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JEE Questions for Maths Applications Of Derivatives Quiz 13 - MCQExams.com
JEE
Maths
Applications Of Derivatives
Quiz 13
In the section each question has some statements (A, B,C,D,…) given in Colum – I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r Match that statements given in Column – I with the intervals/union of intervals given in Column – II
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A →s; B → t; C → r; D → r
0%
A →p; B → r; C →r ; D → t
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A →p; B → q; C → r; D → t
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A →p; B → r; C → r; D → q
In the section each question has some statements (A, B,C,D,…) given in Column– I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r Match that statements given in Column – I with the intervals/union of intervals given in Column – II
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A→r; B→q, s; C→r, s; D→p, r
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A→p; B→r, s; C→r, s; D→p, r
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A→r; B→s, s; C→r, p; D→p, q
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A→q; B→q, p; C→r, s; D → s
In the section each question has some statements (A, B,C,D,…) given in Colum – I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r In the following [
x
] denotes the greatest integer less than or equal to
x
. Match the functions in Column – I with the properties in column – II
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A→ p, q, r; B → p, s; C → r, s; D → p, q
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A→ s; B → q, s; C → r, D → p,
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A→ s; B → p, q; C → r, p; D → p, q
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A→ p, q, r; B → q, s; C → r, p; D → p, q
In the section each question has some statements (A, B,C,D,…) given in Colum – I and some statements (p,q,r,s,t,…) in column – II. Any given statement is column – I can have correct matching with ONE OR MORE statement(s) in column – II for example, if for a given questions, statement B matches with the statements given in q and r, then for that particular question against statement B, darken the bubbles corresponding to q and r in the ORS. i.e., answer r will be q and r
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A → p; B → r
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A → r; B → q
0%
A → p; B → q
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A → q; B → r
The value of the function (
x
– 1)(
x
– 2)
2
at its maxima is
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1
0%
2
0%
0
0%
4/27
The maximum and minimum values of the function |sin 4
x
+ 3| are
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1, 2
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4, 2
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2, 4
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–1, 1
Local maximum and local minimum values of the function (
x
– 1)(
x
+ 2)
2
are
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–4, 0
0%
0, –4
0%
4, 0
0%
None of these
The function
x
5
– 5
x
4
+ 5
x
3
– 10 has a maximum where
x
=
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3
0%
2
0%
1
0%
0
The minimum value 4e
2x
+ 9e
–2x
is
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11
0%
12
0%
10
0%
14
The maximum value of the function
x
3
+
x
2
+ x – 4 is
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127
0%
4
0%
Does not have a maximum value
0%
None of the above
The function
x
2
log
x
in the interval (1,e) has
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A point of maximum
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A point of minimum
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Point of maximum as well as of minimum
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Neither a point of maximum nor minimum
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0
0%
2
0%
4
0%
6
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0%
e
0%
1
0%
0%
2e
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Local maximum at π and 2 π
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Local minimum at π and 2 π
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Local minimum at π and local maximum at 2 π
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Local maximum at π and local minimum at 2 π
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A local maxima
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A local minima
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Neither a local maxima nor a local minima
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None of the above
If two sides of a triangle be given, then the area of the triangle will be maximum if the angle between the given sides be
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are
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10 cm and 40 cm
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20 cm and 30 cm
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25 cm and 25 cm
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15 cm and 35 cm
The necessary condition to be maximum or minimum for the function is
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f’(x) = 0 and it is sufficient
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f’’(x) = 0 and it is sufficient
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f’(x) = 0 but it is not sufficient
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f’(x) = 0 and f’’(x) = – vet
The area of a rectangle will be maximum for the given perimeter, when rectangle is a
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Parallelogram
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Trapezium
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Square
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None of these
Of the given perimeter, the triangle having maximum area is
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Isosceles triangle
0%
Right angle triangle
0%
Equilateral
0%
None of these
The sufficient conditions for the functions f : R → R is to be maximum at
x
= a will be
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f’(a) = 0 and f’(a) > 0
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f’(a) = 0 and f’’(a) = 0
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f’(a) = 0 and f’’(a) < 0
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f’(a) > 0 and f’’(a) < 0
Divide 12 into two parts such that the product of the square on one part and the fourth of the second part is maximum
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6, 6
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5, 7
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4, 8
0%
3, 9
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Min. at x = 0
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Max at x = 0
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Neither min . nor max. at x = 0
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None of the above
The point for the curve y =
x
e
x
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x = –1 is minimum
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x = 0 is minimum
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x = – 1 is maximum
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x = 0 is maximum
The point (0,is closest to the curve
x
2
= 2y at
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0%
(0, 0)
0%
(2, 2)
0%
None of these
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0%
0%
2)
0%
0%
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(–3, 19)
0%
(3, 19)
0%
(–19, 3)
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(–19,–3)
The sum of two numbers is fixed. Then its multiplication is maximum, when
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Each number is half of the sum
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2)
0%
0%
None of the above
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1
0%
2
0%
3
0%
4
The number that exceeds its square by the greatest amount is
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–1
0%
0
0%
0%
1
If for a function f(
x
), f’(a) = 0, f’’(a) = 0, f’’’(a) = 0 then
x
= a, f(
x
) is
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Minimum
0%
Maximum
0%
Not an extreme point
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Extreme point
Explanation
It is a fundamental property.
The least value of the sum of any positive real number and its reciprocal is
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1
0%
2
0%
3
0%
4
x
x
has a stationary point at
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x = e
0%
2)
0%
0%
Report Question
0%
1
0%
2
0%
3
0%
0
If sum of two numbers is 3, then maximum value of the product of first and the square of second is
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0%
4
0%
3
0%
2
0%
1
The minimum value of the value of the function 2 cos 2
x
– cos 4
x
in 0 ≤
x
≤ π is
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0%
0
0%
1
0%
0%
–3
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
120
0%
–120
0%
52
0%
128
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0%
0%
2)
0%
0%
Report Question
0%
0%
2)
0%
5
0%
0
If from a wire of length 36 metre a rectangle of greatest area is made, then its two adjacent sides in metre are
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6, 12
0%
9, 9
0%
10, 8
0%
13, 5
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0%
0
0%
1
0%
2
0%
3
The minimum value of the function y = 2
x
3
– 21
x
2
+ 36
x
– 20 is
Report Question
0%
–128
0%
–126
0%
–120
0%
None of these
The sum of two non – zero numbers is 4. The minimum value of the sum of their reciprocals is
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0%
0%
2)
0%
1
0%
None of these
Report Question
0%
12
0%
1
0%
9
0%
8
Report Question
0%
0%
2)
0%
0%
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x = –2
0%
x = 1
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x = 2
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x = –1
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Does not exist because f is unbounded
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Is not attained even though f is bounded
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Is equal to 1
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Is equal to –1
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