The value of the sum 1 · 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 +&n

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMatch The Following

1.

Match the following columns.
       
A The centroid of the triangle formed by (2, 3, - 1), (5, 6, 3), (2, -3 ,1) is p (2, 2, 2)
B The circumcentre of the triangle formed by (1,2, 3) (2, 3, 1), (3, 1, 2) is q (3, 1, 4)
C The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is r (1, 1, 0)
D The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is  s (3, 2, 1)
E The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is t (0, 0, 0)

 

A. A B C D (i) s p q r
B. A B C D (ii) p q r s
C. A B C D (iii) s r q r
D. A B C D (iv) s p t r

 Multiple Choice QuestionsMultiple Choice Questions

2.

If f : R  R, g : R  R are defined by fx = 5x - 3, gx = x2 + 3, then gof - 13 = ?

  • 253

  • 11125

  • 925

  • 25111


3.

If A = x  Rlπ4  x π3 and fx = sinx - x, then fA =?

  • 32 - π3, 12 - π4

  • - 12 - π4, 32 - π3

  • - π3, - π4

  • π4, π3


Advertisement

4.

The value of the sum 1 · 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 +  ... upto n terms is equal to

  • 16n22n2 + 1

  • 16n2 - 12n - 12n + 3

  • 18n2 + 1n2 +5

  • 14nn +1n + 2n + 3


D.

14nn +1n + 2n + 3

Let given series beS = 1 . 2. 3 + 2 . 3 . 4 + 3 . 4 . 5 +n termNow, nth terms of the seriesTn = 1 +n - 1 . 12 +n - 1 . 13 + n - 1 . 1      Tn = a + n - 1d= 1 + n - 12 +n - 13 +n - 1= nn + 1n + 2= nn2 +2n +n +2= nn2 + 3n +2= n3 + 3n2 + 2Nnow, S = Tn =  n3 + 3n2 + 2= n3 +3 n2 + 2 n

= nn + 1n2 + 3nn + 12n + 16 + 2nn + 12= nn + 12nn + 12 + 2n +1 = 2= nn + 12n2 +n + 4n + 2 + 42= nn + 1nn + 2 + 3n + 24= nn + 1n + 2n + 34


Advertisement
Advertisement
5.

k = 16 sin27 - icos27 = ?

  •  - 1

  • 0

  •  - i

  • i


6.

If ω is a complex cube root of unity, thenω13 + 29 + 427 +     + ω12 + 38 + 932 +    = ?

  • 1

  • - 1

  • ω

  • i


7.

The common roots of the equations z3 +2z2 + 2z + 1 = 0,  z2014 + z2015 + 1 = 0 are

  • ω, ω2

  • 1, ω, ω2

  • - 1, ω, ω2

  • - ω, - ω2


8.

If a, b, c are distinct and the roots of (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then a, b and c are in

  • anthmet1c progression

  • geometnc progression

  • harmonic progression

  • arithmetico-geometnc progression


Advertisement
9.

If the roots of x3 - kx2 + 14x - 8 = 0 are in geometric progression, then k is equal to

  • - 3

  • 7

  • 4

  • 0


10.

If the harmonic mean of the roots of 2x2 - bx + 8 - 2d = 0 is 4, then the value of b is

  • 2

  • 3

  • 4 - 5

  • 4 + 5


Advertisement