The greatest value of f (x) = (x + 1)⅓ – (x – 1)⅓ on [0, 1] is
1) 1 2) 2 3) 3 4) 4 Solution: (2) 2 f (x) = (x + 1)⅓ – (x –... View Article
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The sum of two numbers is fixed. Then its multiplication is maximum, when
1) Each number is half of the sum 2) Each number is 1 / 3 and 2 / 3 respectively... View Article
Maximum value of (1 / x)x is
1) (e)e 2) (e)1/e 3) (e)-e 4) (1 / e)e Solution: (2) (e)1/e f (x) = (1 / x)x f’... View Article
The point (0, 5) is closest to the curve x2 = 2y at
1) (2√2, 0) 2) (0, 0) 3) (2, 2) 4) None of these Solution: (4) None of these Let a... View Article
The point for the curve y = xex
1) x = –1 is minimum 2) x = 0 is minimum 3) x = – 1 is maximum 4)... View Article
If y = {sin (x + a)} / {sin (x + b)}, a ≠ b, then y is
1) Min. at x = 0 2) Max at x = 0 3) Neither min . nor max. at x... View Article
Divide 12 into two parts such that the product of the square on one part and the fourth of the second part is maximum
1) 6, 6 2) 5, 7 3) 4, 8 4) 3, 9 Solution: (3) 4, 8 Let the parts be... View Article
The sufficient conditions for the functions f : R → R is to be maximum at x = a will be
1) f’(a) = 0 and f’(a) > 0 2) f’(a) = 0 and f’’(a) = 0 3) f’(a) = 0... View Article
Of the given perimeter, the triangle having maximum area is
1) Isosceles triangle 2) Right angle triangle 3) Equilateral 4) None of these Solution: (3) Equilateral AB, the area of... View Article
The area of a rectangle will be maximum for the given perimeter when the rectangle is a
1) Parallelogram 2) Trapezium 3) Square 4) None of these Solution: (3) Square S = 2 (x + y); x... View Article
The necessary condition to be maximum or minimum for the function is
1) f’(x) = 0 and it is sufficient 2) f’’(x) = 0 and it is sufficient 3) f’(x) = 0... View Article
The adjacent sides of a rectangle with a given perimeter as 100 cm and enclosing maximum area are
1) 10 cm and 40 cm 2) 20 cm and 30 cm 3) 25 cm and 25 cm 4) 15... View Article
d/dx (ex log sin 2x) =
(1) ex(log sin 2x + 2 cot 2x) (2) ex(log cos 2x + 2 cot 2x) (3) ex(log cos 2x... View Article
d/dx tan-1 ( sec x + tan x) =
(1) 1 (2) 1/2 (3) cos x (4) sec x Solution: Let y = tan-1 ( sec x + tan... View Article
d/dx log (√(x-a) + √(x-b)) =
(1) 1/2 √(x-a) +√(x-b) (2) 1/2 √((x-a)(x-b)) (3) 1/√((x-a)(x-b)) (4) none of these Solution: Let y = log (√(x-a) +... View Article
If y = x + x2 + x3/2! + x4/3! +…then x(dy/dx) =
(1) xex (2) y(x+1) (3) x(y+1) (4) y log (1+x) Solution: Given y = x + x2 + x3/2! +... View Article
[latex]\frac{d}{dx}e^{x+3\log x}=[/latex]
(1) ex.x2(x+3) (2) ex.x(x+3) (3) ex+3/x (4) none of these Solution : Given y = ex+ 3log x = ex.e3... View Article
If y = log ((1+√x)/(1-√x)), then dy/dx =
(1) √x/(1-x) (2) 1/√x(1-x) (3) √x/(1+x) (4) 1/√x(1+x) Solution: Given y = log ((1+√x)/(1-√x)) We know log a/b = log... View Article
If y = 2log x, then dy/dx is
(1) 2log x/log 2 (2) 2log x log 2 (3) 2log x/x (4) 2log x log 2/x Solution: y =... View Article
If x2/3 + y2/3 = a2/3, then dy/dx =
(1) (y/3)1/3 (2) (-y/x)1/3 (3) (x/y)1/3 (4) (-x/y)1/3 Solution: Given x2/3 + y2/3 = a2/3 y2/3 = a2/3 – x2/3... View Article
