Increasing and Decreasing Functions - Uttarakhand Board (UBSE) STD 12 Science Maths Questions

Every invertible function is:

✓
Monotonic function.
B
Constant function.
C
Identity function.
D
Not necessarily monotonic function.

Answer: A.

If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:

✓
Increasing.
B
Decreasing.
C
Constant.
D
None of these.

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark

If the function $\text{f}(\text{x})=\cos|\text{x}|-2\text{ax}+\text{b}$ increases along entire number scale, then:

A
$\text{a}=\text{b}$
B
$\text{a}=\frac{1}{2}\text{b}$
✓
$\text{a}\leq-\frac{1}{2}$
D
$\text{a}>-\frac{3}{2}$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark

The function $\text{f}(\text{x})=\log_\text{e}\Big(\text{x}^3+\sqrt{\text{x}^6+1}\Big)$ is of the following type:

A
Even and increasing.
✓
Odd and increasing.
C
Even and decreasing.
D
Odd and decreasing.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark

Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when:

A
$\lambda>\frac{1}{2}$
B
$\lambda<\frac{1}{2}$
✓
$\lambda<2$
D
$\lambda>2$

Answer: C.

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Q 62 Marks Questions2 Marks

Find the values of b for which the function $\text{f}(\text{x})=\sin\text{x}-\text{b}\text{x}+\text{c}$ is a decreasing function on R.

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Q 72 Marks Questions2 Marks

Write the set of values of a for which the function f(x) = ax + b is decreasing for all $\text{x}\in\text{R}.$

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Q 82 Marks Questions2 Marks

Prove that the function $\text{f}(\text{x})=\log_{\text{e}}\text{x}$ is increasing on $(0,\infty).$

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Q 92 Marks Questions2 Marks

Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Strictly increasing in $(\pi,2\pi)$

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Q 102 Marks Questions2 Marks

Find the value(s) of a for which $f(x) = x^3 - ax$ is an increasing function on R.

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Q 113 Marks Question3 Marks

Show that $f(x) = x^9 + 4x^7 + 11$ is an increasing function for all $\text{x}\in\text{R}.$.

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Q 123 Marks Question3 Marks

Show that $f(x) = e^{2x}$ is increasing on $R.$

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Q 133 Marks Question3 Marks

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = 2x^3 - 9x^2 - 12x + 1$

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Q 143 Marks Question3 Marks

Find the set of values of 'b' for which $\text{f}(\text{x})=\text{b}(\text{x}+\cos\text{x})+4$ is decreasing on R.

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Q 153 Marks Question3 Marks

Show that $\text{f}(\text{x})=\frac{1}{\text{x}}$ is decreasing function on $(0,\infty).$

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Q 165 Marks Questions5 Marks

Find the intervals in which the following functions are increasing or decreasing.
$\text{f}(\text{x})=\log(2+\text{x})-\frac{2\text{x}}{2+\text{x}},\text{x}\in\text{R}$

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Q 175 Marks Questions5 Marks

Find the intervals in which f(x) is increasing or decreasing:
$\text{f}(\text{x})=\sin\text{x}(1+\cos\text{x}),0<\text{x}<\frac{\pi}{2}$

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Q 185 Marks Questions5 Marks

Determine the values of x for which the function $f(x) = x^2 - 6x + 9$ is increasing or decreasing. Also, find the coordinates of the point on the curve $y = x^2 - 6x + 9$ where the normal is parallel to the line $y = x + 5.$

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Q 195 Marks Questions5 Marks

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = x^3- 12x^2 + 36x + 17$

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Q 205 Marks Questions5 Marks

Find the intervals in which the following functions are increasing or decreasing.
$\text{f}(\text{x})=5\text{x}^{\frac{3}{2}}-3\text{x}^{\frac{5}{2}},\text{x}>0$

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Increasing and Decreasing Functions question types

Increasing and Decreasing Functions questions

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Increasing and Decreasing Functions Maths - Increasing and Decreasing Functions

Increasing and Decreasing Functions question types

Increasing and Decreasing Functions questions

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