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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.
| 1. |
For a series the value of mean deviation is 15. The most likely value of its quartile deviation is |
| A. | 12.5 |
| B. | 11.6 |
| C. | 13 |
| D. | 9.7 |
| Answer» B. 11.6 | |
| 2. |
If the plane \[2ax-3ay+4az+6=0\] passes through the midpoint of the line joining the centres of the spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\] and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8\], then \[a\] equals [AIEEE 2005] |
| A. | ? 2 |
| B. | 2 |
| C. | ? 1 |
| D. | 1 |
| Answer» B. 2 | |
| 3. |
Three persons A, B and C are to speak at a function along with five others. If they all speak in random order, the probability that A speaks before B and B speaks before C, is |
| A. | \[\frac{3}{8}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{3}{5}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{5}\] | |
| 4. |
The average marks obtained by the students in a class are 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class? |
| A. | 15 |
| B. | 17 |
| C. | 18 |
| D. | 20 |
| Answer» B. 17 | |
| 5. |
In a class 30% students like tea, 20% like coffee and 10% like both tea and coffee. A student is selected at random then what is the probability that he does not like tea if it is known that he likes coffee? |
| A. | 44228 |
| B. | 44289 |
| C. | 44256 |
| D. | None of these |
| Answer» B. 44289 | |
| 6. |
The system of equations \[\lambda x+y+z=0,\] \[-x+\lambda y+z=0,\] \[-x-y+\lambda z=0\], will have a non zero solution if real values of \[\lambda \]are given by [IIT 1984] |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | \[\sqrt{3}\] |
| Answer» B. 1 | |
| 7. |
A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{1}{12}\] |
| D. | \[\frac{1}{24}\] |
| Answer» D. \[\frac{1}{24}\] | |
| 8. |
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is |
| A. | \[\frac{^{20}{{C}_{10}}\times {{5}^{6}}}{{{6}^{20}}}\] |
| B. | \[\frac{120\times {{5}^{7}}}{{{6}^{10}}}\] |
| C. | \[\frac{84\times {{5}^{6}}}{{{6}^{10}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 9. |
For the three events A, B and C, P (exactly one of the events A or B occurs)=P (exactly one of the two events B or C occurs)=P(exactly one of the events C or A occurs)=P and P (all the three events occur simultaneously)\[={{P}^{2}}\], where 0 |
| A. | \[\frac{3p+2{{p}^{2}}}{2}\] |
| B. | \[\frac{p+3{{p}^{2}}}{4}\] |
| C. | \[\frac{p+3{{p}^{2}}}{2}\] |
| D. | \[\frac{3p+2{{p}^{2}}}{4}\] |
| Answer» B. \[\frac{p+3{{p}^{2}}}{4}\] | |
| 10. |
The number of values of k for which the system of equations \[(k+1)x+8y=4k,\] \[kx+(k+3)y=3k-1\] has infinitely many solutions, is [IIT Screening 2002] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | Infinite |
| Answer» C. 2 | |
| 11. |
A variable line ?L? is drawn through \[O(0,\,\,0)\] to meet the lines \[{{L}_{1}}:y-x-10=0\] and \[{{L}_{2}}:y-x-20=0\] at the points A and B respectively. A point P is taken on ?L? such that\[\frac{2}{OP}=\frac{1}{OA}+\frac{1}{OB}.\] Locus of ?P? is |
| A. | \[3x+3y=40\] |
| B. | \[3x+3y+40=0\] |
| C. | \[3x-3y=40\] |
| D. | \[3y-3x=40\] |
| Answer» E. | |
| 12. |
One ticket is selected at random from 100 tickets numbered 00, 01, 02,?.98, 99, if, \[{{x}_{1}}\] and \[{{x}_{2}}\] denotes the sum and product of the digits on the tickets, then \[P({{x}_{1}}=9/{{x}_{2}}=0)\] is equal to |
| A. | 43497 |
| B. | 19/100 |
| C. | 18264 |
| D. | None of these |
| Answer» B. 19/100 | |
| 13. |
If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25? |
| A. | 0 |
| B. | 44228 |
| C. | 1 |
| D. | 1/1296 |
| Answer» B. 44228 | |
| 14. |
From past experience it is known that an investor will invest in security A with a probability of 0.6, will invest in security B with a probability 0.3 and will invest in both A and B with a probability of 0.2 what is the probability that an investor will invest neither in A nor in B? |
| A. | 0.7 |
| B. | 0.28 |
| C. | 0.3 |
| D. | 0.4 |
| Answer» D. 0.4 | |
| 15. |
Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements, is |
| A. | \[\frac{^{2n}{{C}_{n}}}{{{2}^{2n}}}\] |
| B. | \[\frac{1}{^{2n}{{C}_{n}}}\] |
| C. | \[\frac{1\cdot 3\cdot 5...(2n+1)}{{{2}^{n}}n!}\] |
| D. | \[\frac{{{3}^{n}}}{{{4}^{n}}}\] |
| Answer» B. \[\frac{1}{^{2n}{{C}_{n}}}\] | |
| 16. |
If \[(1+\sin \alpha )(1+\sin \beta )(1+\sin \gamma )=(1-\sin \alpha )\] \[(1-\sin \beta )(1-\sin \gamma )=k,\] then k is equal to: |
| A. | \[2\cos \alpha \cos \beta \cos \gamma \] |
| B. | \[-\cos \alpha \cos \beta \cos \gamma \] |
| C. | \[+\cos \alpha \cos \beta \cos \gamma \] |
| D. | \[+2sin\alpha sin\beta sin\gamma \] |
| Answer» D. \[+2sin\alpha sin\beta sin\gamma \] | |
| 17. |
If the straight line \[y=mx\]is outside the circle\[{{x}^{2}}+{{y}^{2}}-20y+90=0\], then [Roorkee 1999] |
| A. | \[m>3\] |
| B. | \[m<3\] |
| C. | \[|m|>3\] |
| D. | \[|m|<3\] |
| Answer» E. | |
| 18. |
The vectors \[(2\hat{i}-m\hat{j}+3m\hat{k})\And \]\[\{(1+m)\hat{i}-3m\hat{j}+\hat{k}\}\] include an acute angle for |
| A. | All values of m |
| B. | \[m<-2\]or \[m>-1/2\] |
| C. | \[m=-1/2\] |
| D. | \[m\in \left[ -2,-\frac{1}{2} \right]\] |
| Answer» C. \[m=-1/2\] | |
| 19. |
Let \[S(k)=1+3+5...+(2k-1)=3+{{k}^{2}}.\] Then which of the following is true? |
| A. | Principle of mathematical induction can be used to prove the formula |
| B. | \[S(k)\Rightarrow S(k+1)\] |
| C. | \[S(k)\not{\Rightarrow }S(k+1)\] |
| D. | \[S(1)\] is correct |
| Answer» C. \[S(k)\not{\Rightarrow }S(k+1)\] | |
| 20. |
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is [Kerala (Engg.) 2002] |
| A. | 80 percent |
| B. | 40 percent |
| C. | 60 percent |
| D. | 70 percent |
| Answer» D. 70 percent | |
| 21. |
If \[A=\left[ \begin{matrix} -1 & 2 \\ 2 & -1 \\ \end{matrix} \right]\]and \[B=\left[ \begin{align} & 3 \\ & 1 \\ \end{align} \right],AX=B\], then \[X=\] [MP PET 2002] |
| A. | [5 7] |
| B. | \[\frac{1}{3}\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\] |
| C. | \[\frac{1}{3}[5\,\,7]\] |
| D. | \[\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\] |
| Answer» C. \[\frac{1}{3}[5\,\,7]\] | |
| 22. |
The solution set of the equation \[{{x}^{{{\log }_{x}}{{(1-x)}^{2}}}}=9\] is [Pb. CET 2003] |
| A. | {- 2, 4} |
| B. | {4} |
| C. | {0, - 2, 4} |
| D. | None of these |
| Answer» B. {4} | |
| 23. |
If \[z=\frac{7-i}{3-4i}\] then \[{{z}^{14}}=\] [Kerala (Engg.) 2005] |
| A. | \[{{2}^{7}}\] |
| B. | \[{{2}^{7}}i\] |
| C. | \[{{2}^{14}}i\] |
| D. | \[-{{2}^{7}}i\] |
| E. | \[-{{2}^{14}}\] |
| Answer» E. \[-{{2}^{14}}\] | |
| 24. |
What is the equation of the line which passes through (4, -5) and is perpendicular to\[3x+4y+5=0?\] |
| A. | \[4x-3y-31=0\] |
| B. | \[3x-4y-41=0\] |
| C. | \[4x+3y-1=0\] |
| D. | \[3x+4y+8=0\] |
| Answer» B. \[3x-4y-41=0\] | |
| 25. |
The equation of line passing through point of intersection of lines \[3x-2y-1=0\] and \[x-4y+3=0\]and the point \[(\pi ,\ 0),\] is [RPET 1987] |
| A. | \[x-y=\pi \] |
| B. | \[x-y=\pi (y+1)\] |
| C. | \[x-y=\pi (1-y)\] |
| D. | \[x+y=\pi (1-y)\] |
| Answer» D. \[x+y=\pi (1-y)\] | |
| 26. |
The area of the region bounded by \[y=\,\,|x-1|\] and \[y=1\] is [IIT Screening 1994] |
| A. | 2 |
| B. | 1 |
| C. | \[\frac{1}{2}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{2}\] | |
| 27. |
The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-x=0,\,{{x}^{2}}+{{y}^{2}}+x=0\]is [EAMCET 1994] |
| A. | 2 |
| B. | 1 |
| C. | 4 |
| D. | 3 |
| Answer» E. | |
| 28. |
For two mutually exclusive events A and B, \[P(A)=0.2\] and \[P(\bar{A}\bigcap B)=0.3.\] What is \[P(A|(A\bigcup B))\] equal to? |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{2}{7}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{2}{7}\] | |
| 29. |
If \[u={{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\] \[v={{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] and \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the curve \[u+kv=0\]is [MNR 1987] |
| A. | The same straight line u |
| B. | Different straight line |
| C. | It is not a straight line |
| D. | None of these |
| Answer» B. Different straight line | |
| 30. |
The domain of \[f(x)=\frac{1}{\sqrt{2x-1}}-\sqrt{1-{{x}^{2}}}\] is: |
| A. | \[\left] \frac{1}{2},1 \right[\] |
| B. | \[\left[ -1,\infty \right[\] |
| C. | \[\left[ 1,\infty \right[\] |
| D. | None of these |
| Answer» B. \[\left[ -1,\infty \right[\] | |
| 31. |
\[\frac{1}{\tan 3A-\tan A}-\frac{1}{\cot 3A-\cot A}=\] |
| A. | \[\tan A\] |
| B. | \[\tan 2A\] |
| C. | \[\cot A\] |
| D. | \[\cot 2A\] |
| Answer» E. | |
| 32. |
If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6} then A I B consists of all multiples of [UPSEAT 2000] |
| A. | 16 |
| B. | 12 |
| C. | 8 |
| D. | 4 |
| Answer» C. 8 | |
| 33. |
If \[A=\left[ \begin{align} & 1 \\ & 2 \\ & 3 \\ \end{align} \right],\]then \[A{A}'=\] [MP PET 1992] |
| A. | 14 |
| B. | \[\left[ \begin{align} & 1 \\ & 4 \\ & 3 \\ \end{align} \right]\] |
| C. | \[\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \\ \end{matrix} \right]\] |
| D. | None of these |
| Answer» D. None of these | |
| 34. |
Let \[x+y=3-\cos 4\theta \] and \[x-y=4sin2\theta \] then the greatest of \[xy\]is |
| A. | \[\frac{3}{4}\] |
| B. | \[1\] |
| C. | \[\frac{1}{2}\] |
| D. | 2 |
| Answer» C. \[\frac{1}{2}\] | |
| 35. |
If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (-5, 7), then the equation of the side AB is |
| A. | \[x-y-2=0\] |
| B. | \[x-y+12=0\] |
| C. | \[x+y-12=0\] |
| D. | None of these |
| Answer» C. \[x+y-12=0\] | |
| 36. |
Let \[A=\{1,2,3\}\] and \[B=\{a,b,c\}.\] If f is a function from A to B and g is a one-one function from A to B, then the maximum number of definitions of |
| A. | f is 9 |
| B. | g is 9 |
| C. | f is 27 |
| D. | g is 16 |
| Answer» D. g is 16 | |
| 37. |
Variance of the numbers \[3,7,10,18,22\] is equal to |
| A. | 12 |
| B. | 6.4 |
| C. | \[\sqrt{49.2}\] |
| D. | 49.2 |
| Answer» E. | |
| 38. |
The parallelism condition for two straight lines one of which is specified by the equation \[ax+by+c=0\]the other being represented parametrically by \[x=\alpha \text{ }t+\beta ,\] \[y=\gamma \text{ }t+\delta \] is given by [AMU 2000] |
| A. | \[\alpha \gamma -b\alpha =0\], \[\beta =\delta =c=0\] |
| B. | \[a\alpha -b\gamma =0\], \[\beta =\delta =0\] |
| C. | \[a\alpha +b\gamma =0\] |
| D. | \[a\gamma =b\alpha =0\] |
| Answer» D. \[a\gamma =b\alpha =0\] | |
| 39. |
The equations of the tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2rx-2hy+{{h}^{2}}=0\]are [Roorkee 1989; IIT 1988; RPET 1996] |
| A. | \[x=0,y=0\] |
| B. | \[({{h}^{2}}-{{r}^{2}})x-2rhy=0,x=0\] |
| C. | \[y=0,x=4\] |
| D. | \[({{h}^{2}}-{{r}^{2}})x+2rhy=0,x=0\] |
| Answer» C. \[y=0,x=4\] | |
| 40. |
Solution of \[ydx-xdy={{x}^{2}}ydx\]is [MP PET 1999] |
| A. | \[y{{e}^{{{x}^{2}}}}=c{{x}^{2}}\] |
| B. | \[y{{e}^{-{{x}^{2}}}}=c{{x}^{2}}\] |
| C. | \[{{y}^{2}}{{e}^{{{x}^{2}}}}=c{{x}^{2}}\] |
| D. | \[{{y}^{2}}{{e}^{-{{x}^{2}}}}=c{{x}^{2}}\] |
| Answer» D. \[{{y}^{2}}{{e}^{-{{x}^{2}}}}=c{{x}^{2}}\] | |
| 41. |
In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together [EAMCET 1990; MP PET 2001; DCE 2001; UPSEAT 2002;Pb. CET 2000] |
| A. | \[{{(7\,!)}^{2}}\] |
| B. | \[7\,!\,\times \,6\,!\] |
| C. | \[{{(6\,!)}^{2}}\] |
| D. | \[7\,!\] |
| Answer» C. \[{{(6\,!)}^{2}}\] | |
| 42. |
Let A and B be two sets then \[(A\cup B)'\cup (A'\cap B)\] is equal to |
| A. | A? |
| B. | A |
| C. | B? |
| D. | None of these |
| Answer» B. A | |
| 43. |
The domain of the function \[\sqrt{{{x}^{2}}-5x+6}\]\[+\sqrt{2x+8-{{x}^{2}}}\] is |
| A. | \[[2,3]\] |
| B. | \[[-2,4]\] |
| C. | \[[-2,2]\cup [3,4]\] |
| D. | \[[-2,1]\cup [2,4]\] |
| Answer» D. \[[-2,1]\cup [2,4]\] | |
| 44. |
. If ST and SN are the lengths of the subtangent and the subnormal at the point \[\theta =\frac{\pi }{2}\]on the curve \[x=a(\theta +\sin \theta ),y=a(1-\cos \theta ),a\ne 1\], then [Karnataka CET 2005] |
| A. | \[ST=SN\] |
| B. | \[ST=2\,SN\] |
| C. | \[S{{T}^{2}}=a\,S{{N}^{3}}\] |
| D. | \[S{{T}^{3}}=a\,SN\] |
| Answer» B. \[ST=2\,SN\] | |
| 45. |
The values of \[x,y,z\] in order of the system of equations \[3x+y+2z=3,\] \[2x-3y-z=-3\], \[x+2y+z=4,\] are [MP PET 2003] |
| A. | 2, 1, 5 |
| B. | 1, 1, 1 |
| C. | 1, -2, -1 |
| D. | 1, 2, -1 |
| Answer» E. | |
| 46. |
\[a\times (b\times c)+b\times (c\times a)+c\times (a\times b)=\] [RPET 2003] |
| A. | 0 |
| B. | 2[a b c] |
| C. | a + b + c |
| D. | 3[a b c] |
| Answer» B. 2[a b c] | |
| 47. |
\[\tan \frac{A}{2}\]is equal to |
| A. | \[\pm \sqrt{\frac{1-\sin A}{1+\sin A}}\] |
| B. | \[\pm \sqrt{\frac{1+\sin A}{1-\sin A}}\] |
| C. | \[\pm \sqrt{\frac{1-\cos A}{1+\cos A}}\] |
| D. | \[\pm \sqrt{\frac{1+\cos A}{1-\cos A}}\] |
| Answer» D. \[\pm \sqrt{\frac{1+\cos A}{1-\cos A}}\] | |
| 48. |
The general solution of \[\tan 3x=1\] is[Karnataka CET 1991] |
| A. | \[n\pi +\frac{\pi }{4}\] |
| B. | \[\frac{n\pi }{3}+\frac{\pi }{12}\] |
| C. | \[n\pi \] |
| D. | \[n\pi \pm \frac{\pi }{4}\] |
| Answer» C. \[n\pi \] | |
| 49. |
If \[\tan x+\tan \left( \frac{\pi }{3}+x \right)+\tan \left( \frac{2\pi }{3}+x \right)=3,\] then |
| A. | \[\tan x=1\] |
| B. | \[\tan 2x=1\] |
| C. | \[\tan 3x=1\] |
| D. | None of these |
| Answer» D. None of these | |
| 50. |
The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is: |
| A. | \[^{30}{{C}_{7}}\] |
| B. | \[^{21}{{C}_{8}}\] |
| C. | \[^{21}{{C}_{7}}\] |
| D. | \[^{30}{{C}_{8}}\] |
| Answer» D. \[^{30}{{C}_{8}}\] | |