InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If $cos\alpha + sec\alpha$ = $\sqrt{3}$, then the value of $cos^{3}\alpha + sec^{3}\alpha$ is1). 22). 13). 04). 4 |
| Answer» OPTION 3 is the ANSWER | |
| 2. |
The value of $cos 1^{0} cos 2^{0} cos 3^{0} ..... cos 180^{0}$ is1). 02). 13). $\frac{\sqrt{3}}{2}$4). $\frac{1}{2}$ |
| Answer» | |
| 3. |
If $cos 20^{0}$ = mand $cos 70^{0}$ = n, then the value of $m^{2} + n^{2}$ is1). 12). $\frac{3}{2}$3). $\frac{1}{\sqrt{2}}$4). $\frac{1}{2}$ |
| Answer» | |
| 4. |
If $sin\frac{\pi x}{2}$ = $x^{2} - 2x +2$, then the value of x is1). 02). 13). -14). None of these |
| Answer» | |
| 5. |
If $tan\left(\frac{\pi}{2}-\frac{\alpha}{2}\right)$ = $\sqrt{3}$ , then the value of $cos\alpha$ is1). $\frac{1}{\sqrt{2}}$2). $\frac{1}{2}$3). 04). $\frac{\sqrt{3}}{2}$ |
| Answer» CORRECT ANSWER is: OPTION 2 | |
| 6. |
If $sin21^{0}$ = $\frac{x}{y}$ , then $sec21^{0} - sin69^{0}$is equal to1). $\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}$2). $\frac{y^{2}}{x\sqrt{y^{2}-x^{2}}}$3). $\frac{x^{2}}{y\sqrt{x^{2}-y^{2}}}$4). $\frac{y^{2}}{x\sqrt{x^{2}-y^{2}}}$ |
| Answer» | |
| 7. |
If sin 7x = cos 11x , then the value of tan 9x + cot9x is1). 12). 23). 34). 4 |
| Answer» ANSWER for this QUESTION is OPTION 2 | |
| 8. |
In a right-angled triangle XYZ, right-angled at Y, if XY = $2\sqrt{6}$ and XZ - YZ = 2, then sec X + tan X is1). $\frac{1}{\sqrt{6}}$2). $\sqrt{6}$3). $2\sqrt{6}$4). $\frac{\sqrt{6}}{2}$ |
| Answer» OPTION 2 : - $\SQRT{6}$ | |
| 9. |
If $tan\theta$ = 2, then the value of $\frac{8sin\theta + 5cos\theta}{sin^{3}\theta + 2cos^{3}\theta + 3cos\theta}$ is1). $\frac{21}{5}$2). $\frac{8}{5}$3). $\frac{7}{5}$4). $\frac{16}{5}$ |
| Answer» ANSWER for this QUESTION is OPTION 1 | |
| 10. |
The value of $\frac{4}{1+tan^{2}\alpha}+\frac{3}{1+cot^{2}\alpha}+3sin^{2}\alpha$ is1). 42). -13). 24). 3 |
| Answer» | |
| 11. |
If $0^{0} < \theta < 90^{0}$, the value of $sin\theta + cos\theta$ is1). equal to 12). greater than 13). less than 14). equal to 2 |
| Answer» | |
| 12. |
A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each comer of the park is same, then in $\triangle ABC$, the foot of the pole is at the1). centroid2). circumcentre3). incentre4). orthocentre |
| Answer» CIRCUMCENTRE : - is CORRECT HENCE OPTION 2 | |
| 13. |
If $sin\theta - cos\theta$ = $\frac{1}{2}$ then value of $sin\theta + cos\theta$ is:1). -22). $\pm 2$3). $\frac{\sqrt{7}}{2}$4). 2 |
| Answer» CORRECT ANSWER is: OPTION 3 | |
| 14. |
If the height of a pole is $2\sqrt{3}$ metre and the length of its shadow is 2 metre, then the angle of elevation of the sun is1). $90^{0}$2). $45^{0}$3). $30^{0}$4). $60^{0}$ |
| Answer» | |
| 15. |
If tan (A + B) = $\sqrt{3}$ and tan (A-B) = $\frac{1}{\sqrt{3}}$ , $\angle A +\angle B$ < $90^{0}$ ,$A\geq B$ ,then $\angle A $ is1). $90^{0}$2). $30^{0}$3). $45^{0}$4). $60^{0}$ |
| Answer» | |
| 16. |
If the sum of two angles is $135^{0}$ and their difference is $\frac{\pi}{12}$,then the circular measure of the greater angle is1). $\frac{2\pi}{3}$2). $\frac{3\pi}{5}$3). $\frac{5\pi}{12}$4). $\frac{\pi}{3}$ |
| Answer» OPTION option 3 is the CORRECT ANSWER | |
| 17. |
If a 48 m tall building has a shadow of $48\sqrt{3}$ m, then the angle of elevation of the sun is1). $15^{0}$2). $60^{0}$3). $45^{0}$4). $30^{0}$ |
| Answer» | |
| 18. |
$\frac{2 sin68^{0}}{cos22^{0}}- \frac{2 cot15^{0}}{5tan75^{0}}-\frac{3 tan45^{0}.tan20^{0}.tan40^{0}.tan50^{0}.tan70^{0}}{5}$is equal to1). -12). 03). 14). 2 |
| Answer» OPTION 3 is the CORRECT ANSWER as per the answer key | |
| 19. |
If $sin(3x- 20^{0})$ = $cos( 3y + 20^{0})$,then the value of (x+y) is1). $20^{0}$2). $30^{0}$3). $40^{0}$4). $45^{0}$ |
| Answer» CORRECT ANSWER is: $30^{0}$ | |
| 20. |
If the sum and difference of two angles are $\frac{22}{9}$ radian and $36^{0}$ respectively, then the value of smaller angle in degree taking the value of $\pi$ as $\frac{22}{7}$ is :1). $52^{0}$2). $60^{0}$3). $56^{0}$4). $48^{0}$ |
| Answer» OPTION 1 is the RIGHT ONE | |
| 21. |
The value of $sec\theta\left(\frac{1+sin\theta}{cos\theta}+\frac{cos\theta}{1+sin\theta}\right)-2tan^{2}\theta$1). 42). 13). 24). 0 |
| Answer» | |
| 22. |
If $(1+sin\alpha)(1+sin\beta) (1 + sin\gamma)$ =$(1-sin\alpha) (1-sin\beta)(1 - sin\gamma)$ then each side is equal to1). $\pm cos\alpha cos\beta cos\gamma$2). $\pm sin\alpha sin\beta sin\gamma$3). $\pm sin\alpha cos\beta cos\gamma$4). $\pm sin\alpha sin\beta cos\gamma$ |
| Answer» CORRECT ANSWER is: OPTION 1 | |
| 23. |
If $\theta$ be an acute angle and $7 sin^{2}\theta + 3 cos^{2}\theta$ = 4, then the value of $tan\theta$ is1). $\sqrt{3}$2). $\frac{1}{\sqrt{3}}$3). 14). 0 |
| Answer» | |
| 24. |
If $0^{0} < 0 < 90^{0}$ and $2sin^{2}\theta + 3cos\theta$ = 3, then the value of $\theta$ is1). $30^{0}$2). $60^{0}$3). $45^{0}$4). $75^{0}$ |
| Answer» OPTION 2 is the RIGHT ONE | |
| 25. |
If $sin\theta + cos\theta$ = $\sqrt{2} sin (9O^{0} - \theta)$ then $cot\theta $ is equal to :1). $\sqrt{2}$2). 03). $\sqrt{2}-1$4). $\sqrt{2}+1$ |
| Answer» CORRECT ANSWER is: $\SQRT{2}+1$ | |
| 26. |
A 10 metre long ladder is placed against a wall. It is inclined at an angle of $30^{0}$ to the ground. The distance (in m) of the foot of the ladder from the wall is (Given $\sqrt{3}$ = 1.732)1). 8.162). 7.323). 8.264). 8.66 |
| Answer» | |
| 27. |
From a tower 125 metres high, the angle of depression of two objects, which are in horizontal line through the base of the tower, are $45^{0}$ and $30^{0}$ and they are on the same side of the tower.The distance (in metres) between the objects is1). $125\sqrt{3}$2). $125(\sqrt{3}-1)$3). $\frac{125}{(\sqrt{3}-1)}$4). $125(\sqrt{3}+1)$ |
| Answer» | |
| 28. |
The value of x in the equation $tan^{2}\frac{\pi}{4} -cos^{2}\frac{\pi}{3}$ = $x sin\frac{\pi}{4} cos\frac{\pi}{4} tan\frac{\pi}{3} $ is1). $\frac{2}{\sqrt{3}}$2). $\frac{3\sqrt{3}}{4}$3). $\frac{1}{\sqrt{3}}$4). $\frac{\sqrt{3}}{2}$ |
| Answer» | |
| 29. |
Two posts are x metres apart and the height of one is double that of the other. If from the mid point of the line Joining their feet, an observer finds the angular elevations of their tops to be complementary. then the height (in metres) of the shorter post is1). $\frac{x}{2\sqrt{2}}$2). $\frac{x}{4}$3). $x\sqrt{2}$4). $\frac{x}{\sqrt{2}}$ |
| Answer» | |
| 30. |
If $x cos\theta - y sin\theta$ =$\sqrt{x^{2} + y^{2}}$ and $\frac{cos^{2}\theta}{a^{2}}+\frac{sin^{2}\theta}{b^{2}}$ = $\frac{1}{x^{2} + y^{2}}$ , then the correct relation is1). $\frac{x^{2}}{b^{2}} - \frac{y^{2}}{a^{2}}$ = 12). $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 13). $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}}$ = 14). $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}$ = 1 |
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Answer» Right ANSWER for this QUESTION is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 |
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| 31. |
If $\theta$ be acute angle and $cos\theta$ = $\frac{15}{17}$, then the value of, $cot(90^{0}- \theta)$ is1). $\frac{2\sqrt{8}}{15}$2). $\frac{8}{15}$3). $\frac{\sqrt{2}}{17}$4). $\frac{8\sqrt{2}}{17}$ |
| Answer» | |
| 32. |
A kite is flying at a height of 50 metre. If the length of string is 100 metre then the inclination of string to the horizontal ground in degree measure is1). 902). 603). 454). 30 |
| Answer» ANSWER for this QUESTION is OPTION 4 | |
| 33. |
The angle of elevation of a tower from a distance 50 m from its foot is $30^{0}$. The height of the tower is1). $50\sqrt{3}$ m2). $\frac{50}{\sqrt{3}}$ m3). $75\sqrt{3}$ m4). $\frac{75}{\sqrt{3}}$ m |
| Answer» | |
| 34. |
If the angle of elevation of the Sun changes from $30^{0}$ to $45^{0}$ ,the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is1). $20(\sqrt{3} - 1)$m2). $20(\sqrt{3} + 1)$ m3). $10(\sqrt{3} - 1)$ m4). $10(\sqrt{3} + 1)$ m |
| Answer» | |
| 35. |
If $\theta$ is a positive acute angle and $cosec\theta + cot\theta$ = $\sqrt{3}$,then the value of $cosec\theta$ is1). $\frac{1}{\sqrt{3}}$2). $\sqrt{3}$3). $\frac{2}{\sqrt{3}}$4). 1 |
| Answer» | |
| 36. |
If $tan\theta + cot\theta$ = 5, then $tan^{2}\theta + cot^{2}\theta$ is1). 232). 253). 264). 24 |
| Answer» 23 : - is CORRECT HENCE OPTION 1 | |
| 37. |
If A,B and C be the angles of a triangle, then put of the following. the incorrect relation is :1). $sin\frac{A+B}{2}$ = $cos\frac{C}{2}$2). $cos\left(\frac{A+B}{2}\right) = $sin\frac{C}{2}$3). $tan\left(\frac{A+B}{2}\right) = $sec\frac{C}{2}$4). $cot\left(\frac{A+B}{2}\right) = $tan\frac{C}{2}$ |
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Answer» $cos\left(\FRAC{A+B}{2}\right) = $sin\frac{C}{2}$ is the best suited |
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| 38. |
If the sum and difference of two angles are $135^{0}$ and $\frac{\pi}{12}$ respcctlvely, then the value of the angles in degree measure are1). $70^{0}$,$65^{0}$2). $75^{0}$,$60^{0}$3). $45^{0}$,$90^{0}$4). $80^{0}$,$55^{0}$ |
| Answer» CORRECT ANSWER is: $75^{0}$,$60^{0}$ | |
| 39. |
For any real values of $\theta$, $\sqrt{\frac{sec\theta -1}{sec\theta +1}}$ = 1). $cot\theta - cosec\theta$2). $sec\theta - tan\theta$3). $cosec\theta - cot\theta$4). $tan\theta - sec\theta$ |
| Answer» OPTION 3 is the RIGHT ONE | |
| 40. |
$\alpha +\beta$ =$90^{0}$ , then the expression $\frac{tan\alpha}{tan\beta} + sin^{2}\alpha+sin^{2}\beta $ is equal to1). $sec^{2}\beta$2). $tan^{2}\alpha$3). $tan^{2}\beta$4). $sec^{2}\alpha$ |
| Answer» | |
| 41. |
If $\theta$ = $60^{0}$, then $\frac{1}{2}\sqrt{1+sin\theta}+\frac{1}{2}\sqrt{1-sin\theta}$ is equal to1). $cot\frac{\theta}{2}$2). $sec\frac{\theta}{2}$3). $sin\frac{\theta}{2}$4). $cos\frac{\theta}{2}$ |
| Answer» | |
| 42. |
From a point 20 m away from the fool of a tower, the angle of elevation of the top of the tower is $30^{0}$ . The height of the tower is1). $10\sqrt{3}$ m2). $20\sqrt{3}$ m3). $\frac{10}{\sqrt{3}}$ m4). $\frac{20}{\sqrt{3}}$ m |
| Answer» | |
| 43. |
The simplest value of $sin^{2}x + 2 tan^{2}x - 2 sec^{2}x + cos^{2}x$ is1). 12). 03). -14). 2 |
| Answer» 1 : SEEMS CORRECT | |
| 44. |
If x = $a sec\theta cos\phi$ , y = $b sec\theta sin\phi$, z = $c tan\theta$, then the value $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}}$ is :1). 12). 43). 94). 0 |
| Answer» CORRECT ANSWER is: 1 | |
| 45. |
If $sec(7\theta + 28^{0})$ = $coeec(30^{0} - 3\theta)$ then the value of $\theta$ is1). $8^{0}$2). $5^{0}$3). $60^{0}$4). $9^{0}$ |
| Answer» | |
| 46. |
A person of height 6ft. wants to pluck a fruit which is on a $\frac{26}{3}$ ft. high tree. If the person is standing $\frac{8}{\sqrt{3}}$ ft away from the base of the tree, then at what angle should he throw a stone so that it hits the fruit 1). $75^{0}$2). $30^{0}$3). $45^{0}$4). $60^{0}$ |
| Answer» OPTION 2 is the correct ANSWER as per the answer key | |
| 47. |
$\frac{ tan\theta}{1 - cot\theta}+\frac{ cot\theta}{1 - tan\theta}$ is equal to1). $1 - tan\theta - cot\theta$2). $1 + tan\theta - cot\theta$3). $1 - tan\theta + cot\theta$4). $1 + tan\theta + cot\theta$ |
| Answer» | |
| 48. |
If $sin 2\theta$ = $\frac{\sqrt{3}}{2}$, then the value of $sin 3\theta$ is equal to (take $0^{0} \leq \theta \leq 90^{0}$)1). $\frac{1}{2}$2). 13). 04). $\frac{\sqrt{3}}{2}$ |
| Answer» OPTION 2 is the RIGHT ANSWER | |
| 49. |
If $4sin^{2}\theta - 1$ = 0 and angle $\theta $ is less than $90^{0}$,the value of $cos^{2}\theta + tan^{2}\theta$ is : (Take $0^{0} < \theta < 90^{0}$)1). $\frac{17}{15}$2). $\frac{13}{12}$3). $\frac{11}{9}$4). $\frac{12}{11}$ |
| Answer» | |
| 50. |
If $\frac{x - xtan^{2}30^{0}}{1+ tan^{2}30^{0}}$ = $sin^{2}30^{0}+4cot^{2}45^{0}-sec^{2}60^{0}$,then the value of X is :1). $\frac{1}{4}$2). $\frac{1}{5}$3). $\frac{1}{2}$4). $\frac{1}{\sqrt{3}}$ |
| Answer» | |