XI Revision assignment Binomial theorem

                 DCM PRESIDENCY SCHOOL, LUDHIANA

                          MATHS – ASSIGNMENT, CLASS- 11^TH TOPIC -  BINOMIAL THEOREM

1.  Find the number of terms in the following expansion;

      a)   (1+2x+x²)²⁰  b) [(3x+y)⁸ –(3x-y)⁸]

2.   Using binomial theorem expand :       a)  (1 + x +x²)³  b)  (10.1)⁵

3.   Using binomial theorem , prove that  2³ⁿ -7n -1 is divisible by 49, n€N.

4.  Find the 11^th  term from the end of the expansion  (2x – 1/x²)²⁵.

5.  Find the coffiecients of x³² and x^-17  in the expansion (x⁴- 1/x³)¹⁵

6.  If the fourth term in the expansion (ax+ 1/x)ⁿ  is 5/2, then find the value of a and n.

7.  Using the binomial , prove that 6ⁿ -5n always leave the remainder 1 , when divisible by 25.

8.  Prove that the coefficient of the middle term in the expansion of (1 +x)²ⁿ is equal to the sum of the        coefficient of middle term of the expansion (1+x)^2n-1

9.  In the binomial expansion of (1+x)ⁿ, the coefficient of the 5^th ,6^th , and 7^th terms are in A. P . Find all  values of n for which this can happen.

10.  The coefficient of three consecutive term in the expansion(1+x)ⁿ be 76, 95, 76, find n.

XI Revision assignment trigonometry

                       DCM PRESIDENCY SCHOOL, LUDHIANA

                          MATHS – ASSIGNMENT, CLASS- 11^TH TOPIC -             TRIGONOMETRY

1.        Find the value of  (a)  sin 315   (b)   cos 210    (c)   sin (-1125)

2.        If 2tanβ + cot β = tan α , prove that cot β = 2 tan(α - β).

3.        If A + B = π/4 , Prove that ;

       (i)  (1 + tanA) (1 – tan B)  = 2    (ii) (cotA - 1)(cot B - 1) =2

4.        If tan ( α +β) = n tan(α - β) , show that (n + 1)sin 2β = (n -1) sin 2α

5.        If tan A – tan B = x and cot B – cot A = y , prove that cot(A - B) = 1/X + 1/y

6.        Prove that cos 20 cos 40 cos 60 cos 80 = 1/16

7.        Prove that sin 10 sin 30 sin50 sin70 =  1/16

8.        Prove that sin 20 sin 40 sin 60 sin80 = 3/16

9.        Prove that sin A sin ( 60 -A) sin (60 + A) = ¼ sin 3A

10.   Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos2x cos 3x

11.   Prove that tan α + 2tan 2α + 4 tan 4α + 8cot 8α = cotα.

12.   Prove that cos²A + cos²(A + 2π/3) + cos² (A - 2π/3) = 3/2

13.   Prove that cos α + cosβ + cos γ + cos (α +β +γ) = 4 cos α +β /2 cos β +γ/2 cos     γ +α/2

14.   Prove that sinx /sin 3x + sin 3x /cos 9x + sin 9x /cos27x = ½ (tan 27x - tanx)

15.   If cos α +cos β + cosγ = 0 then  prove that , cos3α + cos 3β + cos 3γ = 12 cosα cosβ cosγ

16.   Solve the following equations

(i)                4 cos A -  3 sec A = tan A   (ii)  tan θ  + tan 2θ + tanθ tan2θ = 1

 (iii) tan θ + tan 2θ + tan 3θ = tanθ tan2θ tan 3θ

     17  Prove  that tan 70 = tan 20 + 2 tan 50

    18  Prove that sinα + sin (α + 2π/ 3 ) + sin ( α + 4π/ 3) = 0

    19. If sin α + sinβ = a and  cosα + cosβ = b prove that  cos (α -β) = a² + b² – 2 /2

    20  If 3 tan A tan B  = 1  , prove that  2 cos ( A + B) = cos ( A - B )  

    21. 4 Sin α Sin ( α + π/3) Sin (α + 2π/3 ) = Sin 3α.

    22. If A+ B+ C = 180 Prove that Sin 2A + Sin 2B – Sin 2C = 4 Cos A Cos B Sin C

    23.Prove that Sin 51 + Cos 81 = Cos 21

    24. Prove that tan A + tan( 60 + A) + tan(120 + A) = 3 tan 3A

    25. Solve the equation  Cos 3x + 8 Cos³x = 0

xii maths asignment

xi assign ment sequence and series