If y = mlog(x) + nx2 + x has its extreme values at x = 2 and x =

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The slope of the tangent to the curve y = 3x2 - 5x + 6 at (1, 4) is

  • - 2

  • 1

  • 0

  • - 1


2.

The chord joining the points (5, 5) and (11, 227) on the curve y = 3x2 - 11x - 15 is parallel to tangent at a point on the curve. Then, the abscissa of the point is

  • - 4

  • 4

  • - 8

  • 8


3.

The function f(x) = sin(x) - kx - c, where k and c are constants, decreases always when

  • k > 1

  • k  1

  • k < 1

  • k  1


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4.

If y = mlog(x) + nx2 + x has its extreme values at x = 2 and x = 1, then 2m + 10n is equal to

  • - 1

  • - 4

  • - 2

  • - 3


D.

- 3

It is given that,

       y = m log(x) + nx2 + x

 dydx = mx + 2nx + 1

It is given that, x = 2, x = 1 are points of extreme.

         dydxx = 2 = dydxx = 1 = 0   m2 + 4n + 1 = 0    m + 8n + 2 = 0        ...iAlso, m + 2n + 1 = 0       ...iiOn adding Eqs. (i) and (ii), we get2m + 10n + 3 = 0   2m + 10n = - 3


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5.

If s = 2t3 - 6t2 + at + 5 is the distance travelled by a particle at time t and if the velocity is - 3 when its acceleration is zero, then the value of a is

  • - 3

  • 3

  • 4

  • - 4


6.

The domain of the function f(x) = 7 - 3x + logex is

  • 0 < x < 

  • 73  x < 

  • 0 < x  73

  • -  < x < 0


7.

If f(1) = 1, f(2n) = f(n) and f(2n + 1) = {f(n)}2 - 2 for n = 1, 2, 3, ... , then the value of f(1) + f(2) + ... + f(25) is

  • 1

  • - 15

  • - 17

  • - 1


8.

In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three game is

  • 13

  • 24

  • 28

  • 52


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9.

If  = 1232353612 and ' = 48153612235 then

  • ' = 2

  • ' = - 2

  • ' = 

  •  = - '


10.

The roots of the equation 1 +x3522 +x523x +4 =  0 are

  • 2, 1, - 9

  • 1, 1, - 9

  • - 1, 1, - 9

  • - 2, - 1, - 8


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