Let A = {1, 2, 3, ... , n} and B = {a, b, c}, then the number of

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If the normal to the curve y = f(x) at (3, 4) makes an angle 3π4 with the positive x-axis, then f'(3) is equal to :

  • - 1

  • 34

  • 1

  • 34


2.

The number of integral solutions of x1 + x2 + x3 = 0, with x - 5, is :

  • C215

  • C216

  • C217

  • C218


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3.

Let A = {1, 2, 3, ... , n} and B = {a, b, c}, then the number of functions from A to B that are onto is:

  • 3n - 2n

  • 3n - 2n - 1

  • 3(2n - 1)

  • 3n - 3(2n - 1)


D.

3n - 3(2n - 1)

 A = 1, 2, 3, ..., n and a, b, c

 nA = n and nB = 3

Number of onto function from A to B

= r = 13- 13 - r Cr3 rn= - 12 C13 1n + - 11 C23 2n +- 10 C33 3n= 3n - 3 . 2n  + 3= 3n - 32n - 1


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4.

Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is:

  • 9

  • 12

  • 10

  • 14


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5.

In a group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 7 is :

  • 7

  • 3

  • 9

  • 1


6.

A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even}is:

  • 517

  • 417

  • 516

  • 518


7.

If PA = 112, PB = 512 and PBA = 115, then P(A B) is equal to :

  • 89180

  • 90180

  • 91180

  • 92180


8.

If b2  4ac for the equation ax4 + bx2 + c = 0, then all the roots of the equation will be real if:

  • b > 0, a < 0, c > 0

  • b < 0, a > 0, c > 0

  • b > 0, a > 0, c > 0

  • b > 0, a > 0, c < 0


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9.

If x > 0 and log3(x) + log3x + log3x4 + log3x8 + log3x16 = 4, then x equals:

  • 9

  • 81

  • 1

  • 27


10.

The number of real roots of the equation x + 1x3 + x + 1x = 0 is :

  • 0

  • 2

  • 4

  • 6


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