MCQOPTIONS
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MCQOPTIONS
This section includes 42 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
How many triangles can be formed by joining four points on a circle |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» B. 6 | |
| 2. |
The number of straight lines that can be formed by joining 20 points no three of which are in the same straight line except 4 of them which are in the same line [Kerala (Engg.) 2002] |
| A. | 183 |
| B. | 186 |
| C. | 197 |
| D. | 185 |
| Answer» E. | |
| 3. |
In a plane there are 37 straight lines of which 13 pass through the point \[A\] and 11 pass through the point \[B\]. Besides no three lines pass through one point, no line passes through both points \[A\]and \[B\] and no two are parallel. Then the number of intersection points the lines have is equal to |
| A. | 535 |
| B. | 601 |
| C. | 728 |
| D. | None of these |
| Answer» B. 601 | |
| 4. |
4 Note of Rs. 100 and 5 note in which first of Rs. 1, second of Rs. 2, Third of Rs. 5, fourth of Rs. 20 and fifth one of Rs. 50 distributed in 3 children such that each child receive at least one note of Rs. 100. The total number of ways of distribution [DCE 2005] |
| A. | \[3\times {{5}^{3}}\] |
| B. | \[5\times {{3}^{5}}\] |
| C. | \[{{3}^{6}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5. |
The number of 4 digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contain digit 1 is [AMU 2001] |
| A. | 1225 |
| B. | 1252 |
| C. | 1522 |
| D. | 480 |
| Answer» E. | |
| 6. |
The number of ways in which ten candidates \[{{A}_{1}},\ {{A}_{2}},\ .......{{A}_{10}}\] can be ranked such that \[{{A}_{1}}\] is always above \[{{A}_{10}}\] is |
| A. | \[5\ !\] |
| B. | \[2(5\ !)\] |
| C. | \[10\ !\] |
| D. | \[\frac{1}{2}(10\ !)\] |
| Answer» E. | |
| 7. |
There are 3 candidates for a post and one is to be selected by the votes of 7 men. The number of ways in which votes can be given is |
| A. | \[{{7}^{3}}\] |
| B. | \[{{3}^{7}}\] |
| C. | \[^{7}{{C}_{3}}\] |
| D. | None of these |
| Answer» C. \[^{7}{{C}_{3}}\] | |
| 8. |
The number of arrangements of the letters of the word CALCUTTA [MP PET 1984] |
| A. | 2520 |
| B. | 5040 |
| C. | 10080 |
| D. | 40320 |
| Answer» C. 10080 | |
| 9. |
In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together |
| A. | \[5\,\,!\,\,\times \,\,3\,\,!\] |
| B. | \[^{4}{{P}_{3}}\times 5\,\,!\] |
| C. | \[^{6}{{P}_{3}}\times 5\,\,!\] |
| D. | \[^{5}{{P}_{3}}\times 3\,!\] |
| Answer» D. \[^{5}{{P}_{3}}\times 3\,!\] | |
| 10. |
If \[^{12}{{P}_{r}}=1320\], then r is equal to [Pb. CET 2004] |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» D. 2 | |
| 11. |
The number of ways in which first, second and third prizes can be given to 5 competitors is |
| A. | 10 |
| B. | 60 |
| C. | 15 |
| D. | 125 |
| Answer» C. 15 | |
| 12. |
The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is |
| A. | 72 |
| B. | 96 |
| C. | 90 |
| D. | 98 |
| Answer» D. 98 | |
| 13. |
How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is not allowed) |
| A. | 224 |
| B. | 280 |
| C. | 324 |
| D. | None of these |
| Answer» B. 280 | |
| 14. |
If \[2\times {}^{n}{{C}_{5}}=9\,\,\times \,\,{}^{n-2}{{C}_{5}}\],then the value of n will be |
| A. | 7 |
| B. | 10 |
| C. | 9 |
| D. | 5 |
| Answer» C. 9 | |
| 15. |
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is [Kerala (Engg.) 2005] |
| A. | 140 |
| B. | 196 |
| C. | 280 |
| D. | 346 |
| E. | 265 |
| Answer» B. 196 | |
| 16. |
\[^{n-1}{{C}_{r}}=({{k}^{2}}-3)\,.{{\,}^{n}}{{C}_{r+1}}\] if \[k\in \] [IIT Screening 2004] |
| A. | \[[-\sqrt{3},\,\sqrt{3}]\] |
| B. | \[(-\infty ,\,-2)\] |
| C. | \[(2,\,\infty )\] |
| D. | \[(\sqrt{3},\,2)\] |
| Answer» E. | |
| 17. |
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five question. The number of choices available to him is [AIEEE 2003] |
| A. | 140 |
| B. | 196 |
| C. | 280 |
| D. | 346 |
| Answer» C. 280 | |
| 18. |
A father with 8 children takes them 3 at a time to the Zoological gardens, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is |
| A. | 336 |
| B. | 112 |
| C. | 56 |
| D. | None of these |
| Answer» D. None of these | |
| 19. |
The number of ways in which 10 persons can go in two boats so that there may be 5 on each boat, supposing that two particular persons will not go in the same boat is [Pb. CET 1999] |
| A. | \[\frac{1}{2}{{(}^{10}}{{C}_{5}})\] |
| B. | \[2{{(}^{8}}{{C}_{4}})\] |
| C. | \[\frac{1}{2}{{(}^{8}}{{C}_{5}})\] |
| D. | None of these |
| Answer» C. \[\frac{1}{2}{{(}^{8}}{{C}_{5}})\] | |
| 20. |
\[^{47}{{C}_{4}}+\underset{r=1}{\overset{5}{\mathop{\sum }}}\,{}^{52-r}{{C}_{3}}=\] [IIT 1980; RPET 2002; UPSEAT 2000] |
| A. | \[^{47}{{C}_{6}}\] |
| B. | \[^{52}{{C}_{5}}\] |
| C. | \[^{15}{{C}_{15}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 21. |
In the 13 cricket players 4 are bowlers, then how many ways can form a cricket team of 11 players in which at least 2 bowlers included [RPET 1988] |
| A. | 55 |
| B. | 72 |
| C. | 78 |
| D. | None of these |
| Answer» D. None of these | |
| 22. |
In an election there are 5 candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote [MP PET 1987] |
| A. | 125 |
| B. | 60 |
| C. | 10 |
| D. | 25 |
| Answer» E. | |
| 23. |
How many words can be formed by taking 3 consonants and 2 vowels out of 5 consonants and 4 vowels |
| A. | \[^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}}\] |
| B. | \[\frac{^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}}}{5}\] |
| C. | \[^{5}{{C}_{3}}\times {{\,}^{4}}{{C}_{3}}\] |
| D. | \[{{(}^{5}}{{C}_{3}}\times {{\,}^{4}}{{C}_{2}})\,(5)\,!\] |
| Answer» E. | |
| 24. |
There are 15 persons in a party and each person shake hand with another, then total number of hand shakes is [RPET 2002] |
| A. | \[^{15}{{P}_{2}}\] |
| B. | \[^{15}{{C}_{2}}\] |
| C. | \[15\,!\] |
| D. | \[2\,(15\,!)\] |
| Answer» C. \[15\,!\] | |
| 25. |
If \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}=9:2\] and \[^{n}{{C}_{r}}=10\], then \[r=\] |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 26. |
Everybody in a room shakes hand with everybody else. The total number of hand shakes is 66. The total number of persons in the room is [MNR 1991; Kurukshetra CEE 1998; Kerala (Engg.) 2001] |
| A. | 11 |
| B. | 12 |
| C. | 13 |
| D. | 14 |
| Answer» C. 13 | |
| 27. |
In a conference of 8 persons, if each person shake hand with the other one only, then the total number of shake hands shall be [MP PET 1984] |
| A. | 64 |
| B. | 56 |
| C. | 49 |
| D. | 28 |
| Answer» E. | |
| 28. |
If\[^{{{n}^{2}}-n}{{C}_{2}}{{=}^{{{n}^{2}}-n}}{{C}_{10}}\], then \[n=\] |
| A. | 12 |
| B. | 4 only |
| C. | \[-3\]only |
| D. | 4 or \[-3\] |
| Answer» E. | |
| 29. |
There are three girls in a class of 10 students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is |
| A. | \[7\ !\ {{\times }^{6}}{{P}_{3}}\] |
| B. | \[7\ !\ {{\times }^{8}}{{P}_{3}}\] |
| C. | \[7\ !\ \times 3\ !\] |
| D. | \[\frac{10\ !}{3\ !\ 7\ !}\] |
| Answer» C. \[7\ !\ \times 3\ !\] | |
| 30. |
The number of different words that can be formed out of the letters of the word 'MORADABAD' taken four at a time is |
| A. | 500 |
| B. | 600 |
| C. | 620 |
| D. | 626 |
| Answer» E. | |
| 31. |
The number of ways in which an arrangement of 4 letters of the word 'PROPORTION' can be made is |
| A. | 700 |
| B. | 750 |
| C. | 758 |
| D. | 800 |
| Answer» D. 800 | |
| 32. |
The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is |
| A. | 1200 |
| B. | 2400 |
| C. | 14400 |
| D. | None of these |
| Answer» D. None of these | |
| 33. |
How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed) |
| A. | 1024 |
| B. | 810 |
| C. | 2346 |
| D. | None of these |
| Answer» C. 2346 | |
| 34. |
A question paper is divided into two parts A and B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is [Roorkee 1980] |
| A. | 80 |
| B. | 100 |
| C. | 200 |
| D. | None of these |
| Answer» E. | |
| 35. |
A person goes in for an examination in which there are four papers with a maximum of \[m\] marks from each paper. The number of ways in which one can get \[2m\] marks is |
| A. | \[^{2m+3}{{C}_{3}}\] |
| B. | \[\frac{1}{3}(m+1)(2{{m}^{2}}+4m+1)\] |
| C. | \[\frac{1}{3}(m+1)(2{{m}^{2}}+4m+3)\] |
| D. | None of these |
| Answer» D. None of these | |
| 36. |
The total number of different combinations of one or more letters which can be made from the letters of the word 'MISSISSIPPI' is |
| A. | 150 |
| B. | 148 |
| C. | 149 |
| D. | None of these |
| Answer» D. None of these | |
| 37. |
The exponent of 3 in \[100\ !\] is |
| A. | 33 |
| B. | 44 |
| C. | 48 |
| D. | 52 |
| Answer» D. 52 | |
| 38. |
How many words can be made out from the letters of the word INDEPENDENCE, in which vowels always come together [Roorkee 1989] |
| A. | 16800 |
| B. | 16630 |
| C. | 1663200 |
| D. | None of these |
| Answer» B. 16630 | |
| 39. |
The number of ways in which an examiner can assign 30 marks to 8 questions, awarding not less than 2 marks to any question is |
| A. | \[^{21}{{C}_{7}}\] |
| B. | \[^{30}{{C}_{16}}\] |
| C. | \[^{21}{{C}_{16}}\] |
| D. | None of these |
| Answer» B. \[^{30}{{C}_{16}}\] | |
| 40. |
Ten persons, amongst whom are A, B and C to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is |
| A. | \[\frac{10\ !}{6}\] |
| B. | \[3\ !\ 7\ !\] |
| C. | \[^{10}{{P}_{3}}\ .\ 7\ !\] |
| D. | None of these |
| Answer» B. \[3\ !\ 7\ !\] | |
| 41. |
20 persons are invited for a party. In how many different ways can they and the host be seated at a circular table, if the two particular persons are to be seated on either side of the host [IIT 1977] |
| A. | \[20\ !\] |
| B. | \[2\ .\ 18\ !\] |
| C. | \[18\ !\] |
| D. | None of these |
| Answer» C. \[18\ !\] | |
| 42. |
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by [AIEEE 2003; RPET 2003] |
| A. | 6! × 5! |
| B. | 30 |
| C. | 5! × 4! |
| D. | 7! × 5! |
| Answer» B. 30 | |