Math Class 12 New Book Chapter 1 MCQs Federal Board
Math Class 12 New Book Chapter 1 MCQs Federal Board
Tick the correct option in each of the following.
(i)
Which of the following is an example of exponential growth function?
$$(a)\;f(x)\;=\;3x+4\\(b)\;f(x)\;=\;3^x\times5\\(c)\;f(x)\;=\;x^3\\(d)\;f(x)\;=\;x^2$$
Correct option is (b)
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(ii)
The exponential decay function is expressed by:
$$(a)\;f(x)\;=\;a.b^x;0<b<1\\(b)\;f(x)\;=\;a.b^x;b>1\\(c)\;f(x)\;=\;a.b^x;0<a>1\\(d)\;f(x)\;=\;a.b^x;a<1$$
Correct option is (a)
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(iii)
The logarithm function
$$f(x)\;=\;\log_bx$$ is defined for:
(a) all real numbers
(b) x < 0
(c) x > 0
(d) x ≥ 0
Correct option is (c)
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(iv)
What is the value of
$$\log_5\;125?$$
(a) 25
(b) 5
(c) 4
(d) 3
Correct option is (d)
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(v)
A function f: A → B is said to be onto if:
(a) Every element of the set A has a unique image in the set B.
(b) Every element in the set B has a preimage in the set A.
(c) Some elements of the set B have no preimage in the set A.
(d) f is both one to one and onto.
Correct option is (b)
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(vi)
The function f(x) = x+1, where f: { 1, 2, 3 } → { 2, 3, 4 }, is:
(a) one to one but not onto
(b) onto but not one to one
(c) both one to one and onto
(d) neither one to one nor onto
Correct option is (c)
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(vii)
The function f:R → [ 0, ∞ ] defined by
$$f(x)\;=\;x^2\;+\;1,$$ is:
(a) onto but not on to one
(b) one to one but not onto
(c) neither one to one nor onto
(d) both one to one and onto
Correct option is (c)
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(viii)
A function f: A → B has an inverse if and only if:
(a) f is one to one
(b) f is onto
(c) f is both one to one and onto
(d) f is neither one to one and onto
Correct option is (c)
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(ix)
The inverse function of
$$f(x)\;=\;x^3,$$ is:
$$(a)\;f^{-1\;}(x)\;=\;x^{-3}\\(b)\;f^{-1\;}(x)\;=\;\sqrt{x^{-3}}\\(c)\;f^{-1\;}(x)\;=\;\sqrt[3]{x^{-3}}\\(d)\;f^{-1\;}(x)\;=\;\sqrt[3]x$$
Correct option is (d)
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(x)
The function f(x) = sin x, where
$$\left[-\begin{array}{cc}\frac{\mathrm\pi}2,&\frac{\mathrm\pi}2\end{array}\right]\rightarrow\lbrack-1,1\rbrack,$$ is:
(a) one to one but not onto
(b) onto but not one to one
(c) both one to one and onto
(d) neither one to one nor onto
Correct option is (c)
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(xi)
The inverse function of f(x) = 1/x ; x ≠ 0, is:
$$(a)\;f^{-1\;}(x)\;=\;1\\(b)\;f^{-1\;}(x)\;=\;-x\\(c)\;f^{-1\;}(x)\;=\;x\\(d)\;f^{-1\;}(x)\;=\;\frac1x$$
Correct option is (d)
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(xii)
Scaling refers to:
(a) increasing the size of an object.
(b) decreasing the size of an object.
(c) maintaining the properties while resizing an object.
(d) changing the shape of an object.
Correct option is (c)
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(xiii)
Which of the following statements is true for the uniform scaling?
(a) both width and height change proportionally.
(b) only the width changes.
(c) only the height changes.
(d) width and height remain unchanged.
Correct option is (a)
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(xiv)
What is the effect on the graph of f(x) when it is replaced by f (x + 2)?
(a) It shifts 2 units to the right.
(b) It shifts 2 units to the left.
(c) It shifts 2 units up.
(d) It shifts 2 unit down.
Correct option is (b)
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(xv)
The domain of
$$y\;=\;\sin^{-1}\;(x),$$ is:
(a) [ 0, ∞ )
(b) ( -∞, ∞ )
(c) [ -1, 1 ]
(d) [ 0, 1 ]
Correct option is (c)
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