Math Class 12 New Book Chapter 9 MCQs Federal Board
Math Class 12 New Book Chapter 9 MCQs Federal Board
(i)
If
$$\sin(2x)=\frac{\sqrt3}2$$ with x ∈ [0, 2π], then value of x is:
$$a)\;\frac{\mathrm\pi}6,\frac{\mathrm\pi}3\\b)\;\frac{\mathrm\pi}6,\frac{5\mathrm\pi}{12}\\c)\;\frac{\mathrm\pi}6,\frac{5\mathrm\pi}6\\d)\;\frac{\mathrm\pi}6,\frac{2\mathrm\pi}3$$
Correct option is (a)
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(ii)
For what value of x, a trigonometric equation sin x = cos x remains true?
$$a)\;\frac{\mathrm\pi}4,\frac{3\mathrm\pi}4\\b)\;\frac{\mathrm\pi}4,\frac{5\mathrm\pi}4\\c)\;\frac{3\mathrm\pi}4,\frac{5\mathrm\pi}4\\d)\;\frac{\mathrm\pi}4$$
Correct option is (b)
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(iii)
Solution set of a trigonometric equation
$$2\;\sin\;x\;+\;\sqrt3=0$$ in the 4th quadratic is:
$$a)\;-\frac{\mathrm\pi}6\\b)\;-\frac{\mathrm\pi}3\\c)\;-\frac{5\mathrm\pi}6\\d)\;\frac{11\mathrm\pi}6$$
Correct option is (b)
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(iv)
If
$$\cos^2\;x\;=\;\frac12$$ with x ∈ [0, π], then value of x is:
$$a)\;\frac{\mathrm\pi}4,\frac{7\mathrm\pi}4\\b)\;\frac{\mathrm\pi}4,\frac{3\mathrm\pi}4\\c)\;\frac{3\mathrm\pi}4,\frac{5\mathrm\pi}4\\d)\;\frac{5\mathrm\pi}4,\frac{7\mathrm\pi}4$$
Correct option is (b)
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(v)
What is the solution of sec x = 2, if x ∈ [0, π]?
$$a)\;\left\{-\frac{\mathrm\pi}6\right\}\\b)\;\left\{-\frac{\mathrm\pi}3\right\}\\c)\;\left\{\frac{\mathrm\pi}3\right\}\\d)\;\left\{\frac{\mathrm\pi}6\right\}$$
Correct option is (c)
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(vi)
What is the solution of sin x + cos x = 0, if x ∈ [0, π]?
$$a)\;\left\{\frac{\mathrm\pi}4\right\}\\b)\;\left\{\frac{\mathrm\pi}2\right\}\\c)\;\left\{\frac{2\mathrm\pi}3\right\}\\d)\;\left\{\frac{3\mathrm\pi}4\right\}$$
Correct option is (d)
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(vii)
One solution of a trigonometric equation
$$\cos\;x\;+\;\sin\;x\;=\;\sqrt2,$$ if x ∈ [0, 2π]?
$$a)\;\left\{\frac{\mathrm\pi}4\right\}\\b)\;\left\{-\frac{\mathrm\pi}4\right\}\\c)\;\left\{\frac{2\mathrm\pi}4\right\}\\d)\;\left\{\frac{3\mathrm\pi}2\right\}$$
Correct option is (a)
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(viii)
What is the general solution of a trigonometric equation 1 + cos x = 0? where is an integer.
$$a)\;\left\{\mathrm\pi+\mathrm{nπ}\right\}\\b)\;\left\{\frac{\mathrm\pi}2+n\mathrm\pi\right\}\\c)\;\left\{\mathrm\pi+2\mathrm{nπ}\right\}\\d)\;\left\{2n\mathrm\pi\right\}$$
Correct option is (c)
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(ix)
For what value of x ∈ (0, 2π), sin x = – 1/2?
$$a)\;\frac{7\mathrm\pi}6,\frac{\mathrm\pi}6\\b)\;\frac{7\mathrm\pi}6,\frac{11\mathrm\pi}6\\c)\;\frac{5\mathrm\pi}6,\frac{11\mathrm\pi}6\\d)\;\frac{\mathrm\pi}6,\frac{5\mathrm\pi}6$$
Correct option is (b)
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(x)
If 4 cos x – 3 sin x = 1 then number of values of x between 0 and 2π are:
a) 2
b) 4
c) 6
d) 8
Correct option is (a)
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(xi)
What is the value of c, if
$$\sin^2(\frac{\mathrm\pi}6)\;+\sin^2(\frac{\mathrm\pi}3)\;\\+\tan^2(\frac{\mathrm\pi}4)=c\;?$$
$$a)\;\frac23\\b)\;\frac32\\c)\;3\\d)\;2$$
Correct option is (d)
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