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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.
| 3051. |
The solution of \[\frac{dy}{dx}=\frac{{{x}^{2}}+{{y}^{2}}+1}{2xy}\] satisfying y(1)=1 is given by |
| A. | a system of parabolas |
| B. | a system of circles |
| C. | \[{{y}^{2}}=x(1+x)-1\] |
| D. | \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=5\] |
| Answer» D. \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=5\] | |
| 3052. |
Solution of the differential equation \[(y+x\sqrt{xy}(x+y))\,dx+(y\sqrt{xy}(x+y)-x)dy=0\] is |
| A. | \[\frac{{{x}^{2}}+{{y}^{2}}}{2}+{{\tan }^{-1}}\sqrt{\frac{y}{x}=c}\] |
| B. | \[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\tan }^{-1}}\sqrt{\frac{x}{y}=c}\] |
| C. | \[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\cot }^{-1}}\sqrt{\frac{x}{y}=c}\] |
| D. | None of these |
| Answer» C. \[\frac{{{x}^{2}}+{{y}^{2}}}{2}+2{{\cot }^{-1}}\sqrt{\frac{x}{y}=c}\] | |
| 3053. |
The solution of (y + x + 5) dy = (y - x + 1) dx is |
| A. | \[\log ({{(y+3)}^{2}}+{{(x+2)}^{2}})+ta{{n}^{-1}}\frac{y+3}{y+2}+C\] |
| B. | \[\log ({{(y+3)}^{2}}+{{(x-2)}^{2}})+ta{{n}^{-1}}\frac{y-3}{x-2}=C\] |
| C. | \[\log ({{(y+3)}^{2}}+{{(x+2)}^{2}})+2ta{{n}^{-1}}\frac{y+3}{x+2}=C\] |
| D. | \[\log ({{(y+3)}^{2}}+{{(x+2)}^{2}})-2ta{{n}^{-1}}\frac{y+3}{x+2}=C\] |
| Answer» D. \[\log ({{(y+3)}^{2}}+{{(x+2)}^{2}})-2ta{{n}^{-1}}\frac{y+3}{x+2}=C\] | |
| 3054. |
Solution of \[\frac{dy}{dx}+2xy=y\] is |
| A. | \[y=c{{e}^{x-{{x}^{2}}}}\] |
| B. | \[y=c\,{{e}^{{{x}^{2}}-x}}\] |
| C. | \[y=c\,{{e}^{x}}\] |
| D. | \[y=c\,{{e}^{-{{x}^{2}}}}\] |
| Answer» B. \[y=c\,{{e}^{{{x}^{2}}-x}}\] | |
| 3055. |
The differential equation of all parabolas whose axis are parallel to the y-axis is |
| A. | \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=0\] |
| B. | \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=C\] |
| C. | \[\frac{{{d}^{3}}y}{d{{x}^{3}}}+\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=C\] |
| Answer» B. \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=C\] | |
| 3056. |
If \[y=\frac{x}{\log \left| cx \right|}\] (where c is an arbitrary constant) I the general solution of the differential equation \[dy/dx=y/x+\phi (x/y)\] then the function \[\phi (x/y)\]is |
| A. | \[{{x}^{2}}/{{y}^{2}}\] |
| B. | \[-{{x}^{2}}/{{y}^{2}}\] |
| C. | \[{{y}^{2}}/{{x}^{2}}\] |
| D. | \[-{{y}^{2}}/{{x}^{2}}\] |
| Answer» E. | |
| 3057. |
The solution of the differential equation\[y(2{{x}^{4}}+y)\frac{dy}{dx}=(1-4x{{y}^{2}}){{x}^{2}}\] is given by |
| A. | \[3{{({{x}^{2}}y)}^{2}}+{{y}^{3}}-{{x}^{3}}=c\] |
| B. | \[x{{y}^{2}}+\frac{{{y}^{3}}}{3}-\frac{{{x}^{3}}}{3}+c=0\] |
| C. | \[\frac{2}{3}y{{x}^{5}}+\frac{{{y}^{3}}}{3}=\frac{{{x}^{3}}}{3}-\frac{4x{{y}^{3}}}{3}+c\] |
| D. | None of these |
| Answer» B. \[x{{y}^{2}}+\frac{{{y}^{3}}}{3}-\frac{{{x}^{3}}}{3}+c=0\] | |
| 3058. |
Orthogonal trajectories of family of the curve \[{{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}\], where a is any arbitrary constant, is |
| A. | \[{{x}^{2/3}}-{{y}^{2/3}}=c\] |
| B. | \[{{x}^{4/3}}-{{y}^{4/3}}=c\] |
| C. | \[{{x}^{4/3}}+{{y}^{4/3}}=c\] |
| D. | \[{{x}^{1/3}}-{{y}^{1/3}}=c\] |
| Answer» C. \[{{x}^{4/3}}+{{y}^{4/3}}=c\] | |
| 3059. |
Tangent to a curve intercepts the y-axis at a point P. A line perpendicular to this tangent through P passes through another point (1, 0). The differential equation of the curve |
| A. | \[y\frac{dy}{dx}-x{{\left( \frac{dy}{dx} \right)}^{2}}=1\] |
| B. | \[\frac{x{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}=0\] |
| C. | \[y\frac{dx}{dy}+x=1\] |
| D. | None of these |
| Answer» B. \[\frac{x{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}=0\] | |
| 3060. |
The solution of the differential equation \[\frac{dy}{dx}=\frac{3{{x}^{2}}{{y}^{4}}+2xy}{{{x}^{2}}-2{{x}^{3}}{{y}^{3}}}\] is |
| A. | \[\frac{{{y}^{2}}}{x}-{{x}^{3}}{{y}^{2}}=c\] |
| B. | \[\frac{{{x}^{2}}}{{{y}^{2}}}+{{x}^{3}}{{y}^{3}}=c\] |
| C. | \[\frac{{{x}^{2}}}{y}+{{x}^{3}}{{y}^{2}}=c\] |
| D. | \[\frac{{{x}^{2}}}{3y}-{{x}^{3}}{{y}^{2}}=c\] |
| Answer» D. \[\frac{{{x}^{2}}}{3y}-{{x}^{3}}{{y}^{2}}=c\] | |
| 3061. |
The solution of differential equation \[(2y+x{{y}^{3}})dx+(x+{{x}^{2}}{{y}^{2}})dy=0\] is |
| A. | \[{{x}^{2}}y+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\] |
| B. | \[x{{y}^{2}}+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\] |
| C. | \[{{x}^{2}}y+\frac{{{x}^{4}}{{y}^{4}}}{4}=c\] |
| D. | none of these |
| Answer» B. \[x{{y}^{2}}+\frac{{{x}^{3}}{{y}^{3}}}{3}=c\] | |
| 3062. |
The general solution of the equation \[\frac{dy}{dx}=1+xy\] is |
| A. | \[y=c{{e}^{-{{x}^{2}}/2}}\] |
| B. | \[y=c{{e}^{{{x}^{2}}/2}}\] |
| C. | \[y=(x+c){{e}^{-{{x}^{2}}/2}}\] |
| D. | None of these |
| Answer» E. | |
| 3063. |
If integrating factor of \[x(1-{{x}^{2}})dy+(2{{x}^{2}}y-y-a{{x}^{3}})dx=0\] is \[_{e}\int pdx\], then P is equal to |
| A. | \[\frac{2{{x}^{2}}-a{{x}^{3}}}{x(1-{{x}^{2}})}\] |
| B. | \[2{{x}^{3}}-1\] |
| C. | \[\frac{2{{x}^{2}}-a}{a{{x}^{3}}}\] |
| D. | \[\frac{2{{x}^{2}}-1}{x(1-{{x}^{2}})}\] |
| Answer» E. | |
| 3064. |
The solution of the differential equation \[{{x}^{2}}\frac{dy}{dx}\cos \frac{1}{x}-y\sin \frac{1}{x}=-1\], where \[y\to -1\,\,as\,\,x\to \infty \]is |
| A. | \[y=\sin \frac{1}{x}-\cos \frac{1}{x}\] |
| B. | \[y=\frac{x+1}{x\sin \frac{1}{x}}\] |
| C. | \[y=\cos \frac{1}{x}+sin\frac{1}{x}\] |
| D. | \[y=\frac{x+1}{x\cos 1/x}\] |
| Answer» B. \[y=\frac{x+1}{x\sin \frac{1}{x}}\] | |
| 3065. |
The solution to the differential equation\[y\log y+xy'=0\], where \[y(1)=e\], is |
| A. | \[x(log\,y)=1\] |
| B. | \[xy(log\,y)=1\] |
| C. | \[{{(log\,y)}^{2}}=2\] |
| D. | \[\log y+\left( \frac{{{x}^{2}}}{2} \right)y=1\] |
| Answer» B. \[xy(log\,y)=1\] | |
| 3066. |
If \[x\ne 0\], \[y\ne 0\], \[z\ne 0\] and , then \[{{x}^{-1}}+{{y}^{-1}}+{{z}^{-1}}\] is equal to |
| A. | \[-\,1\] |
| B. | \[-\,2\] |
| C. | \[-\,3\] |
| D. | none of these |
| Answer» D. none of these | |
| 3067. |
The value of the determinant\[\left| \begin{matrix} 1 & 1 & 1 \\ ^{m}{{C}_{1}} & ^{m+1}{{C}_{1}} & ^{m+2}{{C}_{1}} \\ ^{m}{{C}_{2}} & ^{m+1}{{C}_{2}} & ^{m+2}{{C}_{2}} \\ \end{matrix} \right|\] |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | none of these |
| Answer» B. -1 | |
| 3068. |
If a, b, and c are nonzero real number then \[\Delta =\left| \begin{matrix} {{b}^{2}}{{c}^{2}} & bc & b+c \\ {{c}^{2}}{{a}^{2}} & ca & c+a \\ {{a}^{2}}{{b}^{2}} & ab & a+b \\ \end{matrix} \right|\]is equal to |
| A. | abc |
| B. | \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\] |
| C. | bc+ca+ab |
| D. | none of these |
| Answer» E. | |
| 3069. |
The value of the determinant\[\left| \begin{matrix} kb & {{k}^{^{2}}}+{{a}^{2}} & 1 \\ kb & {{k}^{2}}+{{b}^{2}} & 1 \\ kc & {{k}^{2}}+{{c}^{2}} & 1 \\ \end{matrix} \right|\]is |
| A. | \[k(a+b)(b+c)(c+a)\] |
| B. | \[k\,abc({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\] |
| C. | \[k(a-b)(b-c)(c-a)\] |
| D. | \[k(a+b-c)(b+c-a)(c+a-b)\] |
| Answer» D. \[k(a+b-c)(b+c-a)(c+a-b)\] | |
| 3070. |
If \[f(x)=a+bx+c{{x}^{2}}\] and \[\alpha ,\beta ,\gamma \]are the roots of the equation\[{{x}^{3}}=1,\]then is equal to |
| A. | \[f(\alpha )+f(\beta )+f(\gamma )\] |
| B. | \[f(\alpha )f(\beta )+f(\beta )\]\[f(\gamma )+f(\gamma )\]\[f(\alpha )\] |
| C. | \[f(\alpha )f(\beta )f(\gamma )\] |
| D. | \[f(\alpha )f(\beta )f(\gamma )\] |
| Answer» C. \[f(\alpha )f(\beta )f(\gamma )\] | |
| 3071. |
If , then z is |
| A. | purely real |
| B. | purely imaginary |
| C. | \[a+ib,\]where \[a\ne 0,\]\[b\ne 0,\] |
| D. | \[a+ib,\]where b = 4 |
| Answer» C. \[a+ib,\]where \[a\ne 0,\]\[b\ne 0,\] | |
| 3072. |
If \[{{\Delta }_{1}}=\left| \begin{matrix} x & b & b \\ a & x & b \\ a & a & x \\ \end{matrix} \right|\] and \[{{\Delta }_{2}}=\left| \begin{matrix} x & b \\ a & x \\ \end{matrix} \right|\]are the given determinants, then |
| A. | \[{{\Delta }_{1}}=3{{({{\Delta }_{2}})}^{2}}\] |
| B. | \[\frac{d}{dx}({{\Delta }_{1}})=3({{\Delta }_{2}})\] |
| C. | \[\frac{d}{dx}({{\Delta }_{1}})=3{{({{\Delta }_{2}})}^{2}}\] |
| D. | \[{{\Delta }_{1}}=3{{\Delta }_{2}}^{3/2}\] |
| Answer» C. \[\frac{d}{dx}({{\Delta }_{1}})=3{{({{\Delta }_{2}})}^{2}}\] | |
| 3073. |
The determinant is equal to |
| A. | \[\left| \begin{matrix} bx+ay & cx+by \\ b'x+a'y & c'x+b'y \\ \end{matrix} \right|\] |
| B. | \[\left| \begin{matrix} ax+by & bx+cy \\ a'x+b'y & b'x+c'y \\ \end{matrix} \right|\] |
| C. | \[\left| \begin{matrix} bx+cy & ax+by \\ b'x+c'y & a'x+b'y \\ \end{matrix} \right|\] |
| D. | \[\left| \begin{matrix} ax+by & bx+cy \\ a'x+b'y & b'x+c'y \\ \end{matrix} \right|\] |
| Answer» E. | |
| 3074. |
If the value of the determinant \[\left| \begin{matrix} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \\ \end{matrix} \right|\] is positive, then (a, b, c > 0) |
| A. | \[abc>1\] |
| B. | \[abc>-\,8\] |
| C. | \[abc<-\,8\] |
| D. | \[abc>-\,2\] |
| Answer» C. \[abc<-\,8\] | |
| 3075. |
If \[{{l}^{2}}_{1}+{{m}_{1}}^{2}+{{n}_{1}}^{2}=1\], etc. and \[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}+{{n}_{1}}{{n}_{2}}=0\], etc. and \[\Delta =\left| \begin{matrix} {{l}_{1}} & {{m}_{1}} & {{n}_{1}} \\ {{l}_{2}} & {{m}_{2}} & {{n}_{2}} \\ {{l}_{3}} & {{m}_{3}} & {{n}_{3}} \\ \end{matrix} \right|\], then |
| A. | \[\left| \Delta \right|\]=3 |
| B. | \[\left| \Delta \right|\]=2 |
| C. | \[\left| \Delta \right|\]=1 |
| D. | \[\Delta \]=0 |
| Answer» D. \[\Delta \]=0 | |
| 3076. |
The value of the determinant\[\left| \begin{matrix} ^{n}{{C}_{r-1}} & ^{n}{{C}_{r}} & (r+1) & ^{n+2}{{C}_{r+1}} \\ ^{n}{{C}_{r}} & ^{n}{{C}_{r+1}} & (r+2) & ^{n+2}{{C}_{r+2}} \\ ^{n}{{C}_{r+1}} & ^{n}{{C}_{r+2}} & (r+3) & ^{n+2}{{C}_{r+3}} \\\end{matrix} \right|\] is |
| A. | \[{{n}^{2}}+n-1\] |
| B. | 0 |
| C. | \[^{n+3}{{C}_{r+3}}\] |
| D. | \[^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}\] |
| Answer» C. \[^{n+3}{{C}_{r+3}}\] | |
| 3077. |
If \[{{a}_{1}},{{a}_{2}}...{{a}_{n}}....\]form a G.P. and \[{{a}_{i}}\]>0, for all \[i\ge 1\], then\[\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}} \\ \end{matrix} \right|\]is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 3078. |
Suppose and. Then |
| A. | D'=D |
| B. | D'=D(1-pqr) |
| C. | D'=D(1+p+q+r) |
| D. | D'=D(1+pqr) |
| Answer» E. | |
| 3079. |
If \[\left| \begin{matrix} {{x}^{n}} & {{x}^{n+2}} & {{x}^{2n}} \\ 1 & {{x}^{a}} & a \\ {{x}^{n+5}} & {{x}^{a+6}} & {{x}^{2n+5}} \\ \end{matrix} \right|=0,\forall x\in R\] where \[n\in N\], then value of a is |
| A. | n |
| B. | n-1 |
| C. | n+1 |
| D. | none of these |
| Answer» D. none of these | |
| 3080. |
If , then |
| A. | \[f'(x)=0and\,f''(x)=0\]has one common root |
| B. | \[f(x)=0\,\,and\,f'(x)=0\]has one common root |
| C. | sum of roots of \[f(x)\]=0 is \[-\,3\,a\] |
| D. | none of these |
| Answer» C. sum of roots of \[f(x)\]=0 is \[-\,3\,a\] | |
| 3081. |
In triangle ABC, if \[\left| \begin{matrix} 1 & 1 & 1 \\ \cos \frac{A}{2} & \cot \frac{A}{2} & \cot \frac{C}{2} \\ \tan \frac{B}{2}+\tan \frac{C}{2} & \tan \frac{C}{2}+\tan \frac{A}{2} & \tan \frac{A}{2}+\tan \frac{B}{2} \\ \end{matrix} \right|=0\] then the triangle must be |
| A. | equilateral |
| B. | isosceles |
| C. | obtuse angled |
| D. | none of these |
| Answer» C. obtuse angled | |
| 3082. |
The function \[f(x)\] defined by\[f(x)=\left\{ \begin{matrix} {{\log }_{(4x-3)}}({{x}^{2}}-2x+5),\,\,\,\,\,\,\frac{3}{4} |
| A. | is continuous at x=1 |
| B. | is discontinuous at x=1 since \[f({{1}^{+}})\]does not exist though \[f({{1}^{-}})\]exists |
| C. | is discontinuous at x=1 since \[f({{1}^{-}})\]does not exist thought \[f({{1}^{+}})\]exists |
| D. | is discontinuous at x=1 since neither \[f({{1}^{+}})\]nor \[f({{1}^{-}})\]exists. |
| Answer» E. | |
| 3083. |
If \[f(x)=\left\{ \begin{matrix} x+2,\,\,\,\,\,\,\,\,\,x |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | none of these |
| Answer» B. 2 | |
| 3084. |
A point where function \[f(x)=[sin[x]]\] is not continuous in \[(0,2\pi )\], [.] denotes the greatest integer \[\le x\], is |
| A. | (3, 0) |
| B. | (2, 0) |
| C. | (1, 0) |
| D. | none of these |
| Answer» E. | |
| 3085. |
Let \[f(x)=\left\{ \begin{matrix} \frac{x-4}{\left| x-4 \right|}+a,\,\,\,\,\,\,x4 \\ \end{matrix} \right.\] Then \[f(x)\] is continuous at x=4 |
| A. | \[a=0,\text{ }b=0\] |
| B. | \[a=1,\text{ }b=1\] |
| C. | \[a=-\,1,\text{ }b=1\] |
| D. | \[a=1,\text{ }b=-1\] |
| Answer» E. | |
| 3086. |
The function \[f(x)=\frac{{{({{3}^{x}}-1)}^{2}}}{\sin x\cdot \ln \,(1+x)},x\ne 0\], is continuous at x=0. Then the value of f(0) is |
| A. | \[2{{\log }_{e}}3\] |
| B. | \[{{(2{{\log }_{e}}3)}^{2}}\] |
| C. | \[{{\log }_{e}}6\] |
| D. | none of these |
| Answer» C. \[{{\log }_{e}}6\] | |
| 3087. |
The value of f(0) so that the function \[f(x)=\frac{2x-{{\sin }^{-1}}x}{2x+{{\tan }^{-1}}x}\]is continuous at each point in its domain, is equal to |
| A. | 2 |
| B. | 44256 |
| C. | 2/3 |
| D. | -0.333333333333333 |
| Answer» C. 2/3 | |
| 3088. |
The set of all points where \[f(x)=\sqrt[3]{{{x}^{2}}\left| x \right|}-\left| x \right|-1\]is not differentiable is |
| A. | {0} |
| B. | \[\left\{ -1,\text{ }0,\text{ }1 \right\}\] |
| C. | {0, 1} |
| D. | none of these |
| Answer» E. | |
| 3089. |
\[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(x-1)}^{2n}}-1}{{{(x-1)}^{2n}}+1}\]is discontinuous at |
| A. | \[x=0\]only |
| B. | \[x=2\]only |
| C. | \[x=0\]and 2 |
| D. | none of these |
| Answer» D. none of these | |
| 3090. |
If \[f(x)=\left\{ \begin{matrix} {{x}^{2}}-ax+3,\,\,\,x\,\,\text{is}\,\,\text{rational} \\ 2-x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\text{is}\,\,\text{irrational} \\ \end{matrix} \right.\]is continuous at exactly two points, then the possible values of a are |
| A. | \[(2,\infty )\] |
| B. | \[(-\infty ,3)\] |
| C. | \[(-\infty ,-3)\cup (3,\infty )\] |
| D. | none of these |
| Answer» D. none of these | |
| 3091. |
If \[f(x)=\left\{ \begin{matrix} x-1,\,\,\,\,\,\,\,x |
| A. | \[f(\left| x \right|)\]is discontinuous at x=0 |
| B. | \[f(\left| x \right|)\]is differentiable at x=0 |
| C. | \[|f(x)|\]is non-differentiable at x=0, 2 |
| D. | \[|f(x)|\]is continuous at x=0 |
| Answer» D. \[|f(x)|\]is continuous at x=0 | |
| 3092. |
If \[f(x)=\left\{ \begin{matrix} {{e}^{{{x}^{2}}+x}}\,\,\,\,\,x>0 \\ ax+b,\,\,x\le 0 \\ \end{matrix} \right.\]is differentiable at x=0, then |
| A. | \[a=1,\text{ }b=-\,1\] |
| B. | \[a=-1,\text{ }b=1\] |
| C. | \[a=1,\text{ }b=1\] |
| D. | \[a=-\,1,\text{ }b=-\,1\] |
| Answer» D. \[a=-\,1,\text{ }b=-\,1\] | |
| 3093. |
If \[f(x)=\left\{ \begin{matrix} {{x}^{3}},\,\,{{x}^{2}}1 \\ \end{matrix} \right.\], then \[f(x)\] is differentiable at |
| A. | \[(-\infty ,\infty )-\{1\}\] |
| B. | \[(-\infty ,\infty )\tilde{\ }\{1,-1\}\] |
| C. | \[(-\infty ,\infty )\tilde{\ }\{1,-1,0\}\] |
| D. | \[(-\infty ,\infty )\tilde{\ }\{-1\}\] |
| Answer» C. \[(-\infty ,\infty )\tilde{\ }\{1,-1,0\}\] | |
| 3094. |
Which of the following function is not differentiable at x=1? |
| A. | \[f(x)=({{x}^{2}}-1)\left| (x-1)(x-2) \right|\] |
| B. | \[f(x)=sin(\left| x-1 \right|)-\left| x-1 \right|\] |
| C. | \[f(x)=\tan (\left| x-1 \right|)-\left| x-1 \right|\] |
| D. | None of these |
| Answer» D. None of these | |
| 3095. |
\[f(x)=\left\{ \begin{matrix} \frac{x}{2{{x}^{2}}+\left| x \right|,}\,\,x\ne 0 \\ 1.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{matrix} \right.\]. Then \[f(x)\] is |
| A. | continuous but non-differentiable at x=0 |
| B. | differentiable at x=0 |
| C. | discontinuous at x=0 |
| D. | none of these |
| Answer» D. none of these | |
| 3096. |
The number of values of \[x\in [0,2]\] at which \[f(x)=\left| x-\frac{1}{2} \right|+\left| x-1 \right|+\tan x\] is not differentiable is |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | none of these |
| Answer» D. none of these | |
| 3097. |
If \[f(x)={{x}^{3}}\sgn x,\]then |
| A. | f is derivable at x=0 |
| B. | f is continuous but not derivable at x=0 |
| C. | LHD at x=0 is 1 |
| D. | RHD at x=0 is 1 |
| Answer» B. f is continuous but not derivable at x=0 | |
| 3098. |
If \[f(x)=\frac{{{x}^{2}}-bx+25}{{{x}^{2}}-7x+10}\] for \[x\ne 5\] is continuous at x=5, then the value of \[f(5)\] is |
| A. | 0 |
| B. | 5 |
| C. | 10 |
| D. | 25 |
| Answer» B. 5 | |
| 3099. |
Which of the following functions have finite number of points of discontinuity in R ([.] represents the greatest integer function)? |
| A. | \[\operatorname{tanx}\] |
| B. | \[x[x]\] |
| C. | \[\frac{\left| x \right|}{x}\] |
| D. | \[\sin [\pi x]\] |
| Answer» D. \[\sin [\pi x]\] | |
| 3100. |
The vertex of a parabola is the point, (a,b) and the latus rectum is of length, l. the axis of the parabola is parallel to the y-axis and the parabola is concave upward, then its equation is |
| A. | \[{{(x+a)}^{2}}=\frac{1}{2}(2y-2b)\] |
| B. | \[{{(x-a)}^{2}}=\frac{1}{2}(2y-2b)\] |
| C. | \[{{(x+a)}^{2}}=\frac{1}{4}(2y-2b)\] |
| D. | \[{{(x-a)}^{2}}=\frac{1}{8}(2y-2b)\] |
| Answer» B. \[{{(x-a)}^{2}}=\frac{1}{2}(2y-2b)\] | |