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Tuesday, 13 July 2021

Mathematics - Paper I - For Class XI (Science Group) - Model papers With Solved Section "B" and "C" - 2020 -2021

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Mathematics - Paper I
For Class XI (Science Group)
Solved Model papers 2020 -2021


By Sir Abdul Ahad
Special Thanks To Sir Fahad And Sir Adnan Akhter



For Solved MCQs and Model Paper CLICK HERE





















SECTION 'C'

Q.7.(i) Prove any two of the following:
(a) Cos4x = 8 Cos4 x - 8 Cos2 x + 1

Proof:
Taking L.H.S
L.H.S
= Cos4x
= Cos(2x + 2x)
∴ Cos(α + β) = Cosα Cosβ - Sinα Sinβ
= Cos2x + Cos2x - Sin2x Sin2x
=Cos22x - Sin22x
∴ Cos2x = 2Cos2x - 1
∴ Sin2x = 2Sin x - Cos x
= (2Cos2 x - 1)2 - (2Sin x Cos x)2
= 4Cos4 x - 4Cos2 x + 1 - 4Sin2 x Cos2 x
= 4Cos4 x - 4Cos2 x + 1 - 4Cos2 x (1 - Cos2 x)
= 4Cos4 x - 4Cos2 x + 1 - 4Cos2 x + 4Cos4 x
= 8Cos4 x - 8Cos2 x + 1 
⇒ L.H.S = R.H.S
Hence proved

Q.7 (i) b:

Q.7 (i) c:

(ii) The measure of the two sides of a triangle are 4 and 5 units. Find the third side so that the area of the triangle is 6 square units.

OR

(ii) In the expansion of ( x2 + 1 / x2)m, m∈N, the binomial coefficient of the fourth and the thirteenth term are equal to each other, find the eleventh term.

6 comments:

  1. Sir g ya federal board ka ha or 5 august ko jo paper hoga isi ma sa hoga

    ReplyDelete
    Replies
    1. Education is the key to success29 July 2021 at 06:20

      This is solution of Mathematics xi model paper 2021 Karachi board. to view question model paper. click on the red link given at the top of this page.
      JAZAKALLAH

      Delete
  2. sir section c ka question 7 ke 3 parts nhi hai

    ReplyDelete
    Replies
    1. Education is the key to success27 August 2021 at 11:38

      We will update it tomorrow inshallah
      JAZAKALLAH

      Delete
  3. Education is the key to success30 August 2021 at 11:51

    JAZAKALLAH

    ReplyDelete