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Permutations an...

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  • Question 1
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    A college offers 77 courses in the morning and 55 courses in the evening. Find the number of ways a student can select exactly one course either in the morning or in the evening.

  • Question 2
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    Seven person P1,P2......,P7P_1,P_2......, P_7 initially seated at chairs C1,C2,.....C7C_1,C_2,.....C_7 respectively.They all left there chairs simultaneously for hand wash. Now in how many ways they can again take seats such that no one sits on his own seat and P1P_1, sits on C2C_2 and P2P_2 sits on C3C_3 ?

  • Question 3
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    If mm denotes the number of 55 digit numbers if each successive digits are in their descending order of magnitude and nn is the corresponding figure. When the digits and in their ascending order of magnitude then (mn)(m-n) has the value

  • Question 4
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    There are 22 identical white balls, 33 identical red balls and 44 green balls of different shades. The number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same colour, is

  • Question 5
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    Two classrooms A and B having capacity of 2525 and (n25)(n-25) seats respectively. AnA_n denotes the number of possible seating arrangements of room A'A', when 'n' students are to be seated in these rooms, starting from room A'A' which is to be filled up to its capacity. If AnAn1=25!(49C25)A_n-A_{n-1}=25!(^{49}C_{25}) then 'n' equals:

  • Question 6
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    Consider the following statements:
    $$S_1: \lim_\limits{x \to 0} \dfrac{[x]}{x}$$ is an indeterminate form (where [.] denotes greatest integer function).
    $$S_2: \lim_\limits{x\to\infty}\dfrac{sin(3^x)}{3^x}=0$$
    $$S_3: \lim_\limits{x \to \infty}\sqrt{\dfrac{x- sinx}{x+cos^2x}}$$ does not exist.
    $$S_4:  \lim_\limits{n\to \infty}\dfrac{(n+2)!+(n+1)!}{(n+3)! }(n \in N=0$$
    State, in order, whether S1,S2,S3,S4S_1, S_2, S_3, S_4 are true or false

  • Question 7
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    Observe the pattern carefully
    11×11=12111\times11=121
    111×111=12321111\times111=12321
    1111×1111=?1111\times1111=\,?

  • Question 8
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    How many 10digit10-digit numbers can be formed by using the digits 11 and 22?

  • Question 9
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    What is the value of nCn^nC_n?

  • Question 10
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    There are infinite, alike, blue, red, green and yellow balls. Find the number of ways to select 1010 balls.

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