MCQOPTIONS
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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.
| 7901. |
There are only two women among 20 persons taking part in a pleasure trip. The 20 persons are divided into two groups, each group consisting of 10 persons. Then the probability that the two women will be in the same group is |
| A. | 43709 |
| B. | 14124 |
| C. | 13028 |
| D. | none |
| Answer» B. 14124 | |
| 7902. |
In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is |
| A. | \[\frac{2{}^{n}{{C}_{2}}}{{}^{({}^{n}{{C}_{2}}-n)}{{C}_{2}}}\] |
| B. | \[\frac{^{n(n-1)}{{C}_{2}}}{{}^{({}^{n}{{C}_{2}}-n)}{{C}_{2}}}\] |
| C. | \[\frac{^{n}{{C}_{4}}}{{}^{({}^{n}{{C}_{2}}-\,n)}{{C}_{2}}}\] |
| D. | none of these |
| Answer» D. none of these | |
| 7903. |
The chances of throwing a total of 3 or 5 or 11 with two dice is [Kurukshetra CEE 1996] |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{1}{9}\] |
| C. | \[\frac{2}{9}\] |
| D. | \[\frac{19}{36}\] |
| Answer» D. \[\frac{19}{36}\] | |
| 7904. |
A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is [MP PET 1987] |
| A. | 5/8 |
| B. | 1/2 |
| C. | 1/3 |
| D. | 2/3 |
| Answer» E. | |
| 7905. |
In a single throw of two dice, the probability of obtaining a total of 7 or 9, is [AISSE 1979] |
| A. | \[\frac{5}{18}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{1}{9}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{6}\] | |
| 7906. |
The corners of regular tetrahedrons are numbered 1, 2, 3, 4. Three tetrahedrons are tossed. The probability that the sum of upward corners will be 5 is [AMU 1999] |
| A. | \[\frac{5}{24}\] |
| B. | \[\frac{5}{64}\] |
| C. | \[\frac{3}{32}\] |
| D. | \[\frac{3}{16}\] |
| Answer» D. \[\frac{3}{16}\] | |
| 7907. |
If X follows a binomial distribution with parameters \[n=6\]and p. If \[9P\,(X=4)=P\,(X=2),\] then \[p=\] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | 1 |
| Answer» D. 1 | |
| 7908. |
In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is [MP PET 1987] |
| A. | \[\frac{9}{25}\] |
| B. | \[\frac{16}{25}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{8}{25}\] |
| Answer» C. \[\frac{4}{5}\] | |
| 7909. |
The value of \[{{1}^{2}}.{{C}_{1}}+{{3}^{2}}.{{C}_{3}}+{{5}^{2}}.{{C}_{5}}+...\] is: |
| A. | \[n{{(n-1)}^{n-2+n{{.2}^{n-1}}}}\] |
| B. | \[n{{(n-1)}^{n-2}}\] |
| C. | \[n{{(n-1)}^{n-3}}\] |
| D. | None of these |
| Answer» E. | |
| 7910. |
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places? |
| A. | 18 |
| B. | 28 |
| C. | 6 |
| D. | 27 |
| Answer» B. 28 | |
| 7911. |
\[f:\{1,2,3,4,5\}\to \{1,2,3,4,5\}\] that are onto and \[f(i)\ne i,\] is equal to |
| A. | 9 |
| B. | 44 |
| C. | 16 |
| D. | None of these |
| Answer» C. 16 | |
| 7912. |
The least positive integral values of n which satisfies the inequality \[^{10}{{C}_{n-1}}>{{2.}^{10}}{{C}_{n}}\] |
| A. | 7 |
| B. | 8 |
| C. | 9 |
| D. | 10 |
| Answer» C. 9 | |
| 7913. |
Six teachers and sic students have to sit round a circular table such that there is a teacher between any two students. The number of ways I which they can sit is |
| A. | \[6!\times 6!\] |
| B. | \[5!\times 6!\] |
| C. | \[5!\,\times 5!\] |
| D. | None of these |
| Answer» C. \[5!\,\times 5!\] | |
| 7914. |
The sides AB, BC, CA, of a triangle ABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is |
| A. | 220 |
| B. | 204 |
| C. | 205 |
| D. | 195 |
| Answer» D. 195 | |
| 7915. |
A seven digit number divisible by 9 is to be formed by using 7 out of number\[\{1,2,3,4,5,6,7,8,9\}\]. The number of ways in which this can be done is |
| A. | \[7!\] |
| B. | \[2\times 7!\] |
| C. | \[3\times 7!\] |
| D. | \[4\times 7!\] |
| Answer» E. | |
| 7916. |
If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is |
| A. | 85 |
| B. | 100 |
| C. | 120 |
| D. | 240 |
| Answer» D. 240 | |
| 7917. |
There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is: |
| A. | 816 |
| B. | 806 |
| C. | 805 |
| D. | 813 |
| Answer» C. 805 | |
| 7918. |
'n' is selected form the set \[\{1,2,3...,100\}\]and the number \[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\] is formed. Total number of ways of selecting 'n' so that the formed number is divisible by 4, is equal to |
| A. | 50 |
| B. | 49 |
| C. | 48 |
| D. | None of these |
| Answer» C. 48 | |
| 7919. |
A boat is to be manned by eight men of whom 2 can only row on bow side and 3 can only row on stroke side, the number of ways in which the crew can be arranged is |
| A. | 4360 |
| B. | 5760 |
| C. | 5930 |
| D. | None of these |
| Answer» C. 5930 | |
| 7920. |
In a 12 -storey house ten people enter a lift cabin. It is known that they will left in groups of 2,3 and 5 people at different storeys. The number of ways they can do so if the left does not stop to the second storey is |
| A. | 78 |
| B. | 112 |
| C. | 720 |
| D. | 132 |
| Answer» D. 132 | |
| 7921. |
If 16 identical pencils are distributed among 4 children such that each gets at least 3 pencils. The number of ways of distributing the pencils is |
| A. | 15 |
| B. | 25 |
| C. | 35 |
| D. | 40 |
| Answer» D. 40 | |
| 7922. |
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 |
| A. | 346 |
| B. | 140 |
| C. | 196 |
| D. | 280 |
| Answer» D. 280 | |
| 7923. |
If \[^{n}{{P}_{3}}{{+}^{n}}{{C}_{n-2}}=14n\], then \[n=\] |
| A. | 5 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» B. 6 | |
| 7924. |
There is a rectangular sheet of dimension \[(2m-1)\]×\[(2n-1)\], (where \[m>0,n>0)\]. It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length [IIT Screening 2005] |
| A. | \[{{(m+n+1)}^{2}}\] |
| B. | \[mn(m+1)\,(n+1)\] |
| C. | \[{{4}^{m+n-2}}\] |
| D. | \[{{m}^{2}}{{n}^{2}}\] |
| Answer» E. | |
| 7925. |
If \[a,\ b,\ c,\ d,\ e\] are prime integers, then the number of divisors of \[a{{b}^{2}}{{c}^{2}}de\] excluding 1 as a factor, is |
| A. | 94 |
| B. | 72 |
| C. | 36 |
| D. | 71 |
| Answer» E. | |
| 7926. |
The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2, and 3 is |
| A. | 26664 |
| B. | 39996 |
| C. | 38664 |
| D. | none of these |
| Answer» D. none of these | |
| 7927. |
Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is |
| A. | \[{{4}^{2}}\] |
| B. | \[{{2}^{4}}\] |
| C. | 4! |
| D. | none of these |
| Answer» E. | |
| 7928. |
If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET 2004] |
| A. | -16 |
| B. | 16 |
| C. | 4 |
| D. | -4 |
| Answer» C. 4 | |
| 7929. |
If the bisectors of the lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\] be \[{{x}^{2}}-2qxy-{{y}^{2}}=0,\] then [MP PET 1993; DCE 1999; RPET 2003; AIEEE 2003; Kerala (Engg.) 2005] |
| A. | \[pq+1=0\] |
| B. | \[pq-1=0\] |
| C. | \[p+q=0\] |
| D. | \[p-q=0\] |
| Answer» B. \[pq-1=0\] | |
| 7930. |
The equation of the pair of straight lines, each of which makes an angle \[\alpha \]with the line \[y=x\], is [MP PET 1990] |
| A. | \[{{x}^{2}}+2xy\sec 2\alpha +{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| C. | \[{{x}^{2}}-2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}-2xy\sec 2\alpha +{{y}^{2}}=0\] |
| Answer» E. | |
| 7931. |
If p : It is snowing, q : I am cold, then the compound statement 'it is snowing and it is not that I am cold'? is given by |
| A. | \[p\wedge (\tilde{\ }q)\] |
| B. | \[p\wedge q\] |
| C. | \[(\tilde{\ }p)\wedge q\] |
| D. | \[(\tilde{\ }p)\wedge (\tilde{\ }q)\] |
| Answer» B. \[p\wedge q\] | |
| 7932. |
The contrapositive of \[p\to (\tilde{\ }q\to \tilde{\ }r)\] is- |
| A. | \[(\tilde{\ }q\wedge r)\to \tilde{\ }p\] |
| B. | \[(q\to r)\to \tilde{\ }p\] |
| C. | \[(q\vee \tilde{\ }r)\to \tilde{\ }p\] |
| D. | None of these |
| Answer» B. \[(q\to r)\to \tilde{\ }p\] | |
| 7933. |
Negation of 'Paris in France and London is in England'' is |
| A. | Paris is in England and London is in France |
| B. | Paris is not in France or London is not in England |
| C. | Paris is in England or London is in France |
| D. | None of these |
| Answer» C. Paris is in England or London is in France | |
| 7934. |
The statement 'If \[{{2}^{2}}=5\] then I get first class'? is logically equivalent to |
| A. | \[{{2}^{2}}=5\] and I do not get first class |
| B. | \[{{2}^{2}}=5\] or I do not get first class |
| C. | \[{{2}^{2}}\ne 5\] or I get first class |
| D. | None of these |
| Answer» D. None of these | |
| 7935. |
The inverse of the statement, if x is zero then we cannot divide by x? is |
| A. | If we cannot divide by x, then x is zero |
| B. | If we cannot divide by x, then x is not zero |
| C. | If x is not zero then we divide by x |
| D. | None. |
| Answer» D. None. | |
| 7936. |
Negation of the proposition: If we control population growth, we prosper |
| A. | If we do not control population growth, we prosper |
| B. | If we control population growth, we do not prosper |
| C. | We control population but we do not prosper |
| D. | We do not control population, but we prosper. |
| Answer» D. We do not control population, but we prosper. | |
| 7937. |
Which of the following statement is a contradiction? |
| A. | \[(\tilde{\ }p\vee \tilde{\ }q)\vee (p\vee \tilde{\ }q)\] |
| B. | \[(p\to q)\vee (p\wedge \tilde{\ }q)\] |
| C. | \[(\tilde{\ }p\wedge q)\wedge (\tilde{\ }q)\] |
| D. | \[(\tilde{\ }p\wedge q)\vee (\tilde{\ }q)\] |
| Answer» D. \[(\tilde{\ }p\wedge q)\vee (\tilde{\ }q)\] | |
| 7938. |
Truth value of the statement ?It is false that \[3+3=33\] Or \[1+2=12'\] is |
| A. | T |
| B. | F |
| C. | Both T and F |
| D. | 54 |
| Answer» B. F | |
| 7939. |
Which of the following is a statement? |
| A. | Open the door. |
| B. | Do your homework. |
| C. | Switch on the fan. |
| D. | Two plus two is four. |
| Answer» E. | |
| 7940. |
The negation of \[(p\vee \tilde{\ }q)\wedge q\] is |
| A. | \[(\tilde{\ }p\vee q)\wedge \tilde{\ }q\] |
| B. | \[(p\wedge \tilde{\ }q)\vee q\] |
| C. | \[(\tilde{\ }p\wedge q)\vee \tilde{\ }q\] |
| D. | \[(p\wedge \tilde{\ }q)\vee \tilde{\ }q\] |
| Answer» D. \[(p\wedge \tilde{\ }q)\vee \tilde{\ }q\] | |
| 7941. |
The contrapositive of \[(p\vee q)\Rightarrow r\] is |
| A. | \[r\Rightarrow (p\vee q)\] |
| B. | \[\tilde{\ }r\Rightarrow (p\vee q)\] |
| C. | \[\tilde{\ }r\Rightarrow \tilde{\ }p\wedge \tilde{\ }q\] |
| D. | \[p\Rightarrow (q\vee r)\] |
| Answer» D. \[p\Rightarrow (q\vee r)\] | |
| 7942. |
Consider the following statementsp: A tumbler is half empty.q: A tumbler is half full.The, the combination form of 'p if and only if q'? is |
| A. | A tumbler is half empty and half full |
| B. | A tumbler is half empty if and only if it is hatful |
| C. | Both (a) and (b) |
| D. | None of the above |
| Answer» C. Both (a) and (b) | |
| 7943. |
Consider the two statements p: He is intelligent and Q: he is strong. Then the symbolic form of the statement ?it is not true that he is either intelligent or strong?? is |
| A. | \[\tilde{\ }P\vee Q\] |
| B. | \[\tilde{\ }P\wedge \tilde{\ }Q\] |
| C. | \[\tilde{\ }P\wedge Q\] |
| D. | \[\tilde{\ }(P\vee Q)\] |
| Answer» E. | |
| 7944. |
\[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is |
| A. | A tautology |
| B. | A contradiction |
| C. | Both a tautology and a contradiction |
| D. | Neither a tautology nor a contradiction |
| Answer» C. Both a tautology and a contradiction | |
| 7945. |
Let p, q and r be any three logical statements. Which of the following is true? |
| A. | \[\tilde{\ }[p\wedge (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge q\] |
| B. | \[\tilde{\ }[(p\vee q)\wedge (\tilde{\ }r)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\vee (\tilde{\ }r)\] |
| C. | \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge q\] |
| D. | \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge \tilde{\ }q\] |
| Answer» D. \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge \tilde{\ }q\] | |
| 7946. |
If \[p\Rightarrow (\tilde{\ }p\,\vee \,q)\] is false, the truth values of p and q are respectively |
| A. | \[F,T\] |
| B. | \[F,F\] |
| C. | \[T,T\] |
| D. | \[T,F\] |
| Answer» E. | |
| 7947. |
For integers m and n, both greater than 1, consider three following three statements: P: m divides n Q: m divides \[{{n}^{2}}\] R: m is prime, then |
| A. | \[Q\wedge R\to P\] |
| B. | \[P\wedge Q\to R\] |
| C. | \[Q\to R\] |
| D. | \[Q\to P\] |
| Answer» B. \[P\wedge Q\to R\] | |
| 7948. |
If p: Ashok works hard q: Ashok gets good grade The verbal form for \[(\tilde{\ }p\to q)\] is |
| A. | If Ashok works hard then gets good grade |
| B. | If Ashok does not work hard then he gets good grade |
| C. | If Ashok does not work hard then he does not get good grade |
| D. | Ashok works hard if and only if he gets grade |
| Answer» C. If Ashok does not work hard then he does not get good grade | |
| 7949. |
Contrapositive of the statement \[p\Rightarrow q\] is |
| A. | \[\tilde{\ }q\Rightarrow \,\tilde{\ }p\] |
| B. | \[p\Leftrightarrow q\] |
| C. | \[q\Rightarrow p\] |
| D. | None of these |
| Answer» B. \[p\Leftrightarrow q\] | |
| 7950. |
\[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\vee ~q)\]is |
| A. | a contradiction |
| B. | a tautology |
| C. | either [a] or [b] |
| D. | neither [a] nor [b] |
| Answer» B. a tautology | |