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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.
| 7251. |
If A and B are two events such that \[P\,(A)=\frac{1}{3}\], \[P\,(B)=\frac{1}{4}\] and \[P\,(A\cap B)=\frac{1}{5},\] then \[P\,\left( \frac{{\bar{B}}}{{\bar{A}}} \right)=\] |
| A. | \[\frac{37}{40}\] |
| B. | \[\frac{37}{45}\] |
| C. | \[\frac{23}{40}\] |
| D. | None of these |
| Answer» B. \[\frac{37}{45}\] | |
| 7252. |
\[arg\left( \frac{3+i}{2-i}+\frac{3-i}{2+i} \right)\] is equal to |
| A. | \[\frac{\pi }{2}\] |
| B. | \[-\frac{\pi }{2}\] |
| C. | 0 |
| D. | \[\frac{\pi }{4}\] |
| Answer» D. \[\frac{\pi }{4}\] | |
| 7253. |
A sample of 4 items is drawn at a random without replacement from a lot of 10 items. Containing 3 defective. If X denotes the number of defective items in the sample then \[P(0 |
| A. | \[\frac{3}{10}\] |
| B. | \[\frac{4}{5}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{6}\] |
| Answer» C. \[\frac{1}{2}\] | |
| 7254. |
The number of circular permutations of n different objects is [Kerala (Engg.) 2001] |
| A. | n! |
| B. | n |
| C. | (n - 2)! |
| D. | (n - 1)! |
| Answer» E. | |
| 7255. |
A particle is moving on a straight line, where its position s (in metre) is a function of time t (in seconds) given by \[s=a{{t}^{2}}+bt+6,t\ge 0\]. If it is known that the particle comes to rest after 4 seconds at a distance of 16 metre from the starting position \[(t=0)\], then the retardation in its motion is [MP PET 1993] |
| A. | \[-1m/{{\sec }^{2}}\] |
| B. | \[\frac{5}{4}m/{{\sec }^{2}}\] |
| C. | \[-\frac{1}{2}m/{{\sec }^{2}}\] |
| D. | \[-\frac{5}{4}m/{{\sec }^{2}}\] |
| Answer» C. \[-\frac{1}{2}m/{{\sec }^{2}}\] | |
| 7256. |
In a Boolean Algebra B, for all x in \[B,({x}'{)}'=\] |
| A. | \[{x}'\] |
| B. | x |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 7257. |
The area formed by triangular shaped region bounded by the curves \[y=\sin x,\,y=\cos x\] and \[x=0\] is [MP PET 2000] |
| A. | \[x={{y}^{2}}\] |
| B. | 1 |
| C. | \[\sqrt{2}\] |
| D. | \[1+\sqrt{2}\] |
| Answer» B. 1 | |
| 7258. |
Acute angle between the lines represented by \[({{x}^{2}}+{{y}^{2}})\sqrt{3}=4xy\] is [MP PET 1992] |
| A. | \[\pi /6\] |
| B. | \[\pi /4\] |
| C. | \[\pi /3\] |
| D. | None of these |
| Answer» B. \[\pi /4\] | |
| 7259. |
If the edge of a cube increases at the rate of 60 cm per second, at what rate the volume is increasing when the edge is 90 cm |
| A. | 486000 cu cm per sec |
| B. | 1458000 cu cm per sec |
| C. | 43740000 cu cm per sec |
| D. | None of these |
| Answer» C. 43740000 cu cm per sec | |
| 7260. |
The angle between the lines \[x\cos {{\alpha }_{1}}+y\sin {{\alpha }_{1}}={{p}_{1}}\] and \[x\cos {{\alpha }_{2}}+y\sin {{\alpha }_{2}}={{p}_{2}}\]is |
| A. | \[({{\alpha }_{1}}+{{\alpha }_{2}})\] |
| B. | \[({{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}})\] |
| C. | \[2{{\alpha }_{1}}\] |
| D. | \[2{{\alpha }_{2}}\] |
| Answer» C. \[2{{\alpha }_{1}}\] | |
| 7261. |
In a Boolean Algebra B, for all x, y in \[B,(x\wedge y{)}'=\] |
| A. | \[{x}'\wedge {y}'\] |
| B. | \[{x}'\vee {y}'\] |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 7262. |
The area between the curve \[y=4+3x-{{x}^{2}}\] and x-axis is [RPET 2001] |
| A. | 125/6 |
| B. | 125/3 |
| C. | 125/2 |
| D. | None of these |
| Answer» B. 125/3 | |
| 7263. |
A contest consists of predicting the results win, draw or defeat of 7 football matches. A sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is |
| A. | \[\frac{8}{{{3}^{7}}}\] |
| B. | \[\frac{16}{{{3}^{7}}}\] |
| C. | \[\frac{280}{{{3}^{7}}}\] |
| D. | \[\frac{560}{{{3}^{7}}}\] |
| Answer» D. \[\frac{560}{{{3}^{7}}}\] | |
| 7264. |
Area included between the two curves \[{{y}^{2}}=4ax\] and \[{{x}^{2}}=4ay,\] is [SCRA 1986; Roorkee 1984; RPET 1999; Kerala (Engg.) 2002, 05] |
| A. | \[\frac{32}{3}\,{{a}^{2}}\] sq. unit |
| B. | \[\frac{16}{3}\] sq. unit |
| C. | \[\frac{32}{3}\] sq. unit |
| D. | \[\frac{16}{3}\,{{a}^{2}}\] sq. unit |
| Answer» E. | |
| 7265. |
The shortest distance between the lines \[{{\mathbf{r}}_{1}}=4\mathbf{i}-3\mathbf{j}-\mathbf{k}+\lambda (\mathbf{i}-4\mathbf{j}+7\mathbf{k})\] and \[{{\mathbf{r}}_{2}}=\mathbf{i}-\mathbf{j}-10\mathbf{k}+\lambda (2\mathbf{i}-3\mathbf{j}+8\mathbf{k})\]is [J & K 2005] |
| A. | 3 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» E. | |
| 7266. |
The line joining the points \[6\mathbf{a}-4\mathbf{b}+4\mathbf{c},\,-4\mathbf{c}\] and the line joining the points \[-\mathbf{a}-2\mathbf{b}-3\mathbf{c},\,\mathbf{a}+2\mathbf{b}-5\mathbf{c}\] intersect at |
| A. | \[-4\mathbf{a}\] |
| B. | \[4\mathbf{a}-\mathbf{b}-\mathbf{c}\] |
| C. | \[4\mathbf{c}\] |
| D. | None of these |
| Answer» E. | |
| 7267. |
\[1+\frac{1}{3}x+\frac{1.4}{3.6}{{x}^{2}}+\frac{1.4.7}{3.6.9}{{x}^{3}}+....\]is equal to |
| A. | x |
| B. | \[{{(1+x)}^{1/3}}\] |
| C. | \[{{(1-x)}^{1/3}}\] |
| D. | \[{{(1-x)}^{-1/3}}\] |
| Answer» E. | |
| 7268. |
The area of the region bounded by the curves \[y={{x}^{2}}\] and \[y=\,|x|\] is [Roorkee 1999] |
| A. | 1/6 |
| B. | 1/3 |
| C. | 5/6 |
| D. | 5/3 |
| Answer» C. 5/6 | |
| 7269. |
One ticket is selected at random from 100 tickets numbered 00, 01, 02, ...... 98, 99. If X and Y denote the sum and the product of the digits on the tickets, then \[P\,(X=9/Y=0)\] equals |
| A. | \[\frac{1}{19}\] |
| B. | \[\frac{2}{19}\] |
| C. | \[\frac{3}{19}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{19}\] | |
| 7270. |
The area between the parabola \[y={{x}^{2}}\] and the line \[y=x\] is [UPSEAT 2004] |
| A. | \[\frac{1}{6}\]sq. unit |
| B. | \[\frac{1}{3}\]sq. unit |
| C. | \[\frac{1}{2}\]sq. unit |
| D. | None of these |
| Answer» B. \[\frac{1}{3}\]sq. unit | |
| 7271. |
A biased die is tossed and the respective probabilities for various faces to turn up are given below Face : 1 2 3 4 5 6 Probability : 0.1 0.24 0.19 0.18 0.15 0.14 If an even face has turned up, then the probability that it is face 2 or face 4, is [MNR 1992] |
| A. | 0.25 |
| B. | 0.42 |
| C. | 0.75 |
| D. | 0.9 |
| Answer» D. 0.9 | |
| 7272. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[\frac{1}{(1-x)(3-x)}\] is |
| A. | \[\frac{{{3}^{n+1}}-1}{{{2.3}^{n+1}}}\] |
| B. | \[\frac{{{3}^{n+1}}-1}{{{3}^{n+1}}}\] |
| C. | \[\left( \frac{{{3}^{n+1}}-1}{{{3}^{n+1}}} \right)\] |
| D. | None of these |
| Answer» B. \[\frac{{{3}^{n+1}}-1}{{{3}^{n+1}}}\] | |
| 7273. |
The circum-radius of the triangle whose sides are 13, 12 and 5 is [Karnataka CET 2005] |
| A. | 15 |
| B. | 44240 |
| C. | 44242 |
| D. | 6 |
| Answer» C. 44242 | |
| 7274. |
The mean and variance of a binomial distribution are 6 and 4. The parameter n is [MP PET 2000] |
| A. | 18 |
| B. | 12 |
| C. | 10 |
| D. | 9 |
| Answer» B. 12 | |
| 7275. |
The rate of change of the surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to [Karnataka CET 2003] |
| A. | \[\frac{1}{r}\] |
| B. | \[\frac{1}{{{r}^{2}}}\] |
| C. | \[\because \]Surface area \[s=4\pi {{r}^{2}}\] and \[\frac{dr}{dt}=2\] \ \[\frac{ds}{dt}=4\pi \times 2r\frac{dr}{dt}\] = \[8\pi r\times 2=16\pi r\]Þ \[\frac{ds}{dt}\propto r\]. |
| D. | \[{{r}^{2}}\] |
| Answer» C. \[\because \]Surface area \[s=4\pi {{r}^{2}}\] and \[\frac{dr}{dt}=2\] \ \[\frac{ds}{dt}=4\pi \times 2r\frac{dr}{dt}\] = \[8\pi r\times 2=16\pi r\]Þ \[\frac{ds}{dt}\propto r\]. | |
| 7276. |
The amplitude of \[\frac{1+\sqrt{3}i}{\sqrt{3}+1}\] is [Karnataka CET 1992; Pb CET 2001] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[-\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | \[-\frac{\pi }{6}\] |
| Answer» B. \[-\frac{\pi }{3}\] | |
| 7277. |
Angle between the lines represented by the equation \[{{x}^{2}}+2xy\sec \theta +{{y}^{2}}=0\] is |
| A. | \[\theta \] |
| B. | \[2\theta \] |
| C. | \[\frac{\theta }{2}\] |
| D. | None of these |
| Answer» B. \[2\theta \] | |
| 7278. |
Cube root of 217 is |
| A. | 6.01 |
| B. | 6.04 |
| C. | 6.02 |
| D. | None of these |
| Answer» B. 6.04 | |
| 7279. |
If A and B are two events such that \[P\,(A)=\frac{3}{8},\,\] \[P\,(B)=\frac{5}{8}\] and \[P\,(A\cup B)=\frac{3}{4},\] then\[P\,\left( \frac{A}{B} \right)=\] |
| A. | \[\frac{2}{5}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{3}{5}\] |
| D. | None of these |
| Answer» B. \[\frac{2}{3}\] | |
| 7280. |
The equation of the plane passing through the points \[(-1,-2,\,0),(2,\,3,\,5)\] and parallel to the line \[\mathbf{r}=-3\mathbf{j}+\mathbf{k}+\mathbf{\lambda }(2\mathbf{i}+5\mathbf{j}-\mathbf{k})\] is [J & K 2005] |
| A. | \[\mathbf{r}.(-30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\] |
| B. | \[\mathbf{r}.(30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\] |
| C. | \[\mathbf{r}.(30\mathbf{i}+13\mathbf{j}-5\mathbf{k})=4\] |
| D. | \[\mathbf{r}.(30\mathbf{i}-13\mathbf{j}-5\mathbf{k})=4\] |
| Answer» B. \[\mathbf{r}.(30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\] | |
| 7281. |
For what value of 'a' the lines \[x=3,y=4\] and \[4x-3y+a=0\] are concurrent [RPET 1984] |
| A. | 0 |
| B. | -1 |
| C. | 2 |
| D. | 3 |
| Answer» B. -1 | |
| 7282. |
The area bounded by curves \[y=\cos x\] and \[y=\sin x\] and ordinates \[x=0\] and \[x=\frac{\pi }{4}\] is [Karnataka CET 2002] |
| A. | \[\sqrt{2}\] |
| B. | \[\sqrt{2}+1\] |
| C. | \[\sqrt{2}-1\] |
| D. | \[\sqrt{2}(\sqrt{2}-1)\] |
| Answer» D. \[\sqrt{2}(\sqrt{2}-1)\] | |
| 7283. |
The maximum value of \[|z|\] where z satisfies the condition \[\left| z+\frac{2}{z} \right|=2\] is |
| A. | \[\sqrt{3}-1\] |
| B. | \[\sqrt{3}+1\] |
| C. | \[\sqrt{3}\] |
| D. | \[\sqrt{2}+\sqrt{3}\] |
| Answer» C. \[\sqrt{3}\] | |
| 7284. |
Angle between the line \[\mathbf{r}=(2\mathbf{i}-\mathbf{j}+\mathbf{k})+\lambda (-\mathbf{i}+\mathbf{j}+\mathbf{k})\] and the plane \[\mathbf{r}.(3\mathbf{i}+2\mathbf{j}-\mathbf{k})=4\] is |
| A. | \[{{\cos }^{-1}}\left( \frac{2}{\sqrt{42}} \right)\] |
| B. | \[{{\cos }^{-1}}\left( \frac{-2}{\sqrt{42}} \right)\] |
| C. | \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{42}} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{-2}{\sqrt{42}} \right)\] |
| Answer» E. | |
| 7285. |
If the area bounded by \[y=a{{x}^{2}}\]and \[x=a{{y}^{2}}\], \[a>0\], is 1, then \[a=\] [IIT Screening 2004] |
| A. | 1 |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{3}\] | |
| 7286. |
Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is [MP PET 2001; Pb. CET 2000] |
| A. | \[\frac{1}{32}\] |
| B. | \[\frac{1}{16}\] |
| C. | \[\frac{3}{16}\] |
| D. | \[\frac{5}{16}\] |
| Answer» E. | |
| 7287. |
A particle moves in a straight line so that \[s=\sqrt{t}\], then its acceleration is proportional to [MP PET 2004] |
| A. | Velocity |
| B. | (Velocity)3/2 |
| C. | (Velocity) 3 |
| D. | (Velocity)2 |
| Answer» B. (Velocity)3/2 | |
| 7288. |
The position vectors of two points P and Q are \[3\mathbf{i}+\mathbf{j}+2\mathbf{k}\] and \[\mathbf{i}-2\mathbf{j}-4\mathbf{k}\] respectively. The equation of the plane through Q and perpendicular to PQ is |
| A. | \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})=28\] |
| B. | \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})=32\] |
| C. | \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})+28=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 7289. |
The equation of motion of a stone thrown vertically upward from the surface of a planet is given by \[s=10\,\,t-3{{t}^{2}}\], and the units of s and t are cm and sec respectively. The stone will return to the surface of the planet after |
| A. | \[\frac{10}{3}\sec \] |
| B. | \[\frac{5}{3}\sec \] |
| C. | \[\frac{20}{3}\sec \] |
| D. | \[\frac{5}{6}\sec \] |
| Answer» B. \[\frac{5}{3}\sec \] | |
| 7290. |
The sums of terms of two arithmatic series are in the ratio \[2n+3:6n+5\], then the ratio of their \[{{13}^{th}}\] terms is [MP PET 2004] |
| A. | 53 : 155 |
| B. | 27 : 77 |
| C. | 29 : 83 |
| D. | 31 : 89 |
| Answer» B. 27 : 77 | |
| 7291. |
Condition that the two lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]to be perpendicular is [Kurukshetra CEE 1998; MP PET 2001] |
| A. | \[ab=-1\] |
| B. | \[a=-b\] |
| C. | \[a=b\] |
| D. | \[ab=1\] |
| Answer» C. \[a=b\] | |
| 7292. |
The angle between the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\] is [MP PET 1994] |
| A. | \[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{2}}+{{a}_{2}}{{b}_{1}}}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}\] |
| B. | \[{{\cot }^{-1}}\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\] |
| C. | \[{{\cot }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] |
| D. | \[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] |
| Answer» C. \[{{\cot }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] | |
| 7293. |
A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/sec. The height of the upper end while it is descending at the rate of 4 cm/sec is [Kerala(Engg.) 2005] |
| A. | \[4\sqrt{3}\]m |
| B. | \[5\sqrt{3}\]m |
| C. | \[5\sqrt{2}\,m\] |
| D. | 8 m |
| E. | 6 m |
| Answer» C. \[5\sqrt{2}\,m\] | |
| 7294. |
If \[f(x+y,x-y)=xy\,,\] then the arithmetic mean of \[f(x,y)\] and \[f(y,x)\] is [AMU 2002, 05] |
| A. | \[x\] |
| B. | \[y\] |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 7295. |
The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is [MP PET 2000] |
| A. | 2489 |
| B. | 4735 |
| C. | 2317 |
| D. | 2632 |
| Answer» E. | |
| 7296. |
There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is [MP PET 1994] |
| A. | 23 |
| B. | 26 |
| C. | 29 |
| D. | 32 |
| Answer» C. 29 | |
| 7297. |
If polar of a circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]with respect to \[(x',y')\] is \[Ax+By+C=0\], then its pole will be [RPET 1995] |
| A. | \[\left( \frac{{{a}^{2}}A}{-C},\frac{{{a}^{2}}B}{-C} \right)\] |
| B. | \[\left( \frac{{{a}^{2}}A}{C},\frac{{{a}^{2}}B}{C} \right)\] |
| C. | \[\left( \frac{{{a}^{2}}C}{A},\frac{{{a}^{2}}C}{B} \right)\] |
| D. | \[\left( \frac{{{a}^{2}}C}{-A},\frac{{{a}^{2}}C}{-B} \right)\] |
| Answer» B. \[\left( \frac{{{a}^{2}}A}{C},\frac{{{a}^{2}}B}{C} \right)\] | |
| 7298. |
Which of the equation represents the pair of perpendicular straight lines |
| A. | \[{{y}^{2}}+xy-{{x}^{2}}=0\] |
| B. | \[{{y}^{2}}-xy+{{x}^{2}}=0\] |
| C. | \[{{x}^{2}}+xy+{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}+xy-2{{y}^{2}}=0\] |
| Answer» B. \[{{y}^{2}}-xy+{{x}^{2}}=0\] | |
| 7299. |
If \[y=3x+6{{x}^{2}}+10{{x}^{3}}+....,\]then the value of x in terms of y is |
| A. | \[1-{{(1-y)}^{-1/3}}\] |
| B. | \[1-{{(1+y)}^{1/3}}\] |
| C. | \[1+{{(1+y)}^{-1/3}}\] |
| D. | \[1-{{(1+y)}^{-1/3}}\] |
| Answer» E. | |
| 7300. |
If x is positive, the first negative term in the expansion of \[{{(1+x)}^{27\,/\,5}}\] is [AIEEE 2003] |
| A. | 7th term |
| B. | 5th term |
| C. | 8th term |
| D. | 6th term |
| Answer» D. 6th term | |