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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.
| 51. |
If $3 sin\theta + 5 cos\theta$ = 5, then the value of $5 sin\theta - 3 cos\theta$ will be1). $\pm 3$2). $\pm 5$3). $\pm 2$4). $\pm 1$ |
| Answer» | |
| 52. |
If $sec\theta - tan\theta$= $\frac{1}{\sqrt{3}}$ , the value of $sec\theta.tan\theta$ is1). $\frac{2}{3}$2). $\frac{2}{\sqrt{3}}$3). $\frac{4}{\sqrt{3}}$4). $\frac{1}{\sqrt{3}}$ |
| Answer» OPTION 1 is the RIGHT ONE | |
| 53. |
The value of x which satisfies the equation $2 cosec^{2}30^{0} + x sin^{2}60^{0} - \frac{3}{4}tan^{2}30^{0}$ = 10 is1). 22). 33). 04). 1 |
| Answer» OPTION 2 : - 3 | |
| 54. |
If x,y are acute angles, $0 < x+ y < 90^{0}$and $sin(2x-20^{0})$ = $cos(2y +20^{0})$, then the value of tan (x + y) is:1). $\frac{1}{\sqrt{3}}$2). $\frac{\sqrt{3}}{2}$3). $\sqrt{3}$4). 1 |
| Answer» 1 : - is CORRECT HENCE OPTION 4 | |
| 55. |
From an aeroplane just over a straight road, the angles of depression of two consecutivekilometre stones situated at opposite sides of the aeroplane were found to be $60^{0}$ and $30^{0}$ respectively. The height (in km) of the aeroplane fromthe road at that instant was (Given $\sqrt{3}$ = 1.732)1). 0.4332). 8.663). 4.334). 0.866 |
| Answer» OPTION 4 is the ANSWER | |
| 56. |
The distance between two pillars of length 16 metres and 9 metres is x metres. If two angles of elevation of their respective top from the bottom of the other are complementary to each other, then the value of x (in metres) is1). 152). 163). 124). 9 |
| Answer» | |
| 57. |
If $3sin\theta + 5cos\theta$ = 5, then $5sin\theta - 3cos\theta$ is equal to1). $\pm 3$2). $\pm 5$3). 14). $\pm 2$ |
| Answer» | |
| 58. |
If x = $a sec\alpha cos\beta$ , y = $b sec\alpha sin\beta$, z = $c tan\alpha$, then the value $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}}$ is1). 22). 03). 14). -1 |
| Answer» 0 : - is CORRECT HENCE OPTION 3 | |
| 59. |
Which one of the following is true for $0^{0} < \theta < 90^{0}$1). $cos\theta \leq cos^{2}\theta$2). $cos\theta > cos^{2}\theta$3). $cos\theta < cos^{2}\theta$4). $cos\theta \geq cos^{2}\theta$ |
| Answer» CORRECT ANSWER is: OPTION 2 | |
| 60. |
If $sin\theta + cosec\theta$ = 2, then value of $sin^{100}\theta + cosec^{100}\theta $is equal to:1). 12). 23). 34). 100 |
| Answer» | |
| 61. |
The value of cot $41^{0}.cot 42^{0}.cot 43^{0}.cot 44^{0}.cot 45^{0}.cot 46^{0}.cot 47^{0}.cot 48^{0}.cot 49^{0}$1). 12). 03). $\frac{\sqrt{3}}{2}$4). $\frac{1}{\sqrt{2}}$ |
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Answer» This QUESTION was ASKED some where in previous YEAR papers of ssc, and CORRECT answer was option 1 |
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| 62. |
A man 6 ft tall casts a shadow 4 ft long, at the same time when a flag pole casta a shadow 50 ft long. The height of the flag pole is1). 80 ft2). 75 ft3). 60 ft4). 70 ft |
| Answer» OPTION 2 is the RIGHT ANSWER | |
| 63. |
The expression $\frac{tan57^{0}+ cot37^{0}}{tan33^{0} + cot53^{0}}$ is equal to1). $tan 33^{0}cot 57^{0}$2). $tan 57^{0}cot 37^{0}$3). $tan 33^{0}cot 53^{0}$4). $tan 53^{0}cot 37^{0}$ |
| Answer» | |
| 64. |
The value of $cosec^{2}18^{0} - \frac{1}{cot^{2}72^{0}}$ is1). $\frac{1}{\sqrt{3}}$2). $\frac{\sqrt{2}}{3}$3). $\frac{1}{2}$4). 1 |
| Answer» 1 | |
| 65. |
If $tan^{2}\theta$ = $1 - e^{2}$, then the value of $sec\theta + tan^{3}\theta cosec\theta$ is1). $(2 + e^{2})^{\frac{3}{2}}$2). $(2 - e^{2})^{\frac{1}{2}}$3). $(2 + e^{2})^{\frac{1}{2}}$4). $(2 - e^{2})^{\frac{3}{2}}$ |
| Answer» OPTION 4 is the RIGHT ANSWER | |
| 66. |
The value of $(tan35^{0} tan45^{0} tan55^{0})$ is1). $\frac{1}{2}$2). 23). 04). 1 |
| Answer» 1 : - is CORRECT HENCE OPTION 4 | |
| 67. |
If $sin17^{0}$ = $\frac{x}{y}$, then $sec 17^{0} - sin 73^{0}$ is equal to1). $\frac{y}{(\sqrt{y^{2}-x^{2}})}$2). $\frac{y^{2}}{(x\sqrt{y^{2}-x^{2}})}$3). $\frac{x}{(y\sqrt{y^{2}-x^{2}})}$4). $\frac{x^{2}}{(y\sqrt{y^{2}-x^{2}})}$ |
| Answer» | |
| 68. |
If $tan(2\theta + 45^{0})$ = $cot3\theta$ where $(2\theta + 45^{0})$ and $3\theta$ are acute angles, then the value of $\theta$ is1). $5^{0})$2). $9^{0})$3). $12^{0})$4). $15^{0})$ |
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Answer» This question was asked some where in previous year PAPERS of SSC, and correct answer was OPTION 2 |
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| 69. |
If tan A = n tan B and sin A = m sin B, then the value of $cos^{2}A$ is1). $\frac{m^{2} -1}{n^{2} +1}$2). $\frac{m^{2} +1}{n^{2} -1}$3). $\frac{m^{2} +1}{n^{2} +1}$4). $\frac{m^{2} -1}{n^{2} -1}$ |
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Answer» I have read it somewhere $\FRAC{m^{2} -1}{n^{2} -1}$ is CORRECT |
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| 70. |
If $\theta$ is an acute angle and $tan\theta + cot\theta$ = 2, then the value of $tan^{5}\theta + cot^{5}\theta$ is1). 12). 23). 34). 4 |
| Answer» OPTION 2 is the ANSWER | |
| 71. |
If $sin\theta + sin^{2}\theta$ = 1, then the value of $cos^{2}\theta + cos^{4}\theta$ is1). 22). 43). 04). 1 |
| Answer» CORRECT ANSWER is: OPTION 4 | |
| 72. |
If $tan\theta$ = $\frac{1}{\sqrt{11}}$ , $0 < \theta < \frac{\pi}{2}$ , then the value of $\frac{cosec^{2}\theta - sec^{2}\theta}{cosec^{2}\theta + sec^{2}\theta}$then the value ofis1). $\frac{3}{4}$2). $\frac{4}{5}$3). $\frac{5}{6}$4). $\frac{6}{7}$ |
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Answer» $\FRAC{4}{5}$ is the correct ANSWER as per the ssc answer key |
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| 73. |
The equation $cos^{2}\theta$ = $\frac{(x+y)^{2}}{4xy}$ is only possible when1). x = -y2). x > y3). x = y4). x < y |
| Answer» | |
| 74. |
If $0^{0} < A < 90^{0}$, then the value of $tan^{2}A + cot^{2}A - sec^{2}A coeec^{2}A$is1). 02). 13). 24). -2 |
| Answer» | |
| 75. |
If $29tan\theta$= 31, then the value of $\frac{1 + 2 sin\theta cos\theta}{1 - 2 sin\theta cos\theta}$ is equal to1). 8102). 9003). 5404). 490 |
| Answer» | |
| 76. |
A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is1). 72 m2). 60 m3). 65 m4). 70 m |
| Answer» | |
| 77. |
If $sec\theta + tan\theta$ = $2+\sqrt{5}$ , then the value of $sin\theta$ is $(0^{0} \leq \theta \leq 90^{0})$1). $\frac{\sqrt{3}}{2}$2). $\frac{2}{\sqrt{5}}$3). $\frac{1}{\sqrt{5}}$4). $\frac{4}{5}$ |
| Answer» RIGHT ANSWER for this QUESTION is $\frac{2}{\sqrt{5}}$ | |
| 78. |
There are two vertical posts, one on each side of a road. Just opposite to each other. One post is 108 metre high. From the top of this post, the angle of depression of the top and foot of the other post are $30^{0}$ and $60^{0}$ respectively. The height of the other post (in metre) is1). 362). 723). 1084). 110 |
| Answer» | |
| 79. |
The angle of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then (in metre) the height of the building is1). $\frac{h cot x}{cot x + cot y}$2). $\frac{h cot y}{cot x + cot y}$3). $\frac{h cot x}{cotx - coty}$4). $\frac{h cot y}{cot x - cot y}$ |
| Answer» | |
| 80. |
In $\triangle ABC$, $\angle B$ = $90^{0}$ and AB : BC = 2 : 1. The value of sin A + cot C is1). $3+\sqrt{5}$2). $\frac{2+\sqrt{5}}{2\sqrt{5}}$3). $2+\sqrt{5}$4). $3\sqrt{5}$ |
| Answer» OPTION 2 : - $\FRAC{2+\sqrt{5}}{2\sqrt{5}}$ | |
| 81. |
$\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}$ is equal to1). $2 cos\theta$2). $2 sin\theta$3). $2 cot\theta$4). $2 sec\theta$ |
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Answer» This question was ASKED some where in previous year PAPERS of SSC, and correct answer was $2 sec\theta$ |
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| 82. |
At a point on a horizontal line through the base of a monument the angle of elevation of the top of the monument is found to be such that its tangent is $\frac{1}{5}$ . On walking 138 metres towards the monument the secant of the angle of elevation is found to be $\frac{\sqrt{193}}{12}$.The height of the monument ( in metre)is1). 352). 493). 424). 56 |
| Answer» | |
| 83. |
The shadow of a tower standing on a level plane is found to be 30 metre longer when the Sun's altitude changes from $60^{0}$ to $45^{0}$. The height of the tower is1). $15(3 +\sqrt{3})$ metre2). $15(\sqrt{3}+1)$ metre3). $15(\sqrt{3}-1)$ metre4). $15(3 -\sqrt{3})$ metre |
| Answer» | |
| 84. |
If (1 + sinA )(1 + sinB) (1 + sinC ) = (1 - sinA )(1 - sinB) (1 - sinC ), $0 < A ,B,C < \frac{\pi}{6}$ ,then each aide is equal to1). sin A sin B sin C2). cos A cos B cos C3). tan A tan B tan C4). 1 |
| Answer» HELLO, COS A cos B cos C is CORRECT | |
| 85. |
The ellminant of $\theta$ from $xcos\theta - y sin\theta$ = 2 and $x sin\theta + y cos\theta$ = 4 will give1). $x^{2} + y^{2}$= 202). $3x^{2} + y^{2$= 203). $x^{2} - y^{2}$= 204). $3x^{2} - y^{2}$= 10 |
| Answer» OPTION 1 is the RIGHT ONE | |
| 86. |
If $tan2\theta. tan4\theta$ = 1, then the value of $tan3\theta$ is1). $\sqrt{3}$2). 03). 14). $\frac{1}{\sqrt{3}}$ |
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Answer» This QUESTION was asked some where in PREVIOUS YEAR papers of SSC, and correct ANSWER was option 3 |
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| 87. |
A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot of the tower are $60^{0}$ and $30^{0}$ respectively. The height of the tower is1). 20 m2). 30 m3). 40 m4). 50 m |
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Answer» it from PREVIOUS YEAR ssc papers, OPTION 3 is the RIGHT answer |
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| 88. |
A telegraph post is bent at point above the ground due to storm. Its top just meets the ground at a distance of $8\sqrt{3}$ metres from its foot and makes an angle of $30^{0}$,then the height of the post is:1). 16 metres2). 23 metres3). 24 metres4). 10 metres |
| Answer» RIGHT ANSWER is 23 METRES | |
| 89. |
The minimum value of $2sin^{2}\theta + 3cos^{2}\theta$ is1). 02). 33). 24). 1 |
| Answer» 3 is the ANSWER | |
| 90. |
The value of $\frac{cos^{2} 60^{0}+ 4 sec^{2} 30^{0}- tan^{2} 45^{0}}{sin^{2} 30^{0} + cos^{2} 30^{0}}$ is1). $\frac{64}{\sqrt{3}}$2). $\frac{55}{12}$3). $\frac{67}{12}$4). $\frac{67}{10}$ |
| Answer» OPTION 2 is the RIGHT ANSWER | |
| 91. |
If $2(cos^{2}\theta - sin^{2}\theta)$ = 1, $\theta$ is a positive acute angle, then the value of $\theta$ is1). $60^{0}$2). $30^{0}$3). $45^{0}$4). $22\frac{1}{2}^{0}$ |
| Answer» ANSWER for this QUESTION is OPTION 2 | |
| 92. |
Find the value of $1 - 2 sin^{2}\theta + sin^{4}\theta$1). $sin^{4}\theta$2). $cos^{4}\theta$3). $cosec^{4}\theta$4). $sec^{4}\theta$ |
| Answer» RIGHT ANSWER for this QUESTION is OPTION 2 | |
| 93. |
$\frac{sec\theta + tan\theta}{sec\theta - tan\theta}$ = $\frac{5}{3}$ , then $sin\theta$ is equal to1). $\frac{1}{4}$2). $\frac{1}{3}$3). $\frac{2}{3}$4). $\frac{3}{4}$ |
| Answer» | |
| 94. |
The simple value of $tan1^{0}.tan2^{0}.tan3^{0} ............ tan89^{0}$is1). $\frac{1}{2}$2). 03). 14). $\frac{2}{3}$ |
| Answer» | |
| 95. |
If $cos^{2}\theta - sin^{2}\theta$ = $\frac{1}{3}$, where $0 \leq \theta \leq\frac{\pi}{2}$, then the value of $cos^{4}\theta - sin^{4}\theta$ is1). $\frac{1}{3}$2). $\frac{2}{3}$3). $\frac{1}{9}$4). $\frac{2}{9}$ |
| Answer» OPTION 1 is the CORRECT answer as PER the answer KEY | |
| 96. |
If $cos^{2}\alpha + cos^{2}\beta$ = 2, then the value of $tan^{3}\alpha + sin^{3}\beta$ to :1). -12). 03). 14). $\frac{1}{\sqrt{3}}$ |
| Answer» 0 SEEMS CORRECT. | |
| 97. |
The angle of elevation of the top of a tower from the point P and Q at distance of 'a' of and 'b' respectively from the base of the tower and in the same straight line with it are complementary.The height of the tower is1). $\sqrt{ab}$2). $\frac{a}{b}$3). ab4). $a^{2}b^{2}$ |
| Answer» HELLO, $\SQRT{AB}$ is CORRECT | |
| 98. |
If $tan\left(\frac{\pi}{2} - \frac{\theta}{2}\right)$ = $\sqrt{3}$ , the value of $cos\theta$ is :1). 02). $\frac{1}{\sqrt{2}}$3). $\frac{1}{2}$4). 1 |
| Answer» OPTION option 3 is the CORRECT ANSWER | |
| 99. |
If $(sin\alpha + coecc\alpha)^{2}(cos\alpha + sec\alpha)^{2}$ = $k+tan^{2}\alpha +cot^{2}\alpha$, then the value of k is1). 12). 73). 34). 5 |
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Answer» This question was asked some where in previous year PAPERS of SSC, and CORRECT answer was 7 |
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| 100. |
If a pole of 12 m height casts a shadow of $4\sqrt{3}$ m long on the ground , then the sun's angle of elevation at that instant is1). $30^{0}$2). $60^{0}$3). $45^{0}$4). $90^{0}$ 16 cm is |
| Answer» | |