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CBSE mathematics

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Question
CBSEENMA12035862
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Using principal value, evaluate the following: sin-1 sin3π5 

Solution

As sin-1 sinθ=θ so sin-1  sin 3π5 =3π5But  3π5 ∉ -π2, π2 

So

sin-1  sin 3π5 = sin-1 sin π- 2π5=  sin-1 sin 2π5=  2π5 ∈ -π2, π2∴ Principal value is  2π5

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Question
CBSEENMA12035865
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If the binary operation * on the set of integers Z, is defined by a * b = a + 3b2 , then find the value of 2 * 4.

Solution

Given: a * b = a + 3b2  ∀ a, b ∈ ZTherefore, 2 * 4 = 2 + 3 x 42 = 50

Question
CBSEENMA12035866
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If A is an invertible matrix of order 3 and |A| = 5, then find |adj. A|.

Solution

 adj A  =  A n-1,  where n is order of square matrix

Given A is an invertible matrix of order 3

 adj A  =  A 3-1 =  A 2Since,   A  = 5∴  adj A  =  5 2 = 25

Question
CBSEENMA12035870
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If matrix A = (1, 2, 3), write AA’, where A’ is the transpose of matrix A.

Solution

Given: A = [ 1  2  3 ]

∴ A' = 123AA' = 123 123 = 1 x 1 + 2 x 2 + 3 x 3       = 14

Question
CBSEENMA12035871
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Write the value of the determinant  2    3   4 5  6   86x  9x  12x

Solution

∆ = 2  3  45  6  86x  9x  12xR3 → 13xR3∆ = 2  3  45  6  82  3  4Now,   R1 =R3 ∴  ∆ = 0

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