Permutations & Combinations · JEE Main previous year questions

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2020 10 questions

Q52020 · 6 Sept 2020 · Shift 1
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
1. A. $2! 3! 4!$
2. B. $(3!)^{3} \cdot (4!)$
3. C. $3! (4!)^{3}$
4. D. $(3!)^{2} \cdot (4!)$
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Answer: B
Q202020 · 6 Sept 2020 · Shift 1
The position of a moving car at time t is given by $f (t) = a t^{2} + b t + c$ , $t > 0$ , where $a, b$ and $c$ are real numbers greater than 1. Then the average speed of the car over the time interval $[t_{1}, t_{2}]$ is attained at the point :
1. A. $\frac{( t _{1} + t _{2} )}{2}$
2. B. $\frac{( t _{2} - t _{1} )}{2}$
3. C. $2 a (t_{1} + t_{2}) + b$
4. D. $a (t_{2} - t_{1}) + b$
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Answer: A
Q232020 · 6 Sept 2020 · Shift 2· Numerical answer
The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .
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Answer: 120
Q212020 · 3 Sept 2020 · Shift 2· Numerical answer
The total number of 3-digit numbers, whose sum of digits is 10, is __________.
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Answer: 54
Q242020 · 2 Sept 2020 · Shift 1· Numerical answer
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
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Answer: 309
Q252020 · 2 Sept 2020 · Shift 2· Numerical answer
For a positive integer $n$ , $(1 + \frac{1}{x})^{n}$ is expanded in increasing powers of $x$ . If three consecutive coefficients in this expansion are in the ratio, $2 : 5 : 12$ , then $n$ is equal to _______.
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Answer: 118
Q12020 · 9 Jan 2020 · Shift 1
If the number of five digit numbers with distinct digits and 2 at the $1 0^{th}$ place is $336 k$ , then $k$ is equal to :
1. A.6
2. B.8
3. C.4
4. D.7
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Answer: B
Q232020 · 8 Jan 2020 · Shift 1· Numerical answer
An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.
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Answer: 490
Q232020 · 8 Jan 2020 · Shift 2· Numerical answer
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______.
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Answer: 2454
Q62020 · 7 Jan 2020 · Shift 1
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :
1. A. $\frac{5}{2} (6!)$
2. B. $6!$
3. C. $5^{6}$
4. D. $\frac{1}{2} (6!)$
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Answer: A