If x is real, then the minimum value of x2 - x&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

311.

The functions f(x) =xe - X x  R attains a maximum value at x is equal

  • 1

  • 2

  • 1e

  • 3


312.

The approximate value of 1.00023000 is

  • 1·2

  • 1·4

  • 1·6

  • 1·8


313.

The sum of two numbers is 20. If the product of the square of one number and cube of the other is maximum, then the numbers are :

  • 12, 8

  • 3, 4

  • 9, 12

  • 15, 18


314.

Gas is being pumped into a spherical balloon at the rate of 30 ft3/min. The rate at which the radius increase when it reaches the value 15ft, is :

  • 130π ft/min

  • 115π ft/min

  • 120π ft/min

  • 125π ft/min


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315.

The minimum value of 2x2 + x - 1 is :

  • - 14

  • 32

  • - 98

  • 98


316.

A point is moving on y = 4 - 2x2. The x-coordinate of the point is decreasing at the rate of 5 units/second. Then, the rate at which y coordinate of the point is changing when the point is at (1, 2) is

  • 5 units/s

  • 10 units/s

  • 15 units/s

  • 20 units/s


 Multiple Choice QuestionsMatch The Following

317.

Match the points on the curve 2y2 = x + 1 with the slopes of normals at those points and choose the correct answer.

      Point           Slope of the normal

A    (7, 2)         1 - 42

B    (0, 12)     2  - 8

C    (1, - 1)       3, 4

D    (3, 2)      4, 0

A. A B C D (i) 2 4 3 1
B. A B C D (ii) 2 5 3 1
C. A B C D (iii) 2 3 5 1
D. A B C D (iv) 2 5 1 3

 Multiple Choice QuestionsMultiple Choice Questions

318.

fx, y = 2x - y2 - x4 - y4 fxxfyy - fxy20, 0

  • 32

  • 16

  • 0

  • - 1


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319.

If x is real, then the minimum value of x2 - x + 1x2 + x + 1, is

  • 13

  • 3

  • 12

  • 1


A.

13

Let fx = x2 - x + 1x2 + x + 1         ...iOn differentiating w.r.t. x, we getf'x = x2 - x + 12x - 1 - x2 - x + 12x + 1x2 + x + 12for maximum or minimum, put f'(x) = 0 x2 + x + 12x - 1 - x2 - x + 12x +1 = 0 x2 + x - 1 - - x2 + x + 1 = 0 2x2 - 2 = 0  x = ± 1Now, f'(x)= 2x2 - 2x2 + x + 12Again differentiating, we getx2 + x + 124x - 2x2 - 2f''x = 2x2 + x + 12x + 1x2 + x + 14at   x = 1, f''x > 0Therefore it is minimum at x = 1Put x = 1 in equation (i), we get  f1 = 1 - 1 + 11 + 1 + 1 = 13

Thus, minimum value is 13.


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320.

A stone thrown upwards, has its equation of motion s = 490t - 4.9t2. Then the maximum height reached by it, is

  • 24500

  • 12500

  • 12250

  • 25400


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