If A = 1- 12- 1 and B = 1a4b and (A

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

A = 1232- 10, B = 1324- 13, then order of AB is

  • 2 x 2

  • 3 x 3

  • 1 x 3

  • 3 x 2


2.

ddxseccos-1x8 is equal to

  • 18

  • - 18

  • 8x2

  • 8x2


3.

If f(x) = 1 + cos2x2, then f'π2 is

  • π6

  • - π6

  • 16

  • π6


4.

If A + I = 3- 241, then (A + I)(A - I) is equal to

  • - 5- 48- 9

  • - 54- 89

  • 5489

  • - 5- 4- 8- 9


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5.

If y = asin3θ and x = acos3θ, then at θ = π3, dydx is equal to

  • π6

  • - 3

  • - 13

  • 3


6.

If x + y = 8, then maximum value of x2y is

  • 20489

  • 204881

  • 20483

  • 204827


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7.

If A = 1- 12- 1 and B = 1a4b and (A + B)2 = A2 + B2. Then, a and b are respectively

  • 1, - 1

  • 2, - 3

  • - 1, 1

  • 3, - 2


A.

1, - 1

Given, A = 1- 12- 1 and B = 1a4bA +B = 1- 12- 1 +1a4b           = 2- 1 + a6- 1 + b A +B2 = 2- 1 + a6- 1 + b2- 1 + a6- 1 + b= 4 - 6 +6a- 2 + 2a + 1 - b - a + ab12 - 6 +6b- 6 + 6a + 1 + b2 - 2b= - 2 + 6a- 1 + a - b + ab6 + 6b- 5 + 6a  - 2b + b2

and A2 = 1- 12- 11- 12- 1           = 1 - 2- 1 + 12 - 2- 2 + 1 = - 100- 1Also, B2 = 1a4b1a4b              = 1 + 4aa + ab4 + 4b4a + b2Given, A +B2 = A2 + B2 - 2 + 6a- 1 + a - b + ab6 + 6b- 5 + 6a - 2b + b2      = - 100- 1 + 1 + 4aa + ab4 + 4b4a + b2 - 2 + 6a- 1 + a - b + ab6 + 6b- 5 + 6a  - 2b + b2 = 4aa + ab4 + 4b - 1 + 4a + b2

On comparing both sides, we get

- 2 + 6a = 4a and 6 + 6b = 4 + 4b

      a = 1 and b = - 1


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8.

If A = 2- 11- 23- 2- 44- 3, then A2 is equal to

  • null matrix

  • itself A

  • unit matrix

  • Scalar matrix


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9.

If f(1) = 10, f(2) = 14, then using Newton's forward formula f(1.3) is equal to 

  • 12.2

  • 11.2

  • 10.2

  • 15.2


10.

If f(x) = x3 - 9x + 1 and x = 3, then using Newton Raphson method, first iteration is

  • 5318

  • 539

  • 3518

  • 359


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