If : R → R and g : R → R are defined by f(x)

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

In the triangle with vertices at A(6, 3), B(- 6, 3) and C(- 6, - 3), the median through A meets BC at P, the line AC meets the x-axis at Q, while R and S respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-I to List-II is

      List-I                        List-II

(i)    P                      (A)    (0, 0)

(ii)   Q                      (B)    (6, 0)

(iii)   R                     (C)    (- 2, 1)

(iv)   S                     (D)    (- 6, 0)

                               (E)    (- 6, - 3)

                               (F)    (- 6, 3)

A. (i) (ii) (iii) (iv) (i) D A E C
B. (i) (ii) (iii) (iv) (ii) D B E C
C. (i) (ii) (iii) (iv) (iii) D A F C
D. (i) (ii) (iii) (iv) (iv) B A F C

2.

If a = 1 - i32, then the correct matching of List-I from List-II is

         List-I                       List-II

(i)      aa                            - π3

(ii)    arg1a                       - i3

(iii)    a - a                        2i3 

(iv)     Im43a                    1

                                        π3

                                        23

correct match is 

A. (i) (ii) (iii) (iv) (i) D E C B
B. (i) (ii) (iii) (iv) (ii) D A B F
C. (i) (ii) (iii) (iv) (iii) F E B C
D. (i) (ii) (iii) (iv) (iv) D A B C

 Multiple Choice QuestionsMultiple Choice Questions

3.

If Q denotes the set of all rational numbers and fpq = p2 - q2 for any pq  Q, then observe the following statements.I. fpq is real for each pq  QII. fpq is  a complex number for each  pq  Q.Which of the following is correct ?

  • Both I and II are true

  • I is true, II is false

  • I is false, II is true

  • Both I and II are false


4.

If R R and is defined by fx = 12 - cos3xfpr each x  R, then the range of f is

  • 13,  - 1

  • 13, 1

  • (1, 2)

  • 1, 2


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5.

If : R  R and g : R  R are defined by f(x) = x - [x] and g(x) = [x] for x  R, where[x] is the greatest integer not exceeding x, then for every x  R, f(g(x)) is equal to

  • x

  • 0

  • f(x)

  • g(x)


B.

0

    Given, f(x) = x - x,  gx = x for x R.       f(g(x)) = fx                      = x - x                      = 0


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6.

2+ 5 - 6 - 35 + 14 - 65  = ?

  • 1

  • 2

  • 3

  • 4


7.

If ax = by = cz = dw, the value of x1y +1z + 1w is

  • logaabc

  • logabcd

  • logbcda

  • logcdab


8.

If Sn = 13 +23 + ... +n3 and Tn = 1 +2 + ... + n, then

  • Sn = Tn3

  • Sn = Tn2

  • Sn = Tn2

  • Sn = Tn3


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9.

If ak is the coefficient of xk in the expansion of 1 + x + x2n for k = 0, 1, 2, . . , 2n, then

  • - a0

  • 3n

  • n 3n + 1

  • n 3n


10.

The sum of the series 34 . 8 - 3 . 54 . 8 . 12 + 3 . 5 . 74 . 8 . 12 . 16 - ...

  • 32 - 34

  • 23 - 34

  • 32 - 14

  • 23 - 14


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