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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.
| 6301. |
If \[\tan (u+iv)=i\], then the value of v is [RPET 2001] |
| A. | 0 |
| B. | \[\infty \] |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 6302. |
The solution of the differential equation \[y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)\] is [AISSE 1989, 90] |
| A. | \[y=c(x+a)(1+ay)\] |
| B. | \[y=c(x+a)(1-ay)\] |
| C. | \[y=c(x-a)(1+ay)\] |
| D. | None of these |
| Answer» C. \[y=c(x-a)(1+ay)\] | |
| 6303. |
If the coefficient of \[{{x}^{7}}\] in \[{{\left( a{{x}^{2}}+\frac{1}{bx} \right)}^{11}}\] is equal to the coefficient of \[{{x}^{-7}}\]in \[{{\left( ax-\frac{1}{b{{x}^{2}}} \right)}^{11}}\], then ab = [MP PET 1999; AMU 2001; Pb. CET 2002; AIEEE 2005] |
| A. | 1 |
| B. | 44228 |
| C. | 2 |
| D. | 3 |
| Answer» B. 44228 | |
| 6304. |
The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given by [Pb. CET 2004] |
| A. | \[{{y}^{2}}\frac{dy}{dx}={{k}^{2}}-{{y}^{2}}\] |
| B. | \[{{\left( y\frac{dy}{dx} \right)}^{2}}={{k}^{2}}-{{y}^{2}}\] |
| C. | \[y{{\left( \frac{dy}{dx} \right)}^{2}}={{k}^{2}}+{{y}^{2}}\] |
| D. | \[{{\left( y\frac{dy}{dx} \right)}^{2}}={{k}^{2}}+{{y}^{2}}\] |
| Answer» C. \[y{{\left( \frac{dy}{dx} \right)}^{2}}={{k}^{2}}+{{y}^{2}}\] | |
| 6305. |
If three mutually perpendicular lines have direction cosines \[({{l}_{1}},{{m}_{1}},{{n}_{1}}),({{l}_{2}},{{m}_{2}},{{n}_{2}})\]and \[({{l}_{3}},{{m}_{3}},{{n}_{3}})\], then the line having direction cosines \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}\], \[{{m}_{1}}+\,\,{{m}_{2}}+\,\,{{m}_{3}}\]and \[{{n}_{1}}+{{n}_{2}}+{{n}_{3}}\] make an angle of ..... with each other |
| A. | \[0{}^\circ \] |
| B. | \[30{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» B. \[30{}^\circ \] | |
| 6306. |
Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the number of elements in \[\left( A\text{ }~\times \text{ }B \right)\text{ }\cap \text{ }\left( B\text{ }\times \text{ }A \right)\] is |
| A. | 18 |
| B. | 6 |
| C. | 4 |
| D. | 0 |
| Answer» D. 0 | |
| 6307. |
The coefficient of \[{{x}^{100}}\] in the expansion of \[\sum\limits_{j=0}^{200}{{{(1+x)}^{j}}}\] is [UPSEAT 2004] |
| A. | \[\left( \begin{align} & 200 \\ & 100 \\ \end{align} \right)\] |
| B. | \[\left( \begin{align} & 201 \\ & 102 \\ \end{align} \right)\] |
| C. | \[\left( \begin{align} & 200 \\ & 101 \\ \end{align} \right)\] |
| D. | \[\left( \begin{align} & 201 \\ & 100 \\ \end{align} \right)\] |
| Answer» B. \[\left( \begin{align} & 201 \\ & 102 \\ \end{align} \right)\] | |
| 6308. |
If \[\tan (\cot x)=\cot (\tan x),\]then \[\sin 2x\]= [MP PET 1999; Pb. CET 2001] |
| A. | \[(2n+1)\frac{\pi }{4}\] |
| B. | \[\frac{4}{(2n+1)\pi }\] |
| C. | \[4\pi (2n+1)\] |
| D. | None of these |
| Answer» C. \[4\pi (2n+1)\] | |
| 6309. |
If the vertices of a triangle be (0,0), (6,0) and (6,8), then its incentre will be |
| A. | (2, 1) |
| B. | (1,2) |
| C. | (4, 2) |
| D. | (2,4) |
| Answer» D. (2,4) | |
| 6310. |
The equation of straight line passing through \[(-a,\ 0)\] and making the triangle with axes of area ?T? is [RPET 1987] |
| A. | \[2Tx+{{a}^{2}}y+2aT=0\] |
| B. | \[2Tx-{{a}^{2}}y+2aT=0\] |
| C. | \[2Tx-{{a}^{2}}y-2aT=0\] |
| D. | None of these |
| Answer» C. \[2Tx-{{a}^{2}}y-2aT=0\] | |
| 6311. |
The locus of the point \[P(x,y)\] satisfying the relation \[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}+\sqrt{{{(x+3)}^{2}}+{{(y-1)}^{2}}}=6\] is [Orissa JEE 2002] |
| A. | Straight line |
| B. | Pair of straight lines |
| C. | Circle |
| D. | Ellipse |
| Answer» C. Circle | |
| 6312. |
The minimum value of the objective function \[z=2x+10y\] for linear constraints \[x\ge 0,\ y\ge 0\], \[x-y\ge 0\], \[x-5y\le -5\], is |
| A. | 10 |
| B. | 15 |
| C. | 12 |
| D. | 8 |
| Answer» C. 12 | |
| 6313. |
Let r be the range and \[{{S}^{2}}=\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}\] be the S.D. of a set of observations \[{{x}_{1}},\,{{x}_{2}},\,.....{{x}_{n}}\], then |
| A. | \[S\le r\sqrt{\frac{n}{n-1}}\] |
| B. | \[S=r\sqrt{\frac{n}{n-1}}\] |
| C. | \[S\ge r\sqrt{\frac{n}{n-1}}\] |
| D. | None of these |
| Answer» B. \[S=r\sqrt{\frac{n}{n-1}}\] | |
| 6314. |
The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is [EAMCET 2003] |
| A. | \[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+4x\frac{dy}{dx}=4y\] |
| B. | \[-y\,{{\left( \frac{dy}{dx} \right)}^{2}}=2x\frac{dy}{dx}-y\] |
| C. | \[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+y=2xy\frac{dy}{dx}\] |
| D. | \[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+2xy\frac{dy}{dx}+y=0\] |
| Answer» C. \[y\,{{\left( \frac{dy}{dx} \right)}^{2}}+y=2xy\frac{dy}{dx}\] | |
| 6315. |
In the polynomial \[(x-1)(x-2)(x-3).............(x-100),\]the coefficient of \[{{x}^{99}}\] is [AMU 2002] |
| A. | 5050 |
| B. | -5050 |
| C. | 100 |
| D. | 99 |
| Answer» C. 100 | |
| 6316. |
If the coordinates of the vertices of a triangle be (1,a), (2,b) and \[({{c}^{2}},3)\], then the centroid of the triangle |
| A. | Lies at the origin |
| B. | Cannot lie on x-axis |
| C. | Cannot lie on y-axis |
| D. | None of these |
| Answer» D. None of these | |
| 6317. |
\[\tan \left[ \frac{\pi }{4}+\frac{1}{2}{{\cos }^{-1}}\frac{a}{b} \right]+\tan \left[ \frac{\pi }{4}-\frac{1}{2}{{\cos }^{-1}}\frac{a}{b} \right]=\] [MP PET 1999] |
| A. | \[\frac{2a}{b}\] |
| B. | \[\frac{2b}{a}\] |
| C. | \[\frac{a}{b}\] |
| D. | \[\frac{b}{a}\] |
| Answer» C. \[\frac{a}{b}\] | |
| 6318. |
The area (in square units) of the quadrilateral formed by the two pairs of lines\[{{l}^{2}}{{x}^{2}}-{{m}^{2}}{{y}^{2}}-n(lx+my)=0\]and \[{{l}^{2}}{{x}^{2}}-{{m}^{2}}{{y}^{2}}+n(lx-my)=0\] is [EAMCET 2003] |
| A. | \[\frac{{{n}^{2}}}{2|lm|}\] |
| B. | \[\frac{{{n}^{2}}}{|lm|}\] |
| C. | \[\frac{n}{2|lm|}\] |
| D. | \[\frac{{{n}^{2}}}{4|lm|}\] |
| Answer» B. \[\frac{{{n}^{2}}}{|lm|}\] | |
| 6319. |
The L.P. problem Max\[z={{x}_{1}}+{{x}_{2}}\] such that \[-2{{x}_{1}}+{{x}_{2}}\le 1,\ {{x}_{1}}\le 2,\ {{x}_{1}}+{{x}_{2}}\le 3\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] has |
| A. | One solution |
| B. | Three solution |
| C. | An infinite no. of solution |
| D. | None of these |
| Answer» D. None of these | |
| 6320. |
The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e}^{5x}},\]where A and B are arbitrary constants, is [MNR 1988] |
| A. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+8\frac{dy}{dx}+15y=0\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+15y=0\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\] |
| D. | None of these |
| Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\] | |
| 6321. |
\[\int_{{}}^{{}}{\frac{{{x}^{2}}dx}{{{(a+bx)}^{2}}}}=\] [IIT 1979] |
| A. | \[\frac{1}{{{b}^{2}}}\left[ x+\frac{2a}{b}\log (a+bx)-\frac{{{a}^{2}}}{b}\frac{1}{a+bx} \right]\] |
| B. | \[\frac{1}{{{b}^{2}}}\left[ x-\frac{2a}{b}\log (a+bx)+\frac{{{a}^{2}}}{b}\frac{1}{a+bx} \right]\] |
| C. | \[\frac{1}{{{b}^{2}}}\left[ x+\frac{2a}{b}\log (a+bx)+\frac{{{a}^{2}}}{b}\frac{1}{a+bx} \right]\] |
| D. | \[\frac{1}{{{b}^{2}}}\left[ x+\frac{a}{b}-\frac{2a}{b}\log (a+bx)-\frac{{{a}^{2}}}{b}\frac{1}{a+bx} \right]\] |
| Answer» E. | |
| 6322. |
If \[y=f\left( \frac{2x-1}{{{x}^{2}}+1} \right)\]and \[{f}'(x)=\sin {{x}^{2}},\]then \[\frac{dy}{dx}=\] [IIT 1982] |
| A. | \[\frac{6{{x}^{2}}-2x+2}{{{({{x}^{2}}+1)}^{2}}}\sin {{\left( \frac{2x-1}{{{x}^{2}}+1} \right)}^{2}}\] |
| B. | \[\frac{6{{x}^{2}}-2x+2}{{{({{x}^{2}}+1)}^{2}}}{{\sin }^{2}}\left( \frac{2x-1}{{{x}^{2}}+1} \right)\] |
| C. | \[\frac{-2{{x}^{2}}+2x+2}{{{({{x}^{2}}+1)}^{2}}}{{\sin }^{2}}\left( \frac{2x-1}{{{x}^{2}}+1} \right)\] |
| D. | \[\frac{-2{{x}^{2}}+2x+2}{{{({{x}^{2}}+1)}^{2}}}\sin {{\left( \frac{2x-1}{{{x}^{2}}+1} \right)}^{2}}\] |
| Answer» E. | |
| 6323. |
The equations of the line passing through the point (1,2,-4) and perpendicular to the two lines \[\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}\] and \[\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}\], will be [AI CBSE 1983] |
| A. | \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}\] |
| B. | \[\frac{x-1}{-2}=\frac{y-2}{3}=\frac{z+4}{8}\] |
| C. | \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}\] |
| D. | None of these |
| Answer» B. \[\frac{x-1}{-2}=\frac{y-2}{3}=\frac{z+4}{8}\] | |
| 6324. |
If \[\sec 4\theta -\sec 2\theta =2\], then the general value of \[\theta \] is [IIT 1963] |
| A. | \[(2n+1)\frac{\pi }{4}\] |
| B. | \[(2n+1)\frac{\pi }{10}\] |
| C. | \[n\pi +\frac{\pi }{2}\]or \[\frac{n\pi }{5}+\frac{\pi }{10}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6325. |
The following points A (2a, 4a), B(2a, 6a) and C \[(2a+\sqrt{3}a,\,5a)\], \[(a>0)\] are the vertices of |
| A. | An acute angled triangle |
| B. | A right angled triangle |
| C. | An isosceles triangle |
| D. | None of these |
| Answer» B. A right angled triangle | |
| 6326. |
If\[{{\cos }^{-1}}p+{{\cos }^{-1}}q+{{\cos }^{-1}}r=\pi \]then\[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}+2pqr=\] [Karnataka CET 2004] |
| A. | 3 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» C. 2 | |
| 6327. |
If the pair of straight lines given by \[A{{x}^{2}}+2Hxy+B{{y}^{2}}=0\], \[({{H}^{2}}>AB)\] forms an equilateral triangle with line \[ax+by+c=0\], then \[(A+3B)(3A+B)\] is [EAMCET 2003] |
| A. | \[{{H}^{2}}\] |
| B. | \[-{{H}^{2}}\] |
| C. | \[2{{H}^{2}}\] |
| D. | \[4{{H}^{2}}\] |
| Answer» E. | |
| 6328. |
A pie chart is to be drawn for representing the following data Items of expenditure Number of families Education 150 Food and clothing 400 House rent 40 Electricity 250 Miscellaneous 160 The value of the central angle for food and clothing would be |
| A. | 90° |
| B. | 2.8° |
| C. | 150° |
| D. | 144° |
| Answer» E. | |
| 6329. |
The degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+3{{\left[ \frac{dy}{dx} \right]}^{2}}={{x}^{2}}\log \left[ \frac{{{d}^{2}}y}{d{{x}^{2}}} \right]\] is [Pb. CET 2004] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | None of these |
| Answer» E. | |
| 6330. |
\[\int_{{}}^{{}}{\frac{{{\sin }^{8}}x-{{\cos }^{8}}x}{1-2{{\sin }^{2}}x{{\cos }^{2}}x}\ dx=}\] [IIT 1986] |
| A. | \[\sin 2x+c\] |
| B. | \[-\frac{1}{2}\sin 2x+c\] |
| C. | \[\frac{1}{2}\sin 2x+c\] |
| D. | \[-\sin 2x+c\] |
| Answer» C. \[\frac{1}{2}\sin 2x+c\] | |
| 6331. |
If \[u(x,y)=y\log x+x\,\log y,\] then \[{{u}_{x}}{{u}_{y}}-{{u}_{x}}\log x-{{u}_{y}}\log y+\log x\,\,\log y=\] [EAMCET 2003] |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 6332. |
For a real number \[x,\ [x]\] denotes the integral part of x. The value of \[\left[ \frac{1}{2} \right]+\left[ \frac{1}{2}+\frac{1}{100} \right]+\left[ \frac{1}{2}+\frac{2}{100} \right]+....+\left[ \frac{1}{2}+\frac{99}{100} \right]\] is [IIT Screening 1994] |
| A. | 49 |
| B. | 50 |
| C. | 48 |
| D. | 51 |
| Answer» C. 48 | |
| 6333. |
The angle between two diagonals of a cube will be [MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004] |
| A. | \[{{\sin }^{-1}}1/3\] |
| B. | \[{{\cos }^{-1}}1/3\] |
| C. | Variable |
| D. | None of these |
| Answer» C. Variable | |
| 6334. |
The points D, E, F divide BC, CA and AB of the triangle ABC in the ratio 1 : 4, 3 : 2 and 3 : 7 respectively and the point K divides AB in the ratio \[1:3\], then \[(\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF})\,\,:\,\,\overrightarrow{CK}\] is equal to [MNR 1987] |
| A. | 1 : 1 |
| B. | 0.0868055555555556 |
| C. | 5 : 2 |
| D. | None of these |
| Answer» C. 5 : 2 | |
| 6335. |
If \[A=[(x,\,y):{{x}^{2}}+{{y}^{2}}=25]\] and B = \[[(x,\,y):{{x}^{2}}+9{{y}^{2}}=144]\], then \[A\cap B\] contains [AMU 1996; Pb. CET 2002] |
| A. | One point |
| B. | Three points |
| C. | Two points |
| D. | Four points |
| Answer» E. | |
| 6336. |
The general solution of \[a\cos x+b\sin x=c,\] where \[a,\,\,b,\,\,c\] are constants |
| A. | \[x=n\pi +{{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] |
| B. | \[x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\] |
| C. | \[x=2n\pi -{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] |
| D. | \[x=2n\pi +{{\tan }^{-1}}\left( \frac{b}{a} \right)\pm {{\cos }^{-1}}\left( \frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right)\] |
| Answer» E. | |
| 6337. |
The point of trisection of the line joining the points (0, 3) and (6, -3) are |
| A. | \[(2,\,0)\]and\[(4,\,-1)\] |
| B. | \[(2,\,-1)\]and \[(4,1)\] |
| C. | \[(3,1)\]and\[(4,-1)\] |
| D. | \[(2,1)\]and\[(4,-1)\] |
| Answer» E. | |
| 6338. |
If \[{{\sin }^{-1}}x=\frac{\pi }{5}\] for some \[x\in (-1,\,1)\], then the value of \[{{\cos }^{-1}}x\] is [IIT 1992] |
| A. | \[\frac{3\pi }{10}\] |
| B. | \[\frac{5\pi }{10}\] |
| C. | \[\frac{7\pi }{10}\] |
| D. | \[\frac{9\pi }{10}\] |
| Answer» B. \[\frac{5\pi }{10}\] | |
| 6339. |
The equation of perpendicular bisectors of the sides AB and AC of a triangle ABC are \[x-y+5=0\] and \[x+2y=0\] respectively. If the point A is \[(1,\ -\ 2)\], then the equation of line BC is [IIT 1986] |
| A. | \[23x+14y-40=0\] |
| B. | \[14x-23y+40=0\] |
| C. | \[{{\tan }^{-1}}(2)\] |
| D. | \[14x+23y-40=0\] |
| Answer» E. | |
| 6340. |
Area of the triangle formed by the lines \[{{y}^{2}}-9xy+18{{x}^{2}}=0\] and \[y=9\] is |
| A. | \[\frac{27}{4}sq\]. units |
| B. | \[27sq.\]units |
| C. | \[\frac{27}{2}sq.\] units |
| D. | None of these |
| Answer» B. \[27sq.\]units | |
| 6341. |
An AND gate is the Boolean function defined by |
| A. | \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}}:\,{{x}_{2}},\,\,\,\,{{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}\] |
| B. | \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}}+\,{{x}_{2}},\,\,\,\,{{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}\] |
| C. | \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}},\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}\] |
| D. | \[f({{x}_{1}},\,{{x}_{2}})={{x}_{2}},\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}\] |
| Answer» B. \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}}+\,{{x}_{2}},\,\,\,\,{{x}_{1}},\,{{x}_{2}}\in \{0,\,1\}\] | |
| 6342. |
The following data gives the distribution of height of students Height (in cm) 160 150 152 161 156 154 155 Number of students 12 8 4 4 3 3 7 The median of the distribution is [AMU 1994] |
| A. | 154 |
| B. | 155 |
| C. | 160 |
| D. | 161 |
| Answer» C. 160 | |
| 6343. |
The order and degree of the differential equation \[{{\left( 1+3\frac{dy}{dx} \right)}^{\frac{2}{3}}}=4\frac{{{d}^{3}}y}{d{{x}^{3}}}\] are [AIEEE 2002] |
| A. | \[1,\,\frac{2}{3}\] |
| B. | 3, 1 |
| C. | 3, 3 |
| D. | 1, 2 |
| Answer» D. 1, 2 | |
| 6344. |
\[\int_{{}}^{{}}{\frac{{{x}^{3}}-x-2}{(1-{{x}^{2}})}\ dx=}\] [AI CBSE 1985] |
| A. | \[\log \left( \frac{x+1}{x-1} \right)-\frac{{{x}^{2}}}{2}+c\] |
| B. | \[\log \left( \frac{x-1}{x+1} \right)+\frac{{{x}^{2}}}{2}+c\] |
| C. | \[\log \left( \frac{x+1}{x-1} \right)+\frac{{{x}^{2}}}{2}+c\] |
| D. | \[\log \left( \frac{x-1}{x+1} \right)-\frac{{{x}^{2}}}{2}+c\] |
| Answer» E. | |
| 6345. |
If \[\int_{{}}^{{}}{(\sin 2x+\cos 2x)\ dx=\frac{1}{\sqrt{2}}\sin (2x-c)+a}\], then the value of a and c is [Roorkee 1978] |
| A. | \[c=\pi /4\] and \[a=k\] (an arbitrary constant) |
| B. | \[c=-\pi /4\] and \[a=\pi /2\] |
| C. | \[c=\pi /2\] and a is an arbitrary constant |
| D. | None of these |
| Answer» B. \[c=-\pi /4\] and \[a=\pi /2\] | |
| 6346. |
If \[x{{e}^{xy}}=y+{{\sin }^{2}}x\], then at \[x=0,\frac{dy}{dx}=\] [IIT 1996] |
| A. | -1 |
| B. | -2 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 6347. |
If \[f:R\to R\] and \[g:R\to R\] are given by \[f(x)=\ |x|\] and \[g(x)=\ |x|\] for each \[x\in R\], then \[\{x\in R\ :g(f(x))\le f(g(x))\}=\] [EAMCET 2003] |
| A. | \[Z\cup (-\infty ,\ 0)\] |
| B. | \[(-\infty ,0)\] |
| C. | Z |
| D. | R |
| Answer» E. | |
| 6348. |
The points \[A(4,\,5,\,1),B(0,-1,-1),C(3,\,9,\,4)\]and \[D(-4,\,4,\,4)\]are [Kurukshetra CEE 2002] |
| A. | Collinear |
| B. | Coplanar |
| C. | Non- coplanar |
| D. | Non- Collinear and non-coplanar |
| Answer» C. Non- coplanar | |
| 6349. |
Let the value of \[\mathbf{p}=(x+4y)\,\mathbf{a}+(2x+y+1)\,\mathbf{b}\] and \[\mathbf{q}=(y-2x+2)\,\mathbf{a}+(2x-3y-1)\,\mathbf{b},\] where a and b are non-collinear vectors. If \[3\mathbf{p}=2\mathbf{q},\] then the value of x and y will be [RPET 1984; MNR 1984] |
| A. | - 1, 2 |
| B. | 2, - 1 |
| C. | 1, 2 |
| D. | 2, 1 |
| Answer» C. 1, 2 | |
| 6350. |
The value of \[n\in Z\] for which the function \[f(x)=\frac{\sin nx}{\sin (x/n)}\] has \[4\pi \] as its period, is |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |