If f(x) is continuous on - π, π, wherefx =&n

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

If f(x) is continuous on - π, π, where

fx = - 2sinx,      for - π  x  - π2αsinx + β,   for - π2 < x < π2cosx,            for π2  x  π

then α and β are

  • - 1, - 1

  • 1, - 1

  • 1, 1

  • - 1, 1


B.

1, - 1

Given,fx = - 2sinx,      for - π  x  - π2αsinx + β,   for - π2 < x < π2cosx,            for π2  x  πAt x = π2,LHS = fπ2 - 0 = limxπ+2αsinx + β= limh0αsinπ2 - h + β= α + βand fπ2 = cosπ2 = 0 fx is continuous at x = π2.

 α + β = 0     ...i

At x = - π2,RHL = f- π2 + 0 = limx - π2αsinx + β        = limh0αsin- π2 + h + β        = - α + βand f- π2 = - 2sinπ2 = - 2 fx is continuous at x = - π2.

 - α + β = 0     ...ii

on solving Eqs. (i) and (ii), we getα = 1, β = - 1

 


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2.

If f(x) = log1 - 3x1 +3x,      for x  0k,                                for x = 0 continuous at x = 0, then k is equal to

  • - 2

  • 2

  • 1

  • - 1


3.

If A = 1234, then A2 - 5A is equal to

  • 2I

  • - 2I

  • 3I

  • null matrix


4.

If A = 21- 12, B = 1- 221, C = 1- 321, then

  • A + B = B + A and A + (B + C) = (A + B) + C

  • A + B = B + A and AC = BC

  • A + B = B + A and AB = BC

  • AC = BC and A = BC


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5.

A = - 24- 12, then A2 is equal to

  • null matrix

  • unit matrix

  • 1001

  • 0001


6.

If x = log1 + t2 and y = t - tan-1t. Then, dydx is equal to

  • ex - 1

  • t2 - 1

  • ex - 12

  • ex - y


7.

If A = [x y z], B = ahghbfgfc and C = xyz. Then, ABC = O, if

  • [ax2 + by2 + cz2 + 2gxy + 2fyz + 2czx] = 0

  • [ax2 + cy2 + bz2 + xy + yz + zx] = 0

  • [ax2 + by2 + cz2 + 2hxy + 2by + 2cz] = 0

  • [ax2 + by2 + cz2 + 2zx + 2hxy + 2fyz] = 0


8.

A = 033- 30- 4- 340 and B = xyz, then B'(AB) is

  • null matrix

  • singular matrix

  • unit matrix

  • symmetric matrix


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9.

A square matrix is an orthogonal matrix, if

  • AA' = 0

  • A + A' = I

  • AA' = I

  • None of these


10.

If I is incentre of ABC, then I is

  • aa +bb +cca +b +c

  • aa +bb +cca2 +b2 +c2

  • 13a + b + c

  • a +b + ca +b +c


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