If N denotes the set of all positive integers and if f : N&n

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

Observe the following lists
List I List II
(A) [a b c] 1. abcosab
(B) c × a × b 2 .(a . c)b - (a . b) c
(C) a × b × c 3. a . b × c
(D) a . b 4. ab
  5. (b . c)a - (a . b)c

Then the correct match for List I from List II is

A. A B C D (i) 1 2 3 4
B. A B C D (ii) 3 5 2 1
C. A B C D (iii) 3 5 5 1
D. A B C D (iv) 3 2 5 1

 Multiple Choice QuestionsMultiple Choice Questions

2.

x  R : x - x = 5 is equal to

  • R, the set of all real numbers

  • ϕ, the empty set

  • x  x < 0

  • x  R : x  0


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3.

If N denotes the set of all positive integers and if f : N  N efined by f(n) = the sum of positive divisors of n then, f(2k, 3), where k is a positive integers, is

  • 2k + 1 - 1

  • 2(2k + 1 - 1)

  • 3(2k + 1 - 1)

  • 4(2k + 1 - 1)


C.

3(2k + 1 - 1)

Given that f(x) = the sum of positive divisors of n. f2k . 3 = 31 +2+22 + 23 + ... + 2k                  = 32k + 1 - 12 - 1 = 32k + 1 - 1


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4.

x = 123 + 13, then x2 - 1x - x2 - 1

  • 1

  • 2

  • 3

  • 12


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5.

If a, b, c  0 and belong to the set to {0, 1, 2, 3, ..., 9}, then log10a + 10b + 102c10- 4a + 10- 3b + 10- 2c is equal to

  • 1

  • 2

  • 3

  • 4


6.

nn + 12n + 1 : n  Z 

  • 6k : k  Z

  • 12k : k  Z

  • 18k : k  Z

  • 24k : k  Z


7.

A three digit numbern is such that the last twodigits of it are equal and differ from the first. The number of such n's is

  • 64

  • 72

  • 81

  • 900


8.

If (1 + x)15 = a0 + a1x + ... + a15x15, then r = 115rarar - 1 is equal to

  • 110

  • 115

  • 120

  • 135


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9.

The coefficient of x3y4z5 in the expansion of (xy + yz + xz)6 is

  • 70

  • 60

  • 50

  • None of these


10.

If x < 12, then the coefficient of xr in the expansion of 1 +2x1 - 2x2, is

  • r2r

  • (2r - 1)2r

  • r22r + 1

  • (2r + 1)2r


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