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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.
| 7201. |
. The angle between the lines \[xy=0\] is [MP PET 1990, 92] |
| A. | \[{{45}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{180}^{o}}\] |
| Answer» D. \[{{180}^{o}}\] | |
| 7202. |
The sum of the series \[\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+........\]to 9 terms is [MNR 1985] |
| A. | \[-\frac{5}{6}\] |
| B. | \[-\frac{1}{2}\] |
| C. | 1 |
| D. | \[-\frac{3}{2}\] |
| Answer» E. | |
| 7203. |
If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1, is |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{4}{5}\] |
| C. | \[\frac{7}{8}\] |
| D. | \[\frac{15}{16}\] |
| Answer» E. | |
| 7204. |
If \[z\] is a complex number, then \[(\overline{{{z}^{-1}}})(\overline{z})=\] |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | None of these |
| Answer» B. -1 | |
| 7205. |
The angle between the pair of straight lines \[{{x}^{2}}+4{{y}^{2}}-7xy=0\], is [MNR 1983] |
| A. | \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\] |
| B. | \[{{\tan }^{-1}}3\] |
| C. | \[{{\tan }^{-1}}\frac{\sqrt{33}}{5}\] |
| D. | \[{{\tan }^{-1}}\frac{5}{\sqrt{33}}\] |
| Answer» D. \[{{\tan }^{-1}}\frac{5}{\sqrt{33}}\] | |
| 7206. |
The area bounded by \[y=-{{x}^{2}}+2x+3\]and\[y=0\] is [Orissa JEE 2004] |
| A. | \[32\] |
| B. | \[\frac{32}{3}\] |
| C. | \[\frac{1}{32}\] |
| D. | \[\frac{1}{3}\] |
| Answer» C. \[\frac{1}{32}\] | |
| 7207. |
If z and \[\omega \]are two non-zero complex numbers such that \[|z\omega |\,=1\] and \[arg(z)-arg(\omega )=\frac{\pi }{2},\] then \[\bar{z}\omega \] is equal to [AIEEE 2003] |
| A. | 1 |
| B. | -1 |
| C. | i |
| D. | #NAME? |
| Answer» E. | |
| 7208. |
The equation of motion of a particle is given by \[s=2{{t}^{3}}-9{{t}^{2}}+12t+1\],where s and t are measured in cm and sec. The time when the particle stops momentarily is |
| A. | 1 sec |
| B. | 2 sec |
| C. | 1, 2 sec |
| D. | None of these |
| Answer» D. None of these | |
| 7209. |
If \[{{a}_{1}}={{a}_{2}}=2,\ {{a}_{n}}={{a}_{n-1}}-1\ (n>2)\], then \[{{a}_{5}}\]is |
| A. | 1 |
| B. | \[-1\] |
| C. | 0 |
| D. | \[-2\] |
| Answer» C. 0 | |
| 7210. |
If \[z\] is a purely real number such that \[\operatorname{Re}(z) |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | 0 |
| D. | \[-\frac{\pi }{2}\] |
| Answer» B. \[\frac{\pi }{2}\] | |
| 7211. |
Let \[0 |
| A. | \[P(B/A)=P(B)-P(A)\] |
| B. | \[P({{A}^{c}}\cup {{B}^{c}})=P({{A}^{c}})+P({{B}^{c}})\] |
| C. | \[P{{(A\cup B)}^{c}}=P({{A}^{c}})\,P({{B}^{c}})\] |
| D. | \[P(A/B)=P(A)\] |
| Answer» D. \[P(A/B)=P(A)\] | |
| 7212. |
A bag ?A? contains 2 white and 3 red balls and bag ?B? contains 4 white and 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag ?B? was [BIT Ranchi 1988; IIT 1976] |
| A. | \[\frac{5}{14}\] |
| B. | \[\frac{5}{16}\] |
| C. | \[\frac{5}{18}\] |
| D. | \[\frac{25}{52}\] |
| Answer» E. | |
| 7213. |
If the length of the sides of a triangle are 3, 4 and 5 units, then R (the circumradius) is [UPSEAT 2000] |
| A. | 2.0 unit |
| B. | 2.5 unit |
| C. | 3.0 unit |
| D. | 3.5 unit |
| Answer» C. 3.0 unit | |
| 7214. |
A body moves according to the formula \[v=1+{{t}^{2}}\], where v is the velocity at time t. The acceleration after 3 sec will be (v in cm/sec) [MP PET 1988] |
| A. | \[24\,cm/{{\sec }^{2}}\] |
| B. | \[12\,cm/{{\sec }^{2}}\] |
| C. | \[6\,cm/{{\sec }^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7215. |
If \[a=i+j\] and \[b=2i-k\] are two vectors, then the point of intersection of two lines \[r\times a=b\times a\] and \[r\times b=a\times b\] is [RPET 2000] |
| A. | i + j ? k |
| B. | i ? j + k |
| C. | 3i + j ? k |
| D. | 3i ? j + k |
| Answer» D. 3i ? j + k | |
| 7216. |
A particle is moving along the curve \[x=a{{t}^{2}}+bt+c.\]If \[ac={{b}^{2}},\] then the particle would be moving with uniform [Orissa JEE 2003] |
| A. | Rotation |
| B. | Velocity |
| C. | Acceleration |
| D. | Retardation |
| Answer» D. Retardation | |
| 7217. |
The coefficient of \[{{x}^{3}}\] in the expansion of \[\frac{{{(1+3x)}^{2}}}{1-2x}\] will be |
| A. | 8 |
| B. | 32 |
| C. | 50 |
| D. | None of these |
| Answer» D. None of these | |
| 7218. |
In any triangle ABC, \[a\cot A+b\cot B+c\cot C=\] |
| A. | \[r+R\] |
| B. | \[r-R\] |
| C. | \[2(r+R)\] |
| D. | \[2(r-R)\] |
| Answer» D. \[2(r-R)\] | |
| 7219. |
The area bounded by the curve \[y=4x-{{x}^{2}}\] and the \[x-\]axis, is [MP PET 1999, 2003] |
| A. | \[\frac{30}{7}\] sq. unit |
| B. | \[\frac{31}{7}\] sq. unit |
| C. | \[\frac{32}{3}\] sq. unit |
| D. | \[\frac{34}{3}\] sq. unit |
| Answer» D. \[\frac{34}{3}\] sq. unit | |
| 7220. |
Let \[z\] be a purely imaginary number such that \[\operatorname{Im}(z) |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | 0 |
| D. | \[-\frac{\pi }{2}\] |
| Answer» E. | |
| 7221. |
In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is [EAMCET 2002] |
| A. | 6 |
| B. | 8 |
| C. | 12 |
| D. | 10 |
| Answer» D. 10 | |
| 7222. |
Polar of origin (0, 0) with respect to the circle \[{{x}^{2}}+{{y}^{2}}+2\lambda x+2\mu y+c=0\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\], if [RPET 1992] |
| A. | \[c=r({{\lambda }^{2}}+{{\mu }^{2}})\] |
| B. | \[r=c\,({{\lambda }^{2}}+{{\mu }^{2}})\] |
| C. | \[{{c}^{2}}={{r}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\] |
| D. | \[{{r}^{2}}={{c}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\] |
| Answer» D. \[{{r}^{2}}={{c}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})\] | |
| 7223. |
Three numbers are in A.P. whose sum is 33 and product is 792, then the smallest number from these numbers is [RPET 1988] |
| A. | 4 |
| B. | 8 |
| C. | 11 |
| D. | 14 |
| Answer» B. 8 | |
| 7224. |
If \[x,\ y,\ z\] are real and distinct, then\[u={{x}^{2}}+4{{y}^{2}}+9{{z}^{2}}-6yz-3zx-zxy\] is always [IIT 1979] |
| A. | Non-negative |
| B. | Non-positive |
| C. | Zero |
| D. | None of these |
| Answer» B. Non-positive | |
| 7225. |
In Boolean Algebra, the zero element ?0? |
| A. | Has two values |
| B. | Is unique |
| C. | As at least two values |
| D. | None of these |
| Answer» C. As at least two values | |
| 7226. |
One coin is thrown 100 times. The probability of coming tail in odd number [MP PET 2004] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{8}\] |
| C. | \[\frac{3}{8}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{8}\] | |
| 7227. |
The combined equation of bisectors of angles between coordinate axes, is |
| A. | \[{{x}^{2}}+{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=0\] |
| C. | \[xy=0\] |
| D. | \[x+y=0\] |
| Answer» C. \[xy=0\] | |
| 7228. |
To which of the following types the straight lines represented by \[2x+3y-7=0\] and \[2x+3y-5=0\] belong [MP PET 1982] |
| A. | Parallel to each other |
| B. | Perpendicular to each other |
| C. | Inclined at \[{{45}^{o}}\]to each other |
| D. | Coincident pair of straight lines |
| Answer» B. Perpendicular to each other | |
| 7229. |
The locus of the middle points of chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-6y-10=0\] which passes through the origin, is [Roorkee 1989] |
| A. | \[{{x}^{2}}+{{y}^{2}}+x+3y=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-x+3y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+x-3y=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-x-3y=0\] |
| Answer» E. | |
| 7230. |
If the sum of three consecutive terms of an A.P. is 51 and the product of last and first term is 273, then the numbers are [MP PET 1986] |
| A. | 21, 17, 13 |
| B. | 20,16, 12 |
| C. | 22, 18, 14 |
| D. | 24, 20, 16 |
| Answer» B. 20,16, 12 | |
| 7231. |
If the probability that a student is not a swimmer is 1/5, then the probability that out of 5 students one is swimmer is |
| A. | \[^{5}{{C}_{1}}{{\left( \frac{4}{5} \right)}^{4}}\left( \frac{1}{5} \right)\] |
| B. | \[^{5}{{C}_{1}}\,\frac{4}{5}\,{{\left( \frac{1}{5} \right)}^{4}}\] |
| C. | \[\frac{4}{5}{{\left( \frac{1}{5} \right)}^{4}}\] |
| D. | None of these |
| Answer» C. \[\frac{4}{5}{{\left( \frac{1}{5} \right)}^{4}}\] | |
| 7232. |
If the first, second and last terms of an A.P. be \[a,\ b,\ 2a\] respectively, then its sum will be |
| A. | \[\frac{ab}{b-a}\] |
| B. | \[\frac{ab}{2(b-a)}\] |
| C. | \[\frac{3ab}{2(b-a)}\] |
| D. | \[\frac{3ab}{4(b-a)}\] |
| Answer» D. \[\frac{3ab}{4(b-a)}\] | |
| 7233. |
If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is |
| A. | \[10\ !\ \times 2\] |
| B. | \[10\,!\] |
| C. | \[9\,!\ \times 2\] |
| D. | None of these |
| Answer» C. \[9\,!\ \times 2\] | |
| 7234. |
The values of \[z\]for which \[|z+i|\,=\,|z-i|\] are [Bihar CEE 1994] |
| A. | Any real number |
| B. | Any complex number |
| C. | Any natural number |
| D. | None of these |
| Answer» B. Any complex number | |
| 7235. |
The spheres\[{{r}^{2}}+2{{u}_{1}}\,.\,r+2{{d}_{1}}=0\] and \[{{r}^{2}}+2{{u}_{2}}\,.\,r+2{{d}_{2}}=0\] cut orthogonally, if [AMU 1999] |
| A. | \[{{u}_{1}}\,.\,{{u}_{2}}=0\] |
| B. | \[{{u}_{1}}+{{u}_{2}}=0\] |
| C. | \[{{u}_{1}}\,.\,{{u}_{2}}={{d}_{1}}+{{d}_{2}}\] |
| D. | \[({{u}_{1}}-{{u}_{2}})\,.\,({{u}_{1}}+{{u}_{2}})=d_{1}^{2}+d_{2}^{2}\] |
| Answer» D. \[({{u}_{1}}-{{u}_{2}})\,.\,({{u}_{1}}+{{u}_{2}})=d_{1}^{2}+d_{2}^{2}\] | |
| 7236. |
Let \[{{S}_{n}}\]denotes the sum of \[n\] terms of an A.P. If \[{{S}_{2n}}=3{{S}_{n}}\], then ratio \[\frac{{{S}_{3n}}}{{{S}_{n}}}=\] [MNR 1993; UPSEAT 2001] |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» C. 8 | |
| 7237. |
Length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+5x+7y+9=0\]and \[{{x}^{2}}+{{y}^{2}}+7x+5y+9=0\]is [Kurukshetra CEE 1996] |
| A. | 9 |
| B. | 8 |
| C. | 7 |
| D. | 6 |
| Answer» E. | |
| 7238. |
The bisector of the acute angle formed between the lines \[4x-3y+7=0\]and \[3x-4y+14=0\]has the equation [Pb. CET 2004] |
| A. | \[x+y+3=0\] |
| B. | \[x-y-3=0\] |
| C. | \[x-y+3=0\] |
| D. | \[3x+y-7=0\] |
| Answer» D. \[3x+y-7=0\] | |
| 7239. |
If two of the three lines represented by the equation \[a{{x}^{3}}+b{{x}^{2}}y+cx{{y}^{2}}+d{{y}^{3}}=0\] are perpendicular, then |
| A. | \[{{a}^{2}}+{{d}^{2}}=2ac\] |
| B. | \[{{a}^{2}}+{{d}^{2}}=2bd\] |
| C. | \[{{a}^{2}}+ac+bd+{{d}^{2}}=0\] |
| D. | \[{{a}^{2}}+{{d}^{2}}=4bc\] |
| Answer» D. \[{{a}^{2}}+{{d}^{2}}=4bc\] | |
| 7240. |
The line passes through (1, 0) and \[(-\ 2,\ \sqrt{3})\] makes an angle of ...... with x?axis [RPET 1985] |
| A. | \[{{60}^{o}}\] |
| B. | \[{{120}^{o}}\] |
| C. | \[{{150}^{o}}\] |
| D. | \[{{135}^{o}}\] |
| Answer» D. \[{{135}^{o}}\] | |
| 7241. |
If the sum of three numbers of a arithmetic sequence is 15 and the sum of their squares is 83, then the numbers are [MP PET 1985] |
| A. | 4, 5, 6 |
| B. | 3, 5, 7 |
| C. | 1, 5, 9 |
| D. | 2, 5, 8 |
| Answer» C. 1, 5, 9 | |
| 7242. |
If \[a,\,b,\,c\] are in A.P., then \[(a+2b-c)\]\[(2b+c-a)\]\[(c+a-b)\] equals [Pb. CET 1999] |
| A. | \[\frac{1}{2}abc\] |
| B. | abc |
| C. | 2 abc |
| D. | 4 abc |
| Answer» E. | |
| 7243. |
If \[a,b,c,d,e\] are in A.P. then the value of \[a+b+4c\] \[-4d+e\] in terms of a, if possible is [RPET 2002] |
| A. | 4a |
| B. | 2a |
| C. | 3 |
| D. | None of these |
| Answer» E. | |
| 7244. |
If the roots of the equation \[{{x}^{2}}-2ax+{{a}^{2}}+a-3=0\]are real and less than 3, then [IIT 1999; MP PET 2000] |
| A. | \[a<2\] |
| B. | \[2\le a\le 3\] |
| C. | \[3<a\le 4\] |
| D. | \[a>4\] |
| Answer» B. \[2\le a\le 3\] | |
| 7245. |
If a, b be the roots of the quadratic equation \[a{{x}^{2}}+bx+c=0\] and \[k\] be a real number, then the condition so that \[\alpha |
| A. | \[ac>0\] |
| B. | \[a{{k}^{2}}+bk+c=0\] |
| C. | \[ac<0\] |
| D. | \[{{a}^{2}}{{k}^{2}}+abk+ac<0\] |
| Answer» E. | |
| 7246. |
If the \[{{p}^{th}}\] term of an A.P. be \[q\] and \[{{q}^{th}}\]term be p, then its \[{{r}^{th}}\] term will be [RPET 1999] |
| A. | \[p+q+r\] |
| B. | \[p+q-r\] |
| C. | \[p+r-q\] |
| D. | \[p-q-r\] |
| Answer» C. \[p+r-q\] | |
| 7247. |
A vector r is equally inclined with the co-ordinate axes. If the tip of r is in the positive octant and |r| = 6, then \[\mathbf{r}\] is |
| A. | \[2\sqrt{3}(\mathbf{i}-\mathbf{j}+\mathbf{k})\] |
| B. | \[2\sqrt{3}(-\mathbf{i}+\mathbf{j}+\mathbf{k})\] |
| C. | \[2\sqrt{3}(\mathbf{i}+\mathbf{j}-\mathbf{k})\] |
| D. | \[2\sqrt{3}(\mathbf{i}+\mathbf{j}+\mathbf{k})\] |
| Answer» E. | |
| 7248. |
Area between the curve \[y=\cos x\] and \[x-\]axis when \[0\le x\] is [MP PET 1997] |
| A. | 2 |
| B. | 4 |
| C. | 0 |
| D. | 3 |
| Answer» C. 0 | |
| 7249. |
The volume V and depth x of water in a vessel are connected by the relation \[V=5x-\frac{{{x}^{2}}}{6}\]and the volume of water is increasing at the rate of \[5c{{m}^{3}}/\sec \], when \[x=2cm\]. The rate at which the depth of water is increasing, is |
| A. | \[\frac{5}{18}cm/\sec \] |
| B. | \[\frac{1}{4}cm/\sec \] |
| C. | \[\frac{5}{16}cm/\sec \] |
| D. | None of these |
| Answer» E. | |
| 7250. |
If two events A and B are such that \[P({{A}^{c}})=0.3,\,P(B)=0.4\] and \[P(A{{B}^{c}})=0.5,\] then \[P[B/(A\cup {{B}^{c}})]\] is equal to [IIT 1994] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» D. None of these | |