Permutations & Combinations · JEE Main previous year questions

If a metallic circular plate of radius $50\mathrm{cm}$ is heated so that its radius increases at the rate of $1\mathrm{mm}$ per hour, then the rate at which, the area of the plate increases (in $\mathrm{c}{\mathrm{m}}^2/hour$) is

1. A.$5\pi$
2. B.$10\pi$
3. C.$100\pi$
4. D.$50\pi$

If a circular iron sheet of radius $30\mathrm{cm}$ is heated such that its area increases at the uniform rate of $6\pi \mathrm{c}{\mathrm{m}}^2/hr$, then the rate (in $mm/hr$) at which the radius of the circular sheet increases is

1. A.1.0
2. B.0.1
3. C.1.1
4. D.2.0

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is :

1. A.at least 500 but less than 750
2. B.at least 750 but less than 1000
3. C.at least 1000
4. D.less than 500

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is

1. A.5040
2. B.6210
3. C.385
4. D.1110

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

1. A.601
2. B.600
3. C.603
4. D.602

If non zero numbers $a,b,c$ are in H.P., then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point. That point is :

1. A.$(-1,2)$
2. B.$(-1,-2)$
3. C.$(1,-2)$
4. D.$\left(1,-\frac{1}{2}\right)$

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

1. A.480
2. B.240
3. C.360
4. D.120

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

1. A.${}^8{C}_3$
2. B.21
3. C.$3^8$
4. D.5

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :

1. A.216
2. B.375
3. C.400
4. D.720

Numbers greater than 1000 but less than 4000 are formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :

1. A.125
2. B.105
3. C.374
4. D.625

Five digit numbers divisible by 3 are formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :

1. A.312
2. B.3125
3. C.120
4. D.216