Problemm math

7/29/2019 Problemm math

1/15

Q2. If f(x) = a log |x| + bx2 + x has its extremum values at x = -1 and x = 2, then

(a) a = 1, b = -1

(b) a = 2, b = -1/2

(c) a = -2, b = 1/2

(d) none of these

Q3. The critical point of f(x) |2 - x|/x2 is /are :

(a) x = 0, 2

(b) x = 2, 4

(c) x = 2, -4


2/15

(d) none of these

Q4. The value of a for which the function f(x) = (4a - 3) (x + log 5) + 2 (a - 7)

cot sin2 does not possess critical points is

(a) (- , -4/3)

(b) (- , -1)

(c) [1,

(d)(2,Q5. The critical points of the function f(x) = (x - 2)2/3 (2x + 1) are

(a) 1 and 2

(b) 1 and -1/2


3/15

(c) -1 and 2

(d) 1

Q6. If p and q are positive real numbers such that p2 + q2 = 1, then the maximum

value of p + q,is

(a)

(b)

(c) 2

(d)

Q7. Given p(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P'

(x) = 0. If p (-1) < p(1), then in the interval [-1, 1]

(a) P (-1) is the minimum and P(1) the maximum of P


4/15

(b) P(-1) is not minimum but P(1) the maximum of P

(c) P(-1) is the minimum but P(1) is not maximum of P

(d) Neither P(-1) is the maximum nor P(1) is the maximum of P

Q8. If f (x) is a cubic polynomial which has local maximum at x = -1. If f(2) = 18,

f(1) = -1 and f'(x) has local minimum at x = 0, then

(a) the distance between (-1, 2) and ( , f (

(b) f(x) is increasing for x [1,2 ] and has a local min

(c) the value f(0) is 5

(d) none of these

Q9. Let f(x) = (x - 2)2 xn, n N. Then, f(x) has a minimum at


5/15

(a) x = 2 for all n N

(b) x = 2, if n is even

(c) x = 0, if n is even

(d) x = 0, if n is odd

Q10. If h(x) = f(x) + f(-x), then h(x) has got an extreme value at a point where f(x)

is

(a) an even function

(b) an odd function

(c) zero

(d) none of these


6/15

Q11. If f(x) = a2 x3 - x2 + 3x + b, then the set of values of b for which local

extrema of the function f(x) are positive and maximum occurs at x = , is

(a) (-4, )

(b) (-3/8, )

(c) (-10,3/8)

(d) none of these

Q12. If f(x) = , , then f(x) has

(a) maximum at x = 0

(b) minimum at x = 0


7/15

(c) neither maximum nor minimum

(d) none of these

Q13. The number of values of x where the function f(x) = cos x + cos ( x)

attains its maximum is

(a) 0

(b) 1

(c) 2

(d) Infinite

Q14. The minimum value of the function f(x) = 2 |x -2| + 5| x- 3| for all x N, is


8/15

(a) 3

(b) 2

(c) 5

(d) 7

Q15. Let f be a function defined on R (the set of all real number) such thatf(x) =

2010 (x - 2009) (x - 2010)2 (x - 2011)3 (x - 2012)4 , for all x R. If is a function

defined on R with values in the interval (0, )such that f(x) = In {g(x)} for all

x R then the number of points in R at which g has a local maximum is

(a) 1

(b) 2

(c) 3


9/15

(d) 4

Q16. If the function f(x) = 2x3 - 9 ax2 + 12 a2 x + 1 attains its maximum and

minimum at p and q respectively such that p2 = q, then a equals

(a) 0

(b) 1

(c) 2

(d) none of these

Q17. The maximum slope of the curve y = -x3 + 3x2 + 9x - 27 is

(a) 0

(b) 12


10/15

(c) 16

(d) 32

Q18. The largest value of 2x3 - 3x2 - 12x + 5 for 2

(a) -2

(b) -1

(c) 2

(d) 4

Q19. Let a, b, c be positive real numbers and ax2 + b/x2 c for all x R+ . Then,

(a) 4ab c2


11/15

(b) 4ac b2

(c) 4ac a2

(d) 4ac < b2

Q20. Let f(x) = e

x

sin x, slope of the curve y = f(x) is maximum at x = a, if 'a'equals

(a) 0

(b)

(c)

(d) none of these

Q21. In a triangle ABC, B = 90o and a + b = 4. The are of the triangle is

maximum when C, is


12/15

(a)

(b)

(c)

(d) none of these

Q22. The minimum value of 27cos 2x . 81sin 2x, is

(a)

(b) -5

(c)


13/15

(d)

Q23. The greatest value of the function f(x) = sin-1 x2 in the interval [-1/ , 1/ ]

(a)

(b)

(c)

(d)

Q24. Let f(x) = cos x + 10x + 3x2 + x3, x [-2,3]. The absolute minimum value

of f(x) is

(a) 0


14/15

(b) -15

(c) 3 - 2

(d) none of these

Q25. If f(x) = 2x3 - 21x2 + 36x - 30, then for f(x) which one of the following is

correct?

(a) f(x) has minimum at x = 1

(b) f(x) has maximum at x = 6

(c) f(x) has maximum at x = 1

(d) f(x) has no maximum or minimum


15/15

Q26. If m and M respectively the minimum and maximum of f(x) = (x -1)2 + 3 for

x [-3, 1], then the ordered pair (m,M) is equal to

(a) (-3, 19)

(b) (3, 19)

(c) (-19, -3)

(d) (-19, -3)

Q27. The condition f(x) = x3 + px2 + qx + r (x R) to have no extreme value, is

(a) p2 < 3q

(b) 2p2 < q

(c) p2

Problemm math

Documents

Transcript of Problemm math