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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.
| 7301. |
If \[x\] is real, then the value of \[\frac{{{x}^{2}}+34x-71}{{{x}^{2}}+2x-7}\] does not lie between [Roorkee 1983] |
| A. | -9 and -5 |
| B. | -5 and 9 |
| C. | 0 and 9 |
| D. | 5 and 9 |
| Answer» E. | |
| 7302. |
The centre of the sphere \[\alpha \,\mathbf{r}-2\mathbf{u}.\mathbf{r}=\beta ,(\alpha \ne 0)\] is [AMU 1999] |
| A. | \[-\mathbf{u}/\alpha \] |
| B. | \[\mathbf{u}/\alpha \] |
| C. | \[\alpha \mathbf{u}/\beta \] |
| D. | \[\frac{\alpha +\beta }{\alpha }\mathbf{u}\] |
| Answer» E. | |
| 7303. |
If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P., where \[{{a}_{i}}>0\] for all \[i\], then the value of\[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\] \[........+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}=\] [IIT 1982] |
| A. | \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\] |
| B. | \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\] |
| C. | \[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\] |
| D. | \[\frac{n+1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\] |
| Answer» B. \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\] | |
| 7304. |
The area of the region bounded by the curve \[9{{x}^{2}}+4{{y}^{2}}-36=0\] is [Karnataka CET 2005] |
| A. | \[9\pi \] |
| B. | \[4\pi \] |
| C. | \[36\pi \] |
| D. | \[6\pi \] |
| Answer» E. | |
| 7305. |
If the position vectors of two point P and Q are respectively \[9\mathbf{i}-\mathbf{j}+5\mathbf{k}\] and \[\mathbf{i}+3\mathbf{j}+5\mathbf{k}\], and the line segment PQ intersects the YOZ plane at a point R, the PR : RQ is equal to [J & K 2005] |
| A. | 9 : 1 |
| B. | 1 : 9 |
| C. | ?1 : 9 |
| D. | ? 9 : 1 |
| Answer» E. | |
| 7306. |
In tossing 10 coins, the probability of getting exactly 5 heads is [MP PET 1996] |
| A. | \[\frac{9}{128}\] |
| B. | \[\frac{63}{256}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{193}{256}\] |
| Answer» C. \[\frac{1}{2}\] | |
| 7307. |
If \[|z|\,=1,(z\ne -1)\]and \[z=x+iy,\]then \[\left( \frac{z-1}{z+1} \right)\] is [RPET 1997] |
| A. | Purely real |
| B. | Purely imaginary |
| C. | Zero |
| D. | Undefined |
| Answer» C. Zero | |
| 7308. |
The approximate value of \[{{(7.995)}^{1/3}}\]correct to four decimal places is [MNR 1991; UPSEAT 2000] |
| A. | 1.9995 |
| B. | 1.9996 |
| C. | 1.999 |
| D. | 1.9991 |
| Answer» B. 1.9996 | |
| 7309. |
The equation of motion of a particle moving along a straight line is \[s=2\]\[{{t}^{3}}-9{{t}^{2}}+12t\], where the units of s and t are cm and sec. The acceleration of the particle will be zero after |
| A. | \[\frac{3}{2}\,sec\] |
| B. | \[\frac{2}{3}sec\] |
| C. | \[\frac{1}{2}sec\] |
| D. | Never |
| Answer» B. \[\frac{2}{3}sec\] | |
| 7310. |
If \[arg\,(z)=\theta \], then \[arg\,(\overline{z})=\] [MP PET 1995] |
| A. | \[\theta \] |
| B. | \[-\theta \] |
| C. | \[\pi -\theta \] |
| D. | \[\theta -\pi \] |
| Answer» C. \[\pi -\theta \] | |
| 7311. |
The area of smaller part between the circle \[{{x}^{2}}+{{y}^{2}}=4\]and the line \[x=1\] is [RPET 1999] |
| A. | \[\frac{4\pi }{3}-\sqrt{3}\] |
| B. | \[\frac{8\pi }{3}-\sqrt{3}\] |
| C. | \[\frac{4\pi }{3}+\sqrt{3}\] |
| D. | \[\frac{5\pi }{3}+\sqrt{3}\] |
| Answer» C. \[\frac{4\pi }{3}+\sqrt{3}\] | |
| 7312. |
If the law of motion in a straight line is \[s=\frac{1}{2}v\,t,\] then acceleration is [MP PET 1991] |
| A. | Constant |
| B. | Proportional to t |
| C. | Proportional to v |
| D. | Proportional to s |
| Answer» B. Proportional to t | |
| 7313. |
For \[0\le x\le \pi ,\] the area bounded by \[y=x\] and \[y=x+\sin x,\] is [Roorkee Qualifying 1998] |
| A. | 2 |
| B. | 4 |
| C. | \[2\pi \] |
| D. | \[4\pi \] |
| Answer» B. 4 | |
| 7314. |
If two coins are tossed 5 times, then the probability of getting 5 heads and 5 tails is [AMU 2002] |
| A. | \[\frac{63}{256}\] |
| B. | \[\frac{1}{1024}\] |
| C. | \[\frac{2}{205}\] |
| D. | \[\frac{9}{64}\] |
| Answer» B. \[\frac{1}{1024}\] | |
| 7315. |
If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]cuts off a chord of length 2b from the line \[y=mx+c\], then |
| A. | \[(1-{{m}^{2}})({{a}^{2}}+{{b}^{2}})={{c}^{2}}\] |
| B. | \[(1+{{m}^{2}})({{a}^{2}}-{{b}^{2}})={{c}^{2}}\] |
| C. | \[(1-{{m}^{2}})({{a}^{2}}-{{b}^{2}})={{c}^{2}}\] |
| D. | None of these |
| Answer» C. \[(1-{{m}^{2}})({{a}^{2}}-{{b}^{2}})={{c}^{2}}\] | |
| 7316. |
If the rate of increase of area of a circle is not constant but the rate of increase of perimeter is constant, then the rate of increase of area varies [SCRA 1996] |
| A. | As the square of the perimeter |
| B. | Inversely as the perimeter |
| C. | As the radius |
| D. | Inversely as the radius |
| Answer» D. Inversely as the radius | |
| 7317. |
If \[0 |
| A. | 0 |
| B. | \[2\,amp\text{ }(z)\] |
| C. | \[\pi \] |
| D. | \[-\pi \] |
| Answer» D. \[-\pi \] | |
| 7318. |
. The angle between the lines represented by the equation \[a{{x}^{2}}+xy+b{{y}^{2}}=0\] will be \[{{45}^{o}}\], if |
| A. | \[a=1,b=6\] |
| B. | \[a=1,b=-6\] |
| C. | \[a=6,b=1\] |
| D. | None of these |
| Answer» C. \[a=6,b=1\] | |
| 7319. |
Pair of straight lines perpendicular to each other represented by [Roorkee 1990] |
| A. | \[2{{x}^{2}}=2y(2x+y)\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+3=0\] |
| C. | \[2{{x}^{2}}=y(2x+y)\] |
| D. | \[{{x}^{2}}=2(x-y)\] |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+3=0\] | |
| 7320. |
The acute angle formed between the lines joining the origin to the points of intersection of the curves \[{{x}^{2}}+{{y}^{2}}-2x-1=0\] and \[x+y=1\], is [MP PET 1998] |
| A. | \[{{\tan }^{-1}}\left( -\frac{1}{2} \right)\] |
| B. | \[{{\tan }^{-1}}2\] |
| C. | \[{{\tan }^{-1}}\frac{1}{2}\] |
| D. | \[{{60}^{o}}\] |
| Answer» C. \[{{\tan }^{-1}}\frac{1}{2}\] | |
| 7321. |
The volume of the solid formed by rotating the area enclosed between the curve \[y={{x}^{2}}\] and the line \[y=1\] about \[y=1\] is (in cubic units [UPSEAT 2003] |
| A. | \[9\pi /5\] |
| B. | \[4\pi /3\] |
| C. | \[8\pi /3\] |
| D. | \[7\pi /5\] |
| Answer» C. \[8\pi /3\] | |
| 7322. |
The radius of the circle, having centre at (2,1) whose one of the chord is a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+6=0\] is [IIT Screening 2004] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | \[\sqrt{3}\] |
| Answer» D. \[\sqrt{3}\] | |
| 7323. |
The lines \[y=2x\]and \[x=-2y\]are [MP PET 1993] |
| A. | Parallel |
| B. | Perpendicular |
| C. | Equally inclined to axes |
| D. | Coincident |
| Answer» C. Equally inclined to axes | |
| 7324. |
The equation of the curve that passes through the point \[(1,\,2)\] and satisfies the differential equation \[\frac{dy}{dx}=\frac{-2xy}{({{x}^{2}}+1)}\]is |
| A. | \[y({{x}^{2}}+1)=4\] |
| B. | \[y({{x}^{2}}+1)+4=0\] |
| C. | \[y({{x}^{2}}-1)=4\] |
| D. | None of these |
| Answer» B. \[y({{x}^{2}}+1)+4=0\] | |
| 7325. |
If a and b (a < b) are the roots of the equation \[{{x}^{2}}+bx+c=0,\] where \[c |
| A. | \[0<\alpha <\beta \] |
| B. | \[\alpha <0<\beta <\,|\alpha |\] |
| C. | \[\alpha <\beta <0\] |
| D. | \[\alpha <0<\,|\alpha |\,<\beta \] |
| Answer» C. \[\alpha <\beta <0\] | |
| 7326. |
The length of common chord of the circles \[{{x}^{2}}+{{y}^{2}}=12\]and \[{{x}^{2}}+{{y}^{2}}-4x+3y-2=0\], is [RPET 1990, 99] |
| A. | \[4\sqrt{2}\] |
| B. | \[5\sqrt{2}\] |
| C. | \[2\sqrt{2}\] |
| D. | \[6\sqrt{2}\] |
| Answer» B. \[5\sqrt{2}\] | |
| 7327. |
The value of \[\lambda \] for which the lines \[3x+4y=5,\] \[5x+4y=4\] and \[\lambda x+4y=6\] meet at a point is[Kerala (Engg.) 2002] |
| A. | 2 |
| B. | 1 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 7328. |
After inserting \[n\] A.M.'s between 2 and 38, the sum of the resulting progression is 200. The value of \[n\] is [MP PET 2001] |
| A. | 10 |
| B. | 8 |
| C. | 9 |
| D. | None of these |
| Answer» C. 9 | |
| 7329. |
If the sum of the first 2n terms of \[2,\,5,\,8...\] is equal to the sum of the first n terms of \[57,\,59,\,61...\], then n is equal to [IIT Screening 2001] |
| A. | 10 |
| B. | 12 |
| C. | 11 |
| D. | 13 |
| Answer» D. 13 | |
| 7330. |
The lines \[{{(lx+my)}^{2}}-3{{(mx-ly)}^{2}}=0\] and \[lx+my+n=0\] form |
| A. | An isosceles triangle |
| B. | A right angled triangle |
| C. | An equilateral triangle |
| D. | None of these |
| Answer» D. None of these | |
| 7331. |
If z is a complex number such that \[\frac{z-1}{z+1}\] is purely imaginary, then [MP PET 1998, 2002] |
| A. | \[|z|\,=0\] |
| B. | \[|z|\,=1\] |
| C. | \[|z|\,>1\] |
| D. | \[|z|\,<1\] |
| Answer» C. \[|z|\,>1\] | |
| 7332. |
The area enclosed by the parabolas \[y={{x}^{2}}-1\] and \[y=1-{{x}^{2}}\] is [AMU 1999] |
| A. | 1/3 |
| B. | 2/3 |
| C. | 4/3 |
| D. | 8/3 |
| Answer» E. | |
| 7333. |
The vector equation of the plane through the point \[\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and perpendicular to the line of intersection of the planes \[\mathbf{r}.(3\mathbf{i}-\mathbf{j}+\mathbf{k})=1\] and \[\mathbf{i}+4\mathbf{j}-2\mathbf{k}=2\] is |
| A. | \[\mathbf{r}.(2\mathbf{i}+7\mathbf{j}-13\mathbf{k})=1\] |
| B. | \[\mathbf{r}.(2\mathbf{i}-7\mathbf{j}-13\mathbf{k})=1\] |
| C. | \[\mathbf{r}.(2\mathbf{i}+7\mathbf{j}+13\mathbf{k})=0\] |
| D. | None of these |
| Answer» C. \[\mathbf{r}.(2\mathbf{i}+7\mathbf{j}+13\mathbf{k})=0\] | |
| 7334. |
Area of the region bounded by the curve \[y=\tan x,\] tangent drawn to the curve at \[x=\frac{\pi }{4}\] and the x-axis is [DCE 2001] |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{4}{3}\] |
| C. | \[\log \sqrt{2}-\frac{1}{4}\] |
| D. | None of these |
| Answer» E. | |
| 7335. |
The area bounded by the curve \[y=f(x)\], x-axis and ordinates x = 1 and \[x=b\]is \[\frac{5}{24}\pi \], then \[f(x)\] is [RPET 2000] |
| A. | \[3(x-1)\cos (3x+4)+\sin (3x+4)\] |
| B. | \[(b-1)\sin (3x+4)+3\cos (3x+4)\] |
| C. | \[(b-1)\cos (3x+4)+3\sin (3x+4)\] |
| D. | None of these |
| Answer» B. \[(b-1)\sin (3x+4)+3\cos (3x+4)\] | |
| 7336. |
If there are n independent trials, p and q the probability of success and failure respectively, then probability of exactly r successes or Let p be the probability of happening an event and q its failure, then the total chance of r successes in n trials is [MP PET 1999] |
| A. | \[^{n}{{C}_{n+r}}{{p}^{r}}{{q}^{n-r}}\] |
| B. | \[^{n}{{C}_{r}}{{p}^{r-1}}{{q}^{r+1}}\] |
| C. | \[^{n}{{C}_{r}}{{q}^{n-r}}{{p}^{r}}\] |
| D. | \[^{n}{{C}_{r}}{{p}^{r+1}}{{q}^{r-1}}\] |
| Answer» D. \[^{n}{{C}_{r}}{{p}^{r+1}}{{q}^{r-1}}\] | |
| 7337. |
At least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is |
| A. | 7 |
| B. | 6 |
| C. | 5 |
| D. | None of these |
| Answer» E. | |
| 7338. |
Area under the curve \[y=\sqrt{3x+4}\] between \[x=0\] and \[x=4,\] is [AI CBSE 1979, 80] |
| A. | \[\frac{56}{9}\] sq. unit |
| B. | \[\frac{64}{9}\] sq. unit |
| C. | 8 sq. unit |
| D. | None of these |
| Answer» E. | |
| 7339. |
Which term of the sequence \[(-8+18i),\,(-6+15i),\] \[(-4+12i)\]\[,......\]is purely imaginary |
| A. | 5th |
| B. | 7th |
| C. | 8th |
| D. | 6th |
| Answer» B. 7th | |
| 7340. |
A particle moves in a straight line in such a way that its velocity at any point is given by \[{{v}^{2}}=2-3x\], where x is measured from a fixed point. The acceleration is [MP PET 1992] |
| A. | Uniform |
| B. | Zero |
| C. | Non-uniform |
| D. | Indeterminate |
| Answer» B. Zero | |
| 7341. |
Which of the following lines is concurrent with the lines \[3x+4y+6=0\]and \[6x+5y+9=0\] |
| A. | \[2x+3y+5=0\] |
| B. | \[3x+3y+5=0\] |
| C. | \[7x+9y+3=0\] |
| D. | None of these |
| Answer» C. \[7x+9y+3=0\] | |
| 7342. |
Let \[f(x)\] be a non-negative continous function such that the area bounded by the curve \[y=f(x)\], x-axis and the ordinates \[x=\frac{\pi }{4}\], \[x=\beta >\frac{\pi }{4}\] is \[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)\]. Then \[f\ \left( \frac{\pi }{2} \right)\] is [AIEEE 2005] |
| A. | \[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\] |
| B. | \[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\] |
| C. | \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\] |
| D. | \[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\] |
| Answer» C. \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\] | |
| 7343. |
The part of straight line \[y=x+1\] between \[x=2\] and \[x=3\] is revolved about x-axis, then the curved surface of the solid thus generated is [UPSEAT 2000] |
| A. | \[37\pi /3\] |
| B. | \[7\pi \sqrt{2}\] |
| C. | \[37\pi \] |
| D. | \[y={{x}^{2}}\] |
| Answer» C. \[37\pi \] | |
| 7344. |
The radius of the in circle of triangle when sides are 18, 24 and 30 cms is [Pb. CET 2004] |
| A. | 2 cm |
| B. | 4 cm |
| C. | 6 cm |
| D. | 9 cm |
| Answer» D. 9 cm | |
| 7345. |
The angle between the two lines \[y-2x=9\] and \[x+2y=-\ 7,\] is [RPET 1981, 85, 86; MP PET 1984] |
| A. | \[{{60}^{o}}\] |
| B. | \[{{30}^{o}}\] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{45}^{o}}\] |
| Answer» D. \[{{45}^{o}}\] | |
| 7346. |
If \[r(1-{{m}^{2}})+m(p-q)=0\], then a bisector of the angle between the lines represented by the equation \[p{{x}^{2}}-2rxy+q{{y}^{2}}=0\], is |
| A. | \[y=x\] |
| B. | \[y=-x\] |
| C. | \[y=mx\] |
| D. | \[my=x\] |
| Answer» D. \[my=x\] | |
| 7347. |
If \[{{(a+bx)}^{-2}}=\frac{1}{4}-3x+......\], then \[(a,b)\]= [UPSEAT 2002] |
| A. | (2, 12) |
| B. | \[(-2,12)\] |
| C. | \[(2,\,\,-12)\] |
| D. | None of these |
| Answer» B. \[(-2,12)\] | |
| 7348. |
The equation of the plane containing the line \[\mathbf{r}=\mathbf{i}+\mathbf{j}+\lambda (2\mathbf{i}+\mathbf{j}+4\mathbf{k})\] is |
| A. | \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=3\] |
| B. | \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=6\] |
| C. | \[\mathbf{r}.(-\mathbf{i}-2\mathbf{j}+\mathbf{k})=3\] |
| D. | None of these |
| Answer» B. \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=6\] | |
| 7349. |
If \[|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}-{{z}_{2}}|\], then the difference in the amplitudes of \[{{z}_{1}}\] and \[{{z}_{2}}\] is [EAMCET 1985] |
| A. | \[\frac{\pi }{4}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | 0 |
| Answer» D. 0 | |
| 7350. |
The equation of the bisectors of the angle between the lines represented by the equation \[{{x}^{2}}-{{y}^{2}}=0\], is |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[xy=0\] |
| D. | None of these |
| Answer» D. None of these | |