If A = [x y z], B = ahghbfgfc and C = xy

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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


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


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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


D.

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

Given, A =x y z, B = ahghbfgfc and C = xyz AB = x y zahghbfgfc= xa + yh + zx  xh + yb + zf xg + yf + zcNow, ABC = xa + yh + zx xh + yb + zf xg + yf + zcxyz= ax2 + hxy + gxz + hxy +y2b + fzy + gxz + yfz + z2c + 2hxy + 2fyz= ax2 + by2 + cz2 + 2gxz But  ABC = 0[ax2 +by2 + cz2 + 2gzx + 2hxy +2fyz] = 0


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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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