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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.
Sir g ya federal board ka ha or 5 august ko jo paper hoga isi ma sa hoga
ReplyDeleteThis 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.
DeleteJAZAKALLAH
sir section c ka question 7 ke 3 parts nhi hai
ReplyDeleteWe will update it tomorrow inshallah
DeleteJAZAKALLAH
Thank you very much sir
ReplyDeleteJAZAKALLAH
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