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CBSE mathematics

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Question
CBSEENMA10009677
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What is the value of (Cos267o - sin2 23o)?

Solution

Cos2 67° - sin223°

as cos (90° - θ) = sin θ

Let θ = 23°

cos (90° - 23°) = sin 23°

cos 67° = sin 23°

∴ cos267° = sin223°

∴ cos267° = sin223° = 0

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Question
CBSEENMA10009678
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In an AP, if the common difference (d) = –4, and the seventh term (a7) is 4, then find the first term.

Solution

a7 = 4

a + 6d = 4 

as an = a + (n-1) d

but d = -4

a + (-24) = 4
a = 4 + 24 = 28
therefore first term a = 28

Question
CBSEENMA10009679
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Given ∆ABC ~ ∆PQR, if ABPQ = 13, then find ar∆ABCar∆PQR

Solution

The ratio of the area of a similar triangle is equal to the square of their proportional side

ar ∆ABCar ∆PQR = AB2PQ2ar ∆ABCar ∆PQR =132 = 19

Question
CBSEENMA10009680
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What is the HCF of the smallest prime number and the smallest composite number?

Solution

Smallest prime number is 2.

Smallest composite number is  4

therefore, HCF is 2

Question
CBSEENMA10009681
Wired Faculty App

Find the distance of a point P(x, y) from the origin.

Solution

Given point is P(x,y)

Origin point is O (0,0)

Using distance formula

PO = (x2-x1)2 + (y2-y1)2 = (x-0)2 + (y-0)2= x2 +y2

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