If f(x) = xx - x + 1, then : from Mathemat

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The value of sinsin-113 + sec-13 + costan-112 + tan-12 is :

  • 1

  • 2

  • 3

  • 4


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2.

If f(x) = xx - x +1, then :

  • f(x) is continuous but not differentiable at x = 0

  • f(x) is not differentiable at x = 0

  • f(x) is differentiable at x = 0

  • None of the above


C.

f(x) is differentiable at x = 0

Given, fx = x - x +1

Since, given function is algebraic and every algebraic function is continuous.

 f(x) is continuous at x = 0.

Now we will check differentiability of f(x) at x = 0

 LF'0 = limh0-f0 - h - f00 - h - 0           = limh0- hh - - h + 1- h = 1RF'0 = limh0-f0 + h - f00 + h - 0          = limh0- hh - h + 1h = 1 LF'0 = RF'0 The function is differentiable at x = 0


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3.

Let A, B and C be n x n matrices. Which one of the following is a correct statement?

  • If AB = AC, then B = C

  • If A3 + 2A2 + 3A + 51 = 0, then A is invertible

  • If A2 = 0,then A = 0

  • None of these


4.

The value of cot-19 + csc-1414 is given by :

  • 0

  • π4

  • π2

  • tan-12


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5.

If the line ax + by + c = 0 is a normal to the curve y =1, then :

  • a > 0, b > 0

  • a > 0, b < 0

  • a < 0, b < 0

  • Data is insufficient


6.

If f(x) = cos(log(x)), then f(x)f(y) - 12fxy + fxy has the value :

  • - 1

  • 12

  • - 2

  • zero


7.

If y = 3x - 1 + 3-x - 1 (x real), then the least value ofy is

  • 2

  • 6

  • 2/3

  • None of these


8.

0π2cotxcotx + tanxdx is equal to :

  • 1

  • - 1

  • π2

  • π4


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9.

Area bounded by the curve y = loge(x), x = 0, y  0 and x - axis is :

  • 1 sq unit

  • 12 sq unit

  • 2 sq unit

  • None of these


10.

If a × b2 +a . b2 = 144 and a = 4, then b is equal to

  • 12

  • 3

  • 8

  • 4


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