The number of five digit numbers divisible by 5 that can be forme

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

Let A and B be events in a sample space S suchthat P(A) = 0.5, P(B) = 0.4 andP(A B) = 0.6. Observe the following lists
  List I   List II
(i) PA  B (1) 0.4
(ii) PA  B (2) 0.2
(iii) PA  B (3) 0.3
(iv) PA  B (4) 0.1

The correct match of List I from List II is

A. (i) (ii) (iii) (iv) (i) (1) (2) (3) (4)
B. (i) (ii) (iii) (iv) (ii) (3) (2) (1) (4)
C. (i) (ii) (iii) (iv) (iii) (3) (2) (1) (4)
D. (i) (ii) (iii) (iv) (iv) (3) (1) (2) (4)

 Multiple Choice QuestionsMultiple Choice Questions

2.

If f(x) = x + sinx for x  - π2, π2, then its left hand derivative at x = 0 is

  • 0

  • - 1

  • - 2

  • - 3


3.

If 1° = α. radians, then the approximate value of cos(60° 1') is

  • 12 + α3120

  • 12 - α120

  • 12 - α3120

  • 12 + α120


4.

If u = ux, y = siny + ax - y + ax2, then it implies

  • uxx = a2 . uyy

  • uyy = a2uxx

  • uxx = - a2 . uyy

  • uyy = - a2uxx


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5.

If a, b and n are natural numbers, then a2n - 1  + b2n - 1 is divisible by

  • a + b

  • a - b

  • a3 + b3

  • a2 + b2


6.

A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ballis 14400, then n is equal to

  • 6

  • 5

  • 4

  • 3


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7.

The number of five digit numbers divisible by 5 that can be formed using the numbers 0, 1, 2, 3, 4, 5 without repetition is

  • 240

  • 216

  • 120

  • 96


B.

216

The five digit number is formed only when unit place is either 0 or 5.

Case I. When 0 is in unit place, then rest of numbers can be selected in P45 ways.

= 5! = 120

Case II. When 5 is in unit place, then rest of numbers can be selected in P45 ways 

= 5! = 120

And we have to subtract those cases in which 0 is in thousand place.

The number of ways = P34 = 24

 Required number of ways = 120 + 120 - 24 = 216


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8.

P815 = A + 8 . P714  A = 

  • P614

  •  P814

  •  P715

  •  P916


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9.

If C1n - 1 + C4n - 1 > C3n, then the minimum value of n is 

  • 5

  • 6

  • 7

  • 8


10.

If the coefficients of rth and (r + 1)th terms in the expansion of (3 + 7x)29 are equal, then r is equal to

  • 14

  • 15

  • 18

  • 21


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