If tanθ + tanθ + π3 

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

let α and β be the roots of the quadratic equation ax2 + bx + c = 0. Observe the lists given below
  List-I   List-II
(i) α = β (A) (ac2)1/3 + (a2c)1/3 + b = 0
(ii) α = 2β (B) 2b2 = 9ac
(iii) α = 3β (C) b2 = 6ac
(iv) α = β2 (D) 3b2 = 16ac
    (E) b2 = 4ac
    (F) (ac2)1/3 + (a2c)1/3 = b

The correct match of List-I from List-II is

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

2.

If a = i^ + j^ + k^, b = i^ - j^ + k^, c = i^ + j^ - k^ and d =i^ - j^ - k^, then observe the following lists
  List-I   List-II
(i) a . b (A) a . d
(ii) b . c (B) 3
(iii) a b c (C) b . d
(iv) b × c (D) 2i^ - k^
    (E) 2j^ + 2k^
    (F) 4

Then, correct match of List_I to List-II is

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

 Multiple Choice QuestionsMultiple Choice Questions

3.

The points in the set z  C : argz - 2z - 6i = π2 (where C denotes the set of all complex numbers) lie on the curve which is a

  • circle

  • pair of lines

  • parabola

  • hyperbola


4.

If w is a complex cube root of unity, then sinw10 + w23π - π4 is equal to

  • 12

  • 12

  • 1

  • 32


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5.

If m1, m2, m3 and m4 respectively denote the moduli of the complex numbers 1 + 4i, 3 + i, 1 - i and 2 - 3i, then the correct one, among the following is

  • m1 < m2 < m3 < m4

  • m4 < m3 < m2 < m1

  • m3 < m2 < m4 < m1

  • m3 < m1 < m2 < m4


6.

3csc20° - sec20° is equal to

  • 2

  • 2sin20° - csc40°

  • 4

  • 4sin20° . csc40°


7.

If A = 35°, B = 15° and C = 40°, then tan(A) · tan(B) + tan(B) . tan(C) + tan(C) . tan(A) is equal to

  • 0

  • 1

  • 2

  • 3


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8.

If tanθ + tanθ + π3 + tanθ + 2π3 = 3, then which of the following is equal to 1 ?

  • tan2θ

  • tan3θ

  • tan2θ

  • tan3θ


B.

tan3θ

Given,tanθ + tanθ + π3 + tanθ + 2π3 = 3 tanθ + tanθ + 31 - 3tanθ + tanθ - 31 + 3tanθ = 3 tanθ + 8tanθ1 - 3tan2θ = 3 9tanθ - 3tan3θ1 - 3tan2θ = 3 3tan3θ = 3  tan3θ = 1Hence, option (b) is correct.


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9.

If : RR and g : RR are defined by fx = x and gx = x - 3 for x  R, then gfx : - 85 < x < 85 is equal to

  • {0, 1}

  • {1, 2}

  • {- 3, - 2}

  • {2, 3}


10.

f : [-6, 6] R is defined by f(x) = x2 - 3for x  R, then(fofof) (-1) + (fofof) (0) + (fofof)(1) is equal to

  • f42

  • f32

  • f22

  • f2


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