
Set A has 3 elements and set B has 4 elements. The number of injection that can be defined from A to B is [UPSEAT 2001] |
| A. | 144 |
| B. | 12 |
| C. | 24 |
| D. | 64 |
| Answer» D. 64 | |
| 5002. |
The value of b and c for which the identity \[f(x+1)-f(x)=8x+3\] is satisfied, where \[f(x)=b{{x}^{2}}+cx+d\], are [Roorkee 1992] |
| A. | \[b=2,\ c=1\] |
| B. | \[b=4,\ c=-1\] |
| C. | \[b=-1,\ c=4\] |
| D. | \[b=-1,\ c=1\] |
| Answer» C. \[b=-1,\ c=4\] | |
| 5003. |
Let \[f:N\to N\] defined by \[f(x)={{x}^{2}}+x+1\], \[x\in N\], then f is [AMU 2000] |
| A. | One-one onto |
| B. | Many one onto |
| C. | One-one but not onto |
| D. | None of these |
| Answer» B. Many one onto | |
| 5004. |
Which of the four statements given below is different from others [UPSEAT 2000] |
| A. | \[f:A\to B\] |
| B. | \[f:x\to f(x)\] |
| C. | f is a mapping of A into B |
| D. | f is a function of A into B |
| Answer» C. f is a mapping of A into B | |
| 5005. |
. If \[f:R\to R\], then \[f(x)=\ |x|\] is [RPET 2000] |
| A. | One-one but not onto |
| B. | Onto but not one-one |
| C. | One-one and onto |
| D. | None of these |
| Answer» E. | |
| 5006. |
Mapping \[f:R\to R\] which is defined as \[f(x)=\cos x,\ x\in R\] will be [UPSEAT 1999] |
| A. | Neither one-one nor onto |
| B. | One-one |
| C. | Onto |
| D. | One-one onto |
| Answer» B. One-one | |
| 5007. |
The function \[f:R\to R\] defined by \[f(x)=(x-1)\] \[(x-2)(x-3)\] is [Roorkee 1999] |
| A. | One-one but not onto |
| B. | Onto but not one-one |
| C. | Both one-one and onto |
| D. | Neither one-one nor onto |
| Answer» C. Both one-one and onto | |
| 5008. |
Function \[f:R\to R,\ f(x)={{x}^{2}}+x\] is [RPET 1999] |
| A. | One-one onto |
| B. | One-one into |
| C. | Many-one onto |
| D. | Many-one into |
| Answer» E. | |
| 5009. |
Let \[f(x)=\left\{ \begin{align} & \frac{1}{2},\ if\ 0\le x\le \frac{1}{2} \\ & \frac{1}{3},\ if\ \frac{1}{2} |
| A. | A rational function |
| B. | A trigonometric function |
| C. | A step function |
| D. | An exponential function |
| Answer» D. An exponential function | |
| 5010. |
The function which map [?1, 1] to [0, 2] are [Kurukshetra CEE 1998] |
| A. | One linear function |
| B. | Two linear function |
| C. | Circular function |
| D. | None of these |
| Answer» C. Circular function | |
| 5011. |
If \[f(x)=\sin \log x\], then the value of \[f(xy)+f\left( \frac{x}{y} \right)-2f(x).\cos \log y\] is equal to [Orissa JEE 2004] |
| A. | 1 |
| B. | 0 |
| C. | ?1 |
| D. | \[\sin \log x.\cos \log y\] |
| Answer» C. ?1 | |
| 5012. |
If for two functions g and f, gof is both injective and surjective, then which of the following is true [Kurukshetra CEE 1998] |
| A. | g and f should be injective and surjective |
| B. | g should be injective and surjective |
| C. | f should be injective and surjective |
| D. | None of them may be surjective and injective |
| Answer» B. g should be injective and surjective | |
| 5013. |
The function \[f:R\to R,\ f(x)={{x}^{2}},\forall x\in R\] is [MP PET 1997] |
| A. | Injection but not surjection |
| B. | Surjection but not injection |
| C. | Injection as well as surjection |
| D. | Neither injection nor surjection |
| Answer» E. | |
| 5014. |
Numerical value of the expression \[\left| \ \frac{3{{x}^{3}}+1}{2{{x}^{2}}+2}\ \right|\] for \[x=-3\] is [Orissa JEE 2004; UPSEAT 2004] |
| A. | 4 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» B. 2 | |
| 5015. |
Let x be a non-zero rational number and y be an irrational number. Then xy is [Orissa JEE 2004] |
| A. | Rational |
| B. | Irrational |
| C. | Non-zero |
| D. | None of these |
| Answer» C. Non-zero | |
| 5016. |
If \[f(x)=\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\], for every real numbers. then the minimum value of f [Pb. CET 2001] |
| A. | Does not exist because f is bounded |
| B. | Is not attained even through f is bounded |
| C. | Is equal to +1 |
| D. | Is equal to ?1 |
| Answer» E. | |
| 5017. |
If \[y=f(x)=\frac{ax+b}{cx-a}\], then x is equal to [AMU 2001] |
| A. | \[1/f(x)\] |
| B. | \[1/f(y)\] |
| C. | \[yf(x)\] |
| D. | \[f(y)\] |
| Answer» E. | |
| 5018. |
If \[f(x)=\frac{x}{x-1}=\frac{1}{y}\], then \[f(y)=\] [MP PET 1995, 97] |
| A. | x |
| B. | \[x+1\] |
| C. | \[x-1\] |
| D. | \[1-x\] |
| Answer» E. | |
| 5019. |
The graph of the function \[y=f(x)\] is symmetrical about the line \[x=2\], then [AIEEE 2004] |
| A. | \[f(x)=-f(-x)\] |
| B. | \[f(2+x)=f(2-x)\] |
| C. | \[f(x)=f(-x)\] |
| D. | \[f(x+2)=f(x-2)\] |
| Answer» C. \[f(x)=f(-x)\] | |
| 5020. |
If \[f(x)=2\sin x\], \[g(x)={{\cos }^{2}}x\], then \[(f+g)\left( \frac{\pi }{3} \right)=\] |
| A. | 1 |
| B. | \[\frac{2\sqrt{3}+1}{4}\] |
| C. | \[\sqrt{3}+\frac{1}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5021. |
If \[f(x)=\frac{1-x}{1+x},\] the n \[f[f(\cos \ 2\theta )]=\] [MP PET 1994, 2001; Pb. CET 2002] |
| A. | \[\tan 2\theta \] |
| B. | \[\sec 2\theta \] |
| C. | \[\cos 2\theta \] |
| D. | \[\cot 2\theta \] |
| Answer» D. \[\cot 2\theta \] | |
| 5022. |
If \[{{e}^{f(x)}}=\frac{10+x}{10-x},\ x\in (-10,\ 10)\] and \[f(x)=kf\left( \frac{200x}{100+{{x}^{2}}} \right)\], then \[k=\] [EAMCET 2003] |
| A. | 0.5 |
| B. | 0.6 |
| C. | 0.7 |
| D. | 0.8 |
| Answer» B. 0.6 | |
| 5023. |
If \[f(x)=\frac{1}{\sqrt{x+2\sqrt{2x-4}}}+\frac{1}{\sqrt{x-2\sqrt{2x-4}}}\] for \[x>2\], then \[f(11)=\] [EAMCET 2003] |
| A. | 7/6 |
| B. | 5/6 |
| C. | 6/7 |
| D. | 5/7 |
| Answer» D. 5/7 | |
| 5024. |
Let \[f:(2,\,3)\to (0,\,1)\] be defined by \[f(x)=x-[x]\] then \[{{f}^{-1}}(x)\] equals [Orissa JEE 2005] |
| A. | \[x-2\] |
| B. | \[x+1\] |
| C. | \[x-1\] |
| D. | \[x+2\] |
| Answer» E. | |
| 5025. |
If \[{{e}^{x}}=y+\sqrt{1+{{y}^{2}}}\], then y = [MNR 1990, UPSEAT 2000] |
| A. | \[\frac{{{e}^{x}}+{{e}^{-x}}}{2}\] |
| B. | \[\frac{{{e}^{x}}-{{e}^{-x}}}{2}\] |
| C. | \[{{e}^{x}}+{{e}^{-x}}\] |
| D. | \[{{e}^{x}}-{{e}^{-x}}\] |
| Answer» C. \[{{e}^{x}}+{{e}^{-x}}\] | |
| 5026. |
If\[f(x)=\left\{ \begin{align} & x,\,\,\text{when}\,x\,\text{is}\,\text{rational} \\ & 0\text{,}\,\,\text{when }x\text{ is irrational} \\ \end{align} \right.\]; \[g(x)=\left\{ \begin{align} & 0,\,\,\,\,\text{when}\,x\,\text{is}\,\text{rational} \\ & x,\,\,\,\,\text{when}\,x\,\text{is irrational} \\ \end{align} \right.\] then \[(f-g)\] is [IIT Screening 2005] |
| A. | One-one onto |
| B. | One-one not onto |
| C. | Not one-one but onto |
| D. | Not one-one not onto |
| Answer» B. One-one not onto | |
| 5027. |
A condition for a function \[y=f(x)\] to have an inverse is that it should be |
| A. | Defined for all x |
| B. | Continuous everywhere |
| C. | Strictly monotonic and continuous in the domain |
| D. | An even function |
| Answer» D. An even function | |
| 5028. |
If \[f(x+ay,\ x-ay)=axy\], then \[f(x,\ y)\] is equal to [AMU 2001] |
| A. | xy |
| B. | \[{{x}^{2}}-{{a}^{2}}{{y}^{2}}\] |
| C. | \[\frac{{{x}^{2}}-{{y}^{2}}}{4}\] |
| D. | \[\frac{{{x}^{2}}-{{y}^{2}}}{{{a}^{2}}}\] |
| Answer» D. \[\frac{{{x}^{2}}-{{y}^{2}}}{{{a}^{2}}}\] | |
| 5029. |
If equation of the curve remain unchanged by replacing x and y from ?x and ?y respectively, then the curve is |
| A. | Symmetric along the x-axis |
| B. | Symmetric along the y-axis |
| C. | Symmetric in opposite quadrants |
| D. | Symmetric along the line y =x |
| Answer» D. Symmetric along the line y =x | |
| 5030. |
If \[f({{x}_{1}})-f({{x}_{2}})=f\left( \frac{{{x}_{1}}-{{x}_{2}}}{1-{{x}_{1}}{{x}_{2}}} \right)\] for \[{{x}_{1}},{{x}_{2}}\in [-1,\,1]\], then \[f(x)\] is [Roorkee 1998] |
| A. | \[\log \frac{(1-x)}{(1+x)}\] |
| B. | \[{{\tan }^{-1}}\frac{(1-x)}{(1+x)}\] |
| C. | \[\log \frac{(1+x)}{(1-x)}\] |
| D. | \[{{\tan }^{-1}}\frac{(1+x)}{(1-x)}\] |
| Answer» C. \[\log \frac{(1+x)}{(1-x)}\] | |
| 5031. |
The domain of \[{{\sin }^{-1}}({{\log }_{3}}x)\] is [Kerala (Engg.) 2005] |
| A. | [?1, 1] |
| B. | [0, 1] |
| C. | [0, \[\infty \]] |
| D. | R |
| E. | [1/3, 3] |
| Answer» F. | |
| 5032. |
The Domain of function \[f(x)={{\log }_{e}}(x-[x])\] is [AMU 2005] |
| A. | R |
| B. | R-Z |
| C. | \[(0,+\infty )\] |
| D. | Z |
| Answer» B. R-Z | |
| 5033. |
Let \[g(x)=1+x-[x]\] and \[f(x)=\left\{ \begin{align} & -1,\,\,\,If\,\,x0 \\ \end{align} \right.\]then for all values of x the value of \[fog(x)\] [DCE 2005] |
| A. | x |
| B. | 1 |
| C. | \[f(x)\] |
| D. | \[g(x)\] |
| Answer» C. \[f(x)\] | |
| 5034. |
Function \[f(x)=x-[\,],\] where [ ] shows a greatest integer. This function is [DCE 2005] |
| A. | A periodic function |
| B. | A periodic function whose period is \[\frac{1}{2}\] |
| C. | A periodic function whose period is 1 |
| D. | Not a periodic function |
| Answer» D. Not a periodic function | |
| 5035. |
If \[f(x)=\frac{\alpha x}{x+1},x\ne -1\], for what value of \[\alpha \] is \[f(f(x))=x\] [Kerala (Engg.) 2005] |
| A. | \[\sqrt{2}\] |
| B. | \[-\sqrt{2}\] |
| C. | 1 |
| D. | 2 |
| E. | ?1 |
| Answer» F. | |
| 5036. |
If \[f(x)=2{{x}^{6}}+3{{x}^{4}}+4{{x}^{2}}\] then \[f'(x)\] is [DCE 2005] |
| A. | Even function |
| B. | An odd function |
| C. | Neither even nor odd |
| D. | None of these |
| Answer» C. Neither even nor odd | |
| 5037. |
Let \[f:R\to R\] be defined by \[f(x)=2x+|x|\], then \[f(2x)+f(-x)-f(x)=\] [EAMCET 2000] |
| A. | \[2x\] |
| B. | \[2|x|\] |
| C. | \[-2x\] |
| D. | \[-2|x|\] |
| Answer» C. \[-2x\] | |
| 5038. |
If X and Y are two non- empty sets where \[f:X\to Y\]is function is defined such that \[f(c)=\left\{ f(x):x\in C \right\}\]for \[C\subseteq X\]and \[{{f}^{-1}}(D)=\{x:f(x)\in D\}\]for \[D\subseteq Y\] for any \[A\subseteq X\] and \[B\subseteq Y,\]then [IIT Screening 2005] |
| A. | \[{{f}^{-1}}(f(A))=A\] |
| B. | \[{{f}^{-1}}(f(A))=A\]only if \[f(x)=Y\] |
| C. | \[f({{f}^{-1}}(B))=B\] only if \[B\subseteq f(X)\] |
| D. | \[f({{f}^{-1}}(B))=B\] |
| Answer» D. \[f({{f}^{-1}}(B))=B\] | |
| 5039. |
A real valued function \[f(x)\] satisfies the function equation \[f(x-y)=f(x)f(y)-f(a-x)f(a+y)\] where a is a given constant and \[f(0)=1\], \[f(2a-x)\] is equal to [AIEEE 2005] |
| A. | \[f(a)+f(a-x)\] |
| B. | \[f(-x)\] |
| C. | \[-f(x)\] |
| D. | \[f(x)\] |
| Answer» D. \[f(x)\] | |
| 5040. |
Let \[f:(-1,1)\to B\], be a function defined by \[f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}},\] then f is both one- one and onto when B is the interval [AIEEE 2005] |
| A. | \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\] |
| B. | \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] |
| C. | \[\left( 0,\frac{\pi }{2} \right)\] |
| D. | \[\left[ 0,\frac{\pi }{2} \right)\] |
| Answer» C. \[\left( 0,\frac{\pi }{2} \right)\] | |
| 5041. |
If \[f(x)={{\sin }^{2}}x\] and the composite function \[g\{f(x)\}=|\sin x|\], then the function \[g(x)\] is equal to [Orissa JEE 2003] |
| A. | \[\sqrt{x-1}\] |
| B. | \[\sqrt{x}\] |
| C. | \[\sqrt{x+1}\] |
| D. | \[-\sqrt{x}\] |
| Answer» C. \[\sqrt{x+1}\] | |
| 5042. |
If \[f(x)=\frac{2x+1}{3x-2}\], then \[(fof)(2)\] is equal to [Kerala (Engg.) 2002] |
| A. | 1 |
| B. | 3 |
| C. | 4 |
| D. | 2 |
| Answer» E. | |
| 5043. |
Let \[g(x)=1+x-[x]\] and \[f(x)=\left\{ \begin{align} & -1,\ x\text{0} \\ \end{align} \right.\]then for all \[x,\ f(g(x))\] is equal to [IIT Screening 2001; UPSEAT 2001] |
| A. | x |
| B. | 1 |
| C. | \[f(x)\] |
| D. | \[g(x)\] |
| Answer» C. \[f(x)\] | |
| 5044. |
If \[f(x)=\frac{\alpha \,x}{x+1},\ x\ne -1\]. Then, for what value of \[\alpha \] is \[f(f(x))=x\] [IIT Screening 2001; UPSEAT 2001] |
| A. | \[\sqrt{2}\] |
| B. | \[-\sqrt{2}\] |
| C. | 1 |
| D. | ?1 |
| Answer» E. | |
| 5045. |
The composite mapping \[fog\]of the map \[f:R\to R\], \[f(x)=\sin x\], \[g:R\to R\], \[g(x)={{x}^{2}}\]is [UPSEAT 2000] |
| A. | \[\sin x+{{x}^{2}}\] |
| B. | \[{{(\sin x)}^{2}}\] |
| C. | \[\sin {{x}^{2}}\] |
| D. | \[\frac{\sin x}{{{x}^{2}}}\] |
| Answer» D. \[\frac{\sin x}{{{x}^{2}}}\] | |
| 5046. |
If \[f(x)=4{{x}^{3}}+3{{x}^{2}}+3x+4\], then \[{{x}^{3}}f\left( \frac{1}{x} \right)\] is [SCRA 1996] |
| A. | \[f(-x)\] |
| B. | \[\frac{1}{f(x)}\] |
| C. | \[{{\left( f\left( \frac{1}{x} \right) \right)}^{2}}\] |
| D. | \[f(x)\] |
| Answer» E. | |
| 5047. |
Suppose that \[g(x)=1+\sqrt{x}\] and \[f(g(x))=3+2\sqrt{x}+x\], then \[f(x)\] is [MP PET 2000; Karnataka CET 2002] |
| A. | \[1+2{{x}^{2}}\] |
| B. | \[2+{{x}^{2}}\] |
| C. | \[1+x\] |
| D. | \[2+x\] |
| Answer» C. \[1+x\] | |
| 5048. |
Let f and g be functions defined by \[f(x)=\frac{x}{x+1},\]\[g(x)=\frac{x}{1-x}\], then \[(fog)(x)\] is [SCRA 1996] |
| A. | \[\frac{1}{x}\] |
| B. | \[\frac{1}{x-1}\] |
| C. | \[x-1\] |
| D. | x |
| Answer» E. | |
| 5049. |
If \[f(x)={{\log }_{a}}x\] and \[F(x)={{a}^{x}}\], then \[F[f(x)]\] is [SCRA 1996] |
| A. | \[f[F(x)]\] |
| B. | \[f[F(2x)]\] |
| C. | \[F|f(2x)|\] |
| D. | \[F[(x)]\] |
| Answer» B. \[f[F(2x)]\] | |
| 5050. |
If \[g(x)={{x}^{2}}+x-2\] and \[\frac{1}{2}gof(x)=2{{x}^{2}}-5x+2\], then \[f(x)\] is [Roorkee 1998; MP PET 2002] |
| A. | \[2x-3\] |
| B. | \[2x+3\] |
| C. | \[2{{x}^{2}}+3x+1\] |
| D. | \[2{{x}^{2}}-3x-1\] |
| Answer» B. \[2x+3\] | |