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.