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question_answer1)
\[\Delta ABC\]is right angled at A. If AC = 8 cm and AB = 6 cm, what is the value of cosec B?
A)
\[\frac{5}{4}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[\frac{4}{5}\] done
clear
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question_answer2)
\[\Delta ABC\]is right angled at A .lf\[BC=\sqrt{2}\]and AB = AC =1, what is the measure of\[\angle B\]?
A)
\[\text{6}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{3}0{}^\circ \] done
clear
D)
\[\text{9}0{}^\circ \] done
clear
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question_answer3)
What is the value of\[\theta \]tor which\[\tan \theta =\cot \theta \]?
A)
\[\text{6}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{9}0{}^\circ \] done
clear
D)
\[0{}^\circ \] done
clear
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question_answer4)
Given\[\sin \theta +\frac{1}{\sin \theta }=4\], what is the value
A)
20 done
clear
B)
16 done
clear
C)
14 done
clear
D)
4 done
clear
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question_answer5)
Given\[{{\sin }^{2}}\theta +\frac{1}{{{\sin }^{2}}\theta }\], what is the value of \[\sin \theta +\cos \theta \]?
A)
\[\frac{25}{31}\] done
clear
B)
\[\frac{31}{25}\] done
clear
C)
\[\frac{24}{25}\] done
clear
D)
\[\frac{31}{24}\] done
clear
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question_answer6)
Find the value of \[\text{cos3}0{}^\circ \text{ cos45}{}^\circ \text{ }-\text{ sin3}0{}^\circ \text{ sin45}{}^\circ \].
A)
\[\frac{\sqrt{6}+1}{2}\] done
clear
B)
\[\frac{\sqrt{6}+\sqrt{2}}{4}\] done
clear
C)
\[\frac{\sqrt{6}-\sqrt{2}}{8}\] done
clear
D)
\[\frac{\sqrt{2}(\sqrt{3}-1)}{4}\] done
clear
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question_answer7)
What is the value of\[\text{tan 7}{}^\circ \text{ tan 23}{}^\circ \text{ tan 6}0{}^\circ \text{ tan 67}{}^\circ \text{ tan 83}{}^\circ \]?
A)
\[\frac{1}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}\] done
clear
C)
1 done
clear
D)
\[\propto \] done
clear
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question_answer8)
\[\Delta \text{ABC}\]is an isosceles triangle with the unequal side measuring 12 cm. If both the equal sides measure 19 cm, what is the measure of\[\angle \text{BAC}\]?
A)
\[\text{36}.\text{8}{}^\circ \] done
clear
B)
\[\text{68}{}^\circ \] done
clear
C)
\[\text{38}{}^\circ \] done
clear
D)
\[\text{6}0{}^\circ \] done
clear
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question_answer9)
\[\text{ABCD}\] is a trapezium in which AB = 8 cm, AD = 4 cm and CD = 3 cm.
What is the length of BC to the nearest whole number?
A)
5 cm done
clear
B)
\[\sqrt{41}\,cm\] done
clear
C)
8 cm done
clear
D)
7 cm done
clear
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question_answer10)
The figure shows an isosceles triangle ABC. Find the length of the perpendicular from A to BC.
A)
5.45 cm done
clear
B)
4.55 cm done
clear
C)
5.6 cm done
clear
D)
4.54 cm done
clear
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question_answer11)
If \[\text{sec}\theta =\text{2p}\] and \[\tan \theta =\frac{\text{2}}{p}\] find the value\[2\left( {{p}^{2}}-\frac{1}{{{p}^{2}}} \right)\].
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{\sqrt{2}}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{8}\] done
clear
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question_answer12)
What is the value of\[\theta \]if\[\sqrt{3}\tan 2\theta -3=0\]?
A)
\[\text{45}{}^\circ \] done
clear
B)
\[\text{9}0{}^\circ \] done
clear
C)
\[\text{3}0{}^\circ \] done
clear
D)
\[\text{6}0{}^\circ \] done
clear
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question_answer13)
Given\[\sin \theta +\cos \theta =\sqrt{3}\], what is the value of\[\tan \theta +\cot \theta \]?
A)
\[\frac{1}{\sqrt{2}}\] done
clear
B)
\[\frac{2}{\sqrt{3}}\] done
clear
C)
\[\frac{\sqrt{3}}{2}\] done
clear
D)
1 done
clear
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question_answer14)
If \[\frac{\tan {{26}^{o}}+\tan {{19}^{o}}}{x(1-\tan {{26}^{o}}\tan {{19}^{o}})}=\cos {{60}^{o}}\], what is the value of \[x\]?
A)
1 done
clear
B)
\[\sqrt{2}\] done
clear
C)
2 done
clear
D)
\[\sqrt{3}\] done
clear
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question_answer15)
If \[\sin 2\left( \frac{2}{1}.\frac{3}{2}.\frac{4}{3}....\frac{x-1}{x-2} \right)=1,\]\[0<x<100\], find the value of \[x\].
A)
\[\text{91}{}^\circ \] done
clear
B)
\[\text{8}0{}^\circ \] done
clear
C)
\[\text{49}{}^\circ \] done
clear
D)
\[\text{46}{}^\circ \] done
clear
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question_answer16)
What is the angle between the hour and minute hands of a clock at 02 :15 hours?
A)
\[\text{15}{}^\circ \] done
clear
B)
\[7\frac{{{1}^{o}}}{2}\] done
clear
C)
\[22\frac{{{1}^{o}}}{2}\] done
clear
D)
\[\text{3}0{}^\circ \] done
clear
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question_answer17)
C is the centre of a circle of radius 3 units, and \[\theta \]is the angle as shown in the given figure. If \[\sin \theta +{{\cos }^{2}}\theta =\frac{{{x}^{2}}+1}{{{x}^{2}}}\],find the value of x.
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
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question_answer18)
If\[\tan \theta +\sec \theta =2\], \[0\le \theta \le \frac{\pi }{2}\]find the value of the\[\tan \theta \].
A)
\[\frac{3}{4}\] done
clear
B)
\[\frac{5}{4}\] done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[\frac{5}{2}\] done
clear
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question_answer19)
Graphs of \[y=\sin x\] and\[y=\cos x\], where \[0\le x\le \frac{\pi }{2}\]intersect at a point. Find abscissa.
A)
\[\frac{\pi }{6}\] done
clear
B)
\[\frac{\pi }{4}\] done
clear
C)
\[\frac{\pi }{3}\] done
clear
D)
0 done
clear
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question_answer20)
Find the value of\[\text{sin 15}{}^\circ \].
A)
\[\frac{\sqrt{3}+1}{\sqrt{2}}\] done
clear
B)
\[\frac{\sqrt{3}-1}{\sqrt{2}}\] done
clear
C)
\[\frac{\sqrt{3}+1}{2\sqrt{2}}\] done
clear
D)
\[\frac{\sqrt{3}-1}{2\sqrt{2}}\] done
clear
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question_answer21)
What is the value of \[~\text{sin}0{}^\circ +\text{cos3}0{}^\circ -\text{tan45}{}^\circ +\] \[\text{cosec 6}0{}^\circ \text{ }+\text{ cot9}0{}^\circ \]?
A)
\[\frac{7\sqrt{3}-6}{6}\] done
clear
B)
\[\frac{6+7\sqrt{3}}{6}\] done
clear
C)
0 done
clear
D)
2 done
clear
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question_answer22)
If\[\sin \theta =-\frac{1}{2}\], what are the respective possible values of 9 between 0 and\[2\pi \]?
A)
\[\text{21}0{}^\circ \]and\[\text{3}00{}^\circ \] done
clear
B)
\[\text{24}0{}^\circ \]and \[\text{33}0{}^\circ \] done
clear
C)
\[\text{24}0{}^\circ \]and\[\text{3}00{}^\circ \] done
clear
D)
\[\text{21}0{}^\circ \]and\[\text{33}0{}^\circ \] done
clear
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question_answer23)
In terms of radians what is the equivalent of\[\text{45}{}^\circ \]?
A)
\[25\pi \] done
clear
B)
\[0.25\pi \] done
clear
C)
\[\frac{{{180}^{o}}\pi }{{{45}^{o}}}\] done
clear
D)
\[\frac{{{45}^{o}}}{\pi }\] done
clear
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question_answer24)
Find the value of\[\sqrt{\frac{1-\cos A}{1+\cos A}}\]
A)
\[\text{sec A}-\text{cot A}\] done
clear
B)
\[\text{cosec A}-\text{cot A}\] done
clear
C)
0 done
clear
D)
1 done
clear
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question_answer25)
Find the value of\[\frac{5\cos \alpha -4}{3-5\sin \alpha }-\frac{3+5\sin \alpha }{4+5\cos \alpha }\]
A)
- 1 done
clear
B)
5 done
clear
C)
1 done
clear
D)
0 done
clear
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question_answer26)
If\[x=3\cos A\cos B,y=3\cos A\sin B\]and \[\text{z}=\text{3 sin A}\], find the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\].
A)
3 done
clear
B)
6 done
clear
C)
12 done
clear
D)
9 done
clear
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question_answer27)
Find the value of \[\frac{1+\tan {{75}^{o}}}{1-\tan {{75}^{o}}}\]
A)
\[-\frac{2}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}\] done
clear
C)
\[-\sqrt{3}\] done
clear
D)
\[\frac{1}{\sqrt{3}}\] done
clear
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question_answer28)
If 8 tan A =15, find the value of\[\frac{\text{sinA}-\text{cosA}}{\text{sinA}+\text{cosA}}\]
A)
\[\frac{7}{23}\] done
clear
B)
\[\frac{11}{23}\] done
clear
C)
\[\frac{13}{23}\] done
clear
D)
\[\frac{17}{23}\] done
clear
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question_answer29)
If\[4\sin \theta =3\cos \theta \],find\[\frac{{{\sec }^{2}}\theta }{4(1-{{\tan }^{2}}\theta )}\].
A)
\[\frac{25}{16}\] done
clear
B)
\[\frac{25}{28}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{5}{6}\] done
clear
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question_answer30)
Find the value of\[\text{cos}{{\text{1}}^{o}}\text{cos2}{}^\circ \text{cos3}{}^\circ .....\text{cos89}{}^\circ \text{cos9}{{0}^{o}}\].
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{\sqrt{2}}\] done
clear
D)
0 done
clear
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question_answer31)
If \[\tan x=\frac{x}{y}\], where x and y are whole numbers, find sin\[x\].
A)
\[\frac{y}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done
clear
B)
\[\frac{x}{\sqrt{{{x}^{2}}+{{y}^{2}}}}\] done
clear
C)
\[\frac{y}{\sqrt{{{x}^{2}}+{{y}^{2}}}}\] done
clear
D)
\[\frac{x}{\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done
clear
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question_answer32)
Find\[\frac{{{\sin }^{3}}\varphi +{{\cos }^{3}}\varphi }{\sin \varphi +\cos \varphi }\]
A)
\[\text{1 }+\text{sin}\varphi \text{ cos}\varphi \] done
clear
B)
\[\text{1}-\text{sinc}\varphi \text{ cos}\varphi \] done
clear
C)
\[\text{1}-\text{sin}\varphi \text{ tan}\varphi \] done
clear
D)
1 done
clear
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question_answer33)
If \[x=\text{a sec}\theta +\text{b tan}\theta \] and\[\text{y}=\text{b sec}\theta +\text{a tan}\theta \], find\[{{x}^{2}}-{{y}^{2}}\].
A)
\[4ab\,\sec \theta +a\tan \theta \] done
clear
B)
\[{{a}^{2}}-{{b}^{2}}\] done
clear
C)
\[{{b}^{2}}-{{a}^{2}}\] done
clear
D)
\[{{a}^{2}}+{{b}^{2}}\] done
clear
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question_answer34)
If\[\sec \theta +b\tan \theta =p\], what is the value of\[\cos \theta \]?
A)
\[\frac{{{p}^{2}}+1}{{{P}^{2}}-1}\] done
clear
B)
\[\frac{{{p}^{2}}-1}{{{({{P}^{2}}+1)}^{2}}}\] done
clear
C)
\[\frac{2p}{{{P}^{2}}+1}\] done
clear
D)
\[\frac{4{{p}^{2}}}{{{({{P}^{2}}+1)}^{2}}}\] done
clear
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question_answer35)
What is the numerical value of the expression \[\frac{\sin {{9}^{o}}}{\sin {{48}^{o}}}-\frac{\cos {{81}^{o}}}{\cos {{42}^{o}}}\]?
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
0 done
clear
D)
-1 done
clear
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question_answer36)
Find the value of the expression \[[\cos ec({{75}^{o}}+\theta )-\sec ({{15}^{o}}-\theta )-\]\[\tan ({{55}^{o}}+\theta )+\cot ({{35}^{o}}-\theta )]\]
A)
- 1 done
clear
B)
0 done
clear
C)
1 done
clear
D)
\[\frac{3}{2}\] done
clear
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question_answer37)
If\[\cos (\alpha +\beta )=0\], what is the value of\[\sin (\alpha -\beta )\]?
A)
\[\cos \beta \] done
clear
B)
\[\cos 2\beta \] done
clear
C)
\[\sin \alpha \] done
clear
D)
\[\sin 2\alpha \] done
clear
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question_answer38)
If\[\cos 9\alpha =\sin \alpha \]a and\[9\alpha <{{90}^{o}}\], what is the value of tan 5 a?
A)
\[\frac{1}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}\] done
clear
C)
1 done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer39)
If\[\Delta \text{ABC}\]is right angled at C, find the value of\[\cos (A+B)\].
A)
0 done
clear
B)
1 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{\sqrt{3}}{2}\] done
clear
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question_answer40)
If\[\text{sin A}+\text{sin2 A }=\text{ 1}\], find the value of the expression\[(\text{cos2 A}+\text{cos4 A})\].
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer41)
Given that\[\text{sin}\alpha =\frac{1}{2}\text{and cos}\beta \text{=}\frac{1}{2}\], find the value of\[(\alpha +\beta )\].
A)
\[0{}^\circ \] done
clear
B)
\[\text{3}0{}^\circ \] done
clear
C)
\[\text{6}0{}^\circ \] done
clear
D)
\[\text{9}0{}^\circ \] done
clear
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question_answer42)
Find the value of the expression\[\frac{{{\sin }^{2}}{{22}^{o}}+{{\sin }^{2}}{{68}^{o}}}{{{\cos }^{2}}{{22}^{o}}+{{\cos }^{2}}{{68}^{o}}}+{{\sin }^{2}}{{63}^{o}}+\cos {{63}^{o}}\sin {{27}^{o}}\]
A)
3 done
clear
B)
2 done
clear
C)
1 done
clear
D)
0 done
clear
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question_answer43)
If \[\sin \theta -\cos \theta =0\], find the value of \[({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )\]
A)
1 done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{4}\] done
clear
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question_answer44)
Find the value of \[\sin ({{45}^{o}}+\theta )-\cos ({{45}^{o}}-\theta )\].
A)
\[2\cos \theta \] done
clear
B)
0 done
clear
C)
\[2\sin \theta \] done
clear
D)
1 done
clear
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question_answer45)
What is the value of \[\text{si}{{\text{n}}^{\text{2}}}\text{5}{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{1}0{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{8}0{}^\circ +\text{si}{{\text{n}}^{\text{2}}}\text{85}{}^\circ \]?
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer46)
If \[\sin B=\frac{1}{2}\], find the value of\[\text{3cosB}-\text{4co}{{\text{s}}^{\text{3}}}\text{B}\].
A)
\[\frac{1}{2}\] done
clear
B)
1 done
clear
C)
2 done
clear
D)
0 done
clear
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question_answer47)
If\[\tan x=\text{sin 45}{}^\circ \text{cos 45}{}^\circ +\text{sin3}0{}^\circ \], find the value of\[x\].
A)
\[{{30}^{o}}\] done
clear
B)
\[\text{6}0{}^\circ \] done
clear
C)
\[\text{45}{}^\circ \] done
clear
D)
\[\text{9}0{}^\circ \] done
clear
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question_answer48)
If \[\text{sin(A}+\text{B)}=\text{1}\]and\[\text{cos(A-B)}=\frac{\sqrt{3}}{2}\], find A and B.
A)
\[\text{45}{}^\circ ,\text{45}{}^\circ \] done
clear
B)
\[\text{9}0{}^\circ ,\text{45}{}^\circ \] done
clear
C)
\[\text{45}{}^\circ ,\text{ 3}0{}^\circ \] done
clear
D)
\[\text{6}0{}^\circ ,\text{ 3}0{}^\circ \] done
clear
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question_answer49)
If\[4\tan \theta =1\], find the value of\[\frac{4\sin \theta -2\cos \theta }{4\sin \theta +3\cos \theta }\]
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{6}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{1}{3}\] done
clear
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question_answer50)
If\[\sqrt{3}\tan \theta =3\sin \theta \], find the value of\[{{\sin }^{2}}\theta -{{\cos }^{2}}\theta \].
A)
\[\frac{\sqrt{2}}{\sqrt{3}}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{\sqrt{3}}\] done
clear
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question_answer51)
If \[\cos ec\theta =\frac{13}{12}\], find the value of\[\frac{2\sin \theta -3\cos \theta }{4\sin \theta -9\cos \theta }\]
A)
0 done
clear
B)
1 done
clear
C)
3 done
clear
D)
2 done
clear
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question_answer52)
Find the value \[\text{si}{{\text{n}}^{\text{2}}}\text{3}0{}^\circ \text{co}{{\text{s}}^{\text{2}}}\text{45}{}^\circ +\text{4ta}{{\text{n}}^{\text{2}}}\text{3}0{}^\circ \]\[+\frac{1}{2}{{\sin }^{2}}{{90}^{o}}-2{{\cos }^{2}}{{90}^{o}}+\frac{1}{24}\]
A)
1 done
clear
B)
2 done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[\sqrt{3}\] done
clear
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question_answer53)
Find the value of\[\frac{2}{3}({{\cos }^{4}}{{30}^{o}}-{{\sin }^{4}}{{45}^{o}})\]\[-3({{\sin }^{2}}{{60}^{o}}-{{\sec }^{2}}{{45}^{o}})+\frac{1}{4}{{\cot }^{2}}{{30}^{o}}\]
A)
\[\frac{15}{4}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[2\frac{65}{4}\] done
clear
D)
\[4\frac{17}{24}\] done
clear
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question_answer54)
If \[\text{cos3x}=\text{cos 3}0{}^\circ \text{ sin 6}0{}^\circ \text{ }-\] \[\text{sin 3}0{}^\circ \text{ cos 6}0{}^\circ \] , find the value of x.
A)
\[\text{6}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{2}0{}^\circ \] done
clear
D)
\[\text{3}0{}^\circ \] done
clear
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question_answer55)
In \[\Delta ABC\], if\[\angle \text{B}=\text{9}0{}^\circ ,\text{AB}=\text{5 cm}\] and AC =10 cm, find\[\angle A\]and\[\angle C\]
A)
\[~\text{9}0{}^\circ ,\text{ 45}{}^\circ \] done
clear
B)
\[\text{6}0{}^\circ ,\text{ 3}0{}^\circ \] done
clear
C)
\[\text{45}{}^\circ ,\text{ }0{}^\circ \] done
clear
D)
\[~\text{9}0{}^\circ ,\text{ 6}0{}^\circ \] done
clear
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question_answer56)
lf \[\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{\sqrt{3}+1}{\sqrt{3}-1}\]find the acute angle\[\theta \].
A)
\[\text{9}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{3}0{}^\circ \] done
clear
D)
\[\text{6}0{}^\circ \] done
clear
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question_answer57)
If \[2(\cos \theta +\sec \theta )=5\], what is the value of\[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta \]?
A)
\[\frac{25}{2}\] done
clear
B)
\[\frac{5}{4}\] done
clear
C)
\[\frac{17}{4}\] done
clear
D)
\[\frac{4}{17}\] done
clear
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question_answer58)
How is \[\cot \theta \] expressed in terms of\[\sin \theta \]?
A)
\[\frac{1}{\sqrt{1-{{\sin }^{2}}\theta }}\] done
clear
B)
\[\frac{\sqrt{1-{{\sin }^{2}}\theta }}{\sin \theta }\] done
clear
C)
\[\frac{1}{\sin \theta }\] done
clear
D)
\[\frac{\sin \theta }{\sqrt{1-{{\sin }^{2}}\theta }}\] done
clear
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