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Class 12 Maths
Application Of Derivatives
Quiz 1
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The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is
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10 cm²/s
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√3 cm²/s
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10√3 cm²/s
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\(\frac{10}{3}\) cm²/s
Explanation
10√3 cm²/s
A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is
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\(\frac{1}{10}\) radian/sec
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\(\frac{1}{20}\) radian/sec
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20 radiah/sec
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10 radiah/sec
Explanation
\(\frac{1}{20}\) radian/sec
The curve y – x
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a vertical tangent (parallel to y-axis)
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a horizontal tangent (parallel to x-axis)
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an oblique tangent
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no tangent
Explanation
a horizontal tangent (parallel to x-axis)
The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is
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3x – y = 8
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3x + y + 8 = 0
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x + 3y ± 8 = 0
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x + 3y = 0
Explanation
x + 3y ± 8 = 0
If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is
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1
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0
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-6
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6
Explanation
6
If y = x
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0.32
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0.032
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5.68
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5.968
Explanation
0.32
The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:
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x + 5y = 2
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x – 5y = 2
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5x – y = 2
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5x + y = 2
Explanation
x + 5y = 2
The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are
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(2, – 2), (- 2, -34)
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(2, 34), (- 2, 0)
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(0, 34), (-2, 0)
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(2, 2),(-2, 34).
Explanation
(2, 2),(-2, 34).
The tangent to the curve y = e
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(0, 1)
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(-\(\frac{1}{2}\), 0)
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(2, 0)
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(0, 2)
Explanation
(-\(\frac{1}{2}\), 0)
The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is
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\(\frac{22}{7}\)
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\(\frac{6}{7}\)
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\(\frac{-6}{7}\)
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-6
Explanation
\(\frac{-6}{7}\)
The two curves; x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of
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\(\frac{π}{4}\)
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\(\frac{π}{3}\)
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\(\frac{π}{2}\)
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\(\frac{π}{6}\)
Explanation
\(\frac{π}{4}\)
The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is
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[-1, ∞]
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[-2, -1]
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[-∞, -2]
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[-1, 1]
Explanation
[-2, -1]
Let the f: R → R be defined by f (x) = 2x + cos x, then f
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has a minimum at x = 3t
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has a maximum, at x = 0
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is a decreasing function
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is an increasing function
Explanation
is an increasing function
y = x (x – 3)² decreases for the values of x given by
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1 < x < 3
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x < 0
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x > 0
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0 < x <\(\frac{3}{2}\)
Explanation
1 < x < 3
The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly
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increasing in (π, \(\frac{3π}{2}\))
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decreasing in (\(\frac{π}{2}\), π)
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decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]
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decreasing in [0, \(\frac{π}{2}\)]
Explanation
decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]
Which of the following functions is decreasing on(0, \(\frac{π}{2}\))?
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sin 2x
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tan x
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cos x
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cos 3x
Explanation
cos x
The function f(x) = tan x – x
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always increases
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always decreases
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sometimes increases and sometimes decreases
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never increases
Explanation
always increases
If x is real, the minimum value of x² – 8x + 17 is
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-1
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0
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1
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2
Explanation
2
The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is
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126
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0
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135
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160
Explanation
0
The function f(x) = 2x³ – 3x² – 12x + 4 has
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two points of local maximum
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two points of local minimum
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one maxima and one minima
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no maxima or minima
Explanation
one maxima and one minima
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