184 + Interview Questions in TRIGONOMETRY in Mathematics

1.	The degree measure of 1 radian (taking $\pi$ = $\frac{22}{7}$) is1). $57^{0}61'22"$ (approx)2). $57^{0}16'22"$ (approx)3). $57^{0}22'16"$ (approx)4). $57^{0}32'16"$ (approx)
Answer» $57^{0}16'22"$ (APPROX) SEEMS CORRECT.

Discussion

2.	Value of the expression : $\frac{1 + 2 sin 60^{0} cos 60^{0}}{sin 60^{0}+ cos 60^{0}} + \frac{1 - 2 sin 60^{0} cos 60^{0}}{sin 60^{0}- cos 60^{0}}$ is :1). $2\sqrt{3}$2). 03). $\sqrt{3}$4). 2
Answer» OPTION 3 is the RIGHT ONE

Discussion

3.	If $7 sin^{2}\theta + 3 cos^{2}\theta$ = 4, $(0^{0} < \theta < 90^{0})$, then the value of $tan\theta$ is1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{2}$3). 14). $\sqrt{3}$
Answer» RIGHT ANSWER for this question is $\frac{1}{\SQRT{3}}$

Discussion

4.	The value of $\frac{1}{cosec\theta-cot\theta}-\frac{1}{sin\theta}$ is1). 12). $cot\theta$3). $coses\theta$4). $tan\theta$
Answer» OPTION 2 is the RIGHT ANSWER

Discussion

5.	The value of $tan 4^{0}.tan 43^{0}.tan 47^{0}.tan 86^{0}$ is1). 22). 33). 14). 4
Answer» 3 is the ANSWER

Discussion

6.	If $cot\theta.coeec23^{0}$ = 1, the value of $\theta$ is1). $23^{0}$2). $37^{0}$3). $63^{0}$4). $67^{0}$
Answer» CORRECT ANSWER is: OPTION 4

Discussion

7.	TF is a tower with F on the ground. The angle of elevation of T from A is$x^{0}$ such that $tanx^{0}$ = $\frac{2}{5}$ and AF = 200m.The angle of elevation of T from a nearer point B is $y^{0}$ with BF = 80m. The value of $y^{0}$ is1). $60^{0}$2). $30^{0}$3). $75^{0}$4). $45^{0}$
Answer» OPTION 4 : - $45^{0}$

Discussion

8.	If $sin\theta + cos\theta$ = p and $sec\theta + cosec\theta$ = q , then the value of $q(p^{2} - 1)$ is1). 12). p3). 2p4). 2
Answer» P

Discussion

9.	If $\theta$ is an acute angle and $tan^{2}\theta + \frac{1}{tan^{2}\theta}$ = 2,then the value of $\theta$ is :1). $60^{0}$2). $45^{0}$3). $15^{0}$4). $30^{0}$
Answer» $45^{0}$

Discussion

10.	In $\triangle ABC$, $\angle C$ = $90^{0}$ and AB = c, BC = a, CA = b; then the value of (cosec B - cos A) is1). $\frac{c^{2}}{ab}$2). $\frac{b^{2}}{ca}$3). $\frac{a^{2}}{bc}$4). $\frac{bc}{a^{2}}$
Answer» ANSWER for this QUESTION is OPTION 3

Discussion

11.	The value of the following is : $3(sin^{4}\theta + cos^{4}\theta) + 2(sin^{6}\theta + cos^{6}\theta) + 12 sin^{2}\theta cos^{2}\theta$1). 02). 33). 24). 5
Answer» I have READ it SOMEWHERE 5 is CORRECT

Discussion

12.	The angle of elevation of a tower from a distance of 100 metre from its foot is $30^{0}$. Then the height of the tower is1). $50\sqrt{3}$ metre2). $100\sqrt{3}$ metre3). $\frac{50}{\sqrt{3}}$ metre4). $\frac{100}{\sqrt{3}}$ metre
Answer» This question was ASKED some where in PREVIOUS YEAR papers of ssc, and correct ANSWER was option 4

Discussion

13.	a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation $a^{2}+b^{2}+c^{2}$ =ab + bc + ca, then the value of $sin^{2}A + sin^{2}B + sin^{2}C$ is1). $\frac{3}{4}$2). $\frac{3\sqrt{3}}{2}$3). $\frac{3}{2}$4). $\frac{9}{4}$
Answer» RIGHT ANSWER is $\FRAC{9}{4}$

Discussion

14.	The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from $45^{0}$ to $30^{0}$ . Then the height of the tower is1). $5\sqrt{3}$ metre2). $10(\sqrt{3}+1)$ metre3). $5(\sqrt{3}+1)$ metre4). $10\sqrt{3}$ metre
Answer» $10(\sqrt{3}+1)$ METRE is the best SUITED

Discussion

15.	There are two temples, one on each bank of a river.Just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are $30^{0}$ and $60^{0}$ respectively.The length of the temple is :1). 18 m2). 36 m3). $36\sqrt{3}$ m4). $18\sqrt{3}$ m
Answer» is 36 m is the CORRECT ANSWER am i RIGHT

Discussion

16.	In circular measure,the value of angle $11^{0}15'$ is1). $\frac{\pi^{c}}{16}$2). $\frac{\pi^{c}}{8}$3). $\frac{\pi^{c}}{4}$4). $\frac{\pi^{c}}{12}$
Answer» $\FRAC{\pi^{c}}{16}$ : OPTION 1 is the correct ANSWER

Discussion

17.	If $sin\theta + sin^{2}\theta$ = 1 then $cos^{2}\theta + cos^{4}\theta$ is equal to1). None2). 13). $\frac{sin\theta}{cos^{2}\theta}$4). $\frac{cos^{2}\theta}{sin\theta}$
Answer» RIGHT ANSWER for this QUESTION is 1

Discussion

18.	If $7sin\alpha$ = $24cos\alpha$ : $0 < \alpha < \frac{\pi}{2}$, then the value $14tan\alpha-75cos\alpha - 7sec\alpha$ is equal to1). 32). 43). 14). 2
Answer» 2 is the correct ANSWER as per the SSC answer KEY

Discussion

19.	If $cos\theta + sec\theta$ = 2, the value of $cos^{6}\theta + sec^{6}\theta $ is1). 42). 83). 14). 2
Answer» HELLO, 2 is CORRECT

Discussion

20.	If x = $a (sin\theta + cos\theta)$ and y = $b (sin\theta - cos\theta)$, then the value of $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$ is:1). 42). 33). 14). 2
Answer» OPTION 4 is the RIGHT ANSWER

Discussion

21.	If $tan\theta + cot\theta$ = 2, then the value of $tan^{100}\theta + cot^{100}\theta$ is1). 22). 03). 14). $\sqrt{3}$
Answer» I THINK OPTION 1 is the RIGHT ANSWER

Discussion

22.	If a $\triangle ABC$ ,$\angle B$ = $\frac{\pi}{3}$ ,$\angle C$ = $\frac{\pi}{4}$ ,and D divides BC internally in the ratio 1 : 3 then $\frac{sin\angle BAD}{sin\angle CAD}$ to equal to1). $\frac{1}{\sqrt{2}}$2). $\frac{1}{\sqrt{3}}$3). $\frac{1}{\sqrt{6}}$4). $\sqrt{6}$
Answer» OPTION 3 is the RIGHT ANSWER

Discussion

23.	The minimum value of $4 tan^{2}\theta + 9 cot^{2}\theta$is equal to1). 02). 53). 124). 13
Answer» 5 : OPTION 3 is the CORRECT ANSWER

Discussion

24.	If sin(A + B) = sin A cos B + cos A sin B, then the value of $sin 75^{0}$is1). $\frac{\sqrt{3}+1}{\sqrt{2}}$2). $\frac{\sqrt{2}+1}{2\sqrt{2}}$3). $\frac{\sqrt{3}+1}{2\sqrt{2}}$4). $\frac{\sqrt{3}+1}{2}$
Answer» right ANSWER is $\frac{\sqrt{2}+1}{2\sqrt{2}}$

Discussion

25.	If $2cos\theta - sin\theta$ = $\frac{1}{\sqrt{2}}$ , $(0^{0} < \theta
Answer» $\SQRT{2}$ : SEEMS CORRECT

Discussion

26.	The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from $45^{0}$ to $30^{0}$ . Then the height of the tower is1). $5(\sqrt{3}+ 1)$ metres2). $5(\sqrt{3}- 1)$ metres3). $5\sqrt{3}$ metres4). $\frac{3}{\sqrt{3}}$ metres
Answer» This QUESTION was asked some where in previous YEAR PAPERS of ssc, and CORRECT answer was option 1

Discussion

27.	If $sin\theta + cosec\theta$= 2, then the value of $sin^{5}\theta + cosec^{5}\theta$ when $0^{0}\theta \theta \theta 90^{0}$, to1). 02). 13). 104). 2
Answer» 2 is the correct ANSWER as per the SSC answer key

Discussion

28.	The value of $(2cos^{2}\theta-1)\left(\frac{1 + tan\theta}{1 - tan\theta}+\frac{1 - tan\theta}{1 + tan\theta}\right)$1). 42). 13). 34). 2
Answer» 2 : - is CORRECT HENCE OPTION 4

Discussion

29.	If $sin\theta + cos\theta$ = $\sqrt{2}sin(90^{0} - 0)$, then the value of $cot\theta$ is1). $-\sqrt{2}-1$2). $\sqrt{2}-1$3). $\sqrt{2}+1$4). $-\sqrt{2}+1$
Answer» i THINK OPTION 3 is CORRECT

Discussion

30.	If tan x = $sin 45^{0}.cos 45^{0} + sin 30^{0}$ ,then the value of x is1). $30^{0}$2). $45^{0}$3). $60^{0}$4). $90^{0}$
Answer» I have READ it SOMEWHERE $45^{0}$ is CORRECT

Discussion

31.	If $sin\theta - cos\theta$ = $\frac{7}{13}$ and $0 < \theta < 90^{0} $, then the value of $sin\theta + cos\theta$ is1). $\frac{17}{13}$2). $\frac{13}{17}$3). $\frac{1}{13}$4). $\frac{1}{17}$
Answer» $\frac{17}{13}$ is the correct answer as PER the SSC answer KEY

Discussion

32.	The valueof $\frac{cot30^{0} - cot75^{0}}{tan15^{0} - tan60^{0}}$is equal to1). -12). 03). 14). 2
Answer» ANSWER for this QUESTION is -1

Discussion

33.	If $7sin^{2}\theta + 3cos^{2}\theta$ = 4, then the value of $tan\theta$ is ($\theta$ is acute)1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{\sqrt{2}}$3). $\sqrt{3}$4). 1
Answer» This question was asked some where in previous year papers of SSC, and CORRECT ANSWER was option 1

Discussion

34.	The value of $\theta$, which satisfies the equation $tan^{2}\theta + 3$ = $3 sec\theta$,$0^{0} < \theta < 90^{0}$ is1). $15^{0}$or $0^{0}$2). $30^{0}$or $0^{0}$3). $45^{0}$or $0^{0}$4). $60^{0}$or $0^{0}$
Answer» Its very simple QUESTION $60^{0}$or $0^{0}$ is the correct ANSWER.

Discussion

35.	The simplified value of $(sec x sec y + tan x tan y)^{2} - (sec x tan y + tan x sec y)^{2}$ is :1). -12). 03). $sec^{2}x$4). 1
Answer» I am not SURE, MAY be 1 is CORRECT

Discussion

36.	The value of $(cosec\alpha - sin\alpha ) (sec\alpha- cos\alpha) (tan\alpha + cot\alpha)$ is1). 12). 63). 24). 4
Answer» 1 : - is CORRECT HENCE OPTION 1

Discussion

37.	The value of the expression $sin^{2}1^{0}+sin^{2}11^{0}+sin^{2}21^{0}+sin^{2}31^{0}+sin^{2}41^{0}+sin^{2}45^{0}+sin^{2}49^{0}+sin^{2}59^{0}+sin^{2}69^{0}+sin^{2}79^{0}+sin^{2}89^{0}$is :1). 02). $5\frac{1}{2}$3). 54). $4\frac{1}{2}$
Answer» RIGHT ANSWER is $5\frac{1}{2}$

Discussion

38.	The minimum value of $2sin^{2}\theta + 3cos^{2}\theta$ is1). 32). 43). 24). 1
Answer» This question was asked some where in previous year PAPERS of SSC, and correct ANSWER was option 3

Discussion

39.	If $0^{0} < A < 90^{0}$, the value of $\frac{tan A - sec A -1}{tan A + sec A +1}$ is1). $\frac{sin A -1}{cos A}$2). $\frac{1- sin A}{cos A}$3). $\frac{1-cos A}{sin A}$4). $\frac{sinA + 1}{cos A}$
Answer» RIGHT ANSWER is $\FRAC{SIN A -1}{COS A}$

Discussion

40.	The value of $tan 11^{0} tan 17^{0} tan 79^{0} tan 73^{0}$is1). $\frac{1}{2}$2). 03). 14). $\frac{1}{\sqrt{2}}$
Answer» I THINK OPTION 3 is the RIGHT ANSWER

Discussion

41.	If $cos^{4}\theta - sin^{4}\theta$= $\frac{2}{3}$, then the value of $1 - 2 sin^{2}\theta$ is1). $\frac{2}{3}$2). $\frac{3}{2}$3). 14). 0
Answer» This question was asked some where in previous year PAPERS of SSC, and CORRECT ANSWER was OPTION 1

Discussion

42.	If $sin\alpha sec(30^{0}+ \alpha)$ = 1, $(0 < \alpha < 60^{0})$, then the value of $sin\alpha + cos2\alpha$ is1). 12). $\frac{2+\sqrt{3}}{2\sqrt{3}}$3). 04). $\sqrt{2}$
Answer» 1 : - is CORRECT HENCE OPTION 1

Discussion

43.	$\left(\frac{3\pi}{5}\right)$ radians is equal to1). $100^{0}$2). $120^{0}$3). $108^{0}$4). $180^{0}$
Answer» ANSWER for this QUESTION is $120^{0}$

Discussion

44.	If $sin\theta + coses\theta$ = 2, then the value of $sin^{9}\theta + cosec^{9}\theta$ is :1). 32). 23). 44). 1
Answer» is OPTION 2 is the CORRECT ANSWER am i RIGHT

Discussion

45.	The ratio of the length of a rod and its shadow is 1 :$\sqrt{2}$. The angle of elevation of the sun is :1). $90^{0}$2). $30^{0}$3). $45^{0}$4). $60^{0}$
Answer» This QUESTION was ASKED some where in previous year papers of SSC, and correct ANSWER was OPTION 2

Discussion

46.	The shadow of a tower is $\sqrt{3}$ times its height. Then the angle of elevation of the top of the tower is1). $45^{0}$2). $30^{0}$3). $60^{0}$4). $90^{0}$
Answer» i THINK OPTION 2 is CORRECT

Discussion

47.	If $x cos^{2}30^{0}. sin 60^{0}$ = $\frac{tan^{2}45^{0}. sec 60^{0}}{cosec60^{0}}$ then the value of x is1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{\sqrt{2}}$3). $2\frac{2}{3}$4). $\frac{1}{2}$
Answer» $\FRAC{1}{\SQRT{2}}$

Discussion

48.	If $tan(5x - 10^{0})$ = $cot(5y + 20^{0})$, the value of (x +y ) is1). $15^{0}$2). $16^{0}$3). $24^{0}$4). $20^{0}$
Answer» OPTION 2 : - $16^{0}$

Discussion

49.	The angle of elevation of sun changes from $30^{0}$ to $45^{0}$, the length of the shadow of a pole decreases by 4 metres, the height of the pole is (Assume $\sqrt{3}$ = 1.732)1). 1.464 m2). 9.464 m3). 3.648 cm4). 5.464 m
Answer» i THINK OPTION 4 is CORRECT

Discussion

50.	The numerical value of $\left(\frac{1}{cos\theta}+\frac{1}{cot\theta}\right)\left(\frac{1}{cos\theta}-\frac{1}{cot\theta}\right)$1). 02). -13). +14). 2
Answer» I THINK -1 is RIGHT

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The degree measure of 1 radian (taking $\pi$ = $\frac{22}{7}$) is1). $57^{0}61'22"$ (approx)2). $57^{0}16'22"$ (approx)3). $57^{0}22'16"$ (approx)4). $57^{0}32'16"$ (approx)

Value of the expression : $\frac{1 + 2 sin 60^{0} cos 60^{0}}{sin 60^{0}+ cos 60^{0}} + \frac{1 - 2 sin 60^{0} cos 60^{0}}{sin 60^{0}- cos 60^{0}}$ is :1). $2\sqrt{3}$2). 03). $\sqrt{3}$4). 2

If $7 sin^{2}\theta + 3 cos^{2}\theta$ = 4, $(0^{0} < \theta < 90^{0})$, then the value of $tan\theta$ is1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{2}$3). 14). $\sqrt{3}$

The value of $\frac{1}{cosec\theta-cot\theta}-\frac{1}{sin\theta}$ is1). 12). $cot\theta$3). $coses\theta$4). $tan\theta$

The value of $tan 4^{0}.tan 43^{0}.tan 47^{0}.tan 86^{0}$ is1). 22). 33). 14). 4

If $cot\theta.coeec23^{0}$ = 1, the value of $\theta$ is1). $23^{0}$2). $37^{0}$3). $63^{0}$4). $67^{0}$

TF is a tower with F on the ground. The angle of elevation of T from A is$x^{0}$ such that $tanx^{0}$ = $\frac{2}{5}$ and AF = 200m.The angle of elevation of T from a nearer point B is $y^{0}$ with BF = 80m. The value of $y^{0}$ is1). $60^{0}$2). $30^{0}$3). $75^{0}$4). $45^{0}$

If $sin\theta + cos\theta$ = p and $sec\theta + cosec\theta$ = q , then the value of $q(p^{2} - 1)$ is1). 12). p3). 2p4). 2

If $\theta$ is an acute angle and $tan^{2}\theta + \frac{1}{tan^{2}\theta}$ = 2,then the value of $\theta$ is :1). $60^{0}$2). $45^{0}$3). $15^{0}$4). $30^{0}$

In $\triangle ABC$, $\angle C$ = $90^{0}$ and AB = c, BC = a, CA = b; then the value of (cosec B - cos A) is1). $\frac{c^{2}}{ab}$2). $\frac{b^{2}}{ca}$3). $\frac{a^{2}}{bc}$4). $\frac{bc}{a^{2}}$

The value of the following is : $3(sin^{4}\theta + cos^{4}\theta) + 2(sin^{6}\theta + cos^{6}\theta) + 12 sin^{2}\theta cos^{2}\theta$1). 02). 33). 24). 5

The angle of elevation of a tower from a distance of 100 metre from its foot is $30^{0}$. Then the height of the tower is1). $50\sqrt{3}$ metre2). $100\sqrt{3}$ metre3). $\frac{50}{\sqrt{3}}$ metre4). $\frac{100}{\sqrt{3}}$ metre

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation $a^{2}+b^{2}+c^{2}$ =ab + bc + ca, then the value of $sin^{2}A + sin^{2}B + sin^{2}C$ is1). $\frac{3}{4}$2). $\frac{3\sqrt{3}}{2}$3). $\frac{3}{2}$4). $\frac{9}{4}$

The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from $45^{0}$ to $30^{0}$ . Then the height of the tower is1). $5\sqrt{3}$ metre2). $10(\sqrt{3}+1)$ metre3). $5(\sqrt{3}+1)$ metre4). $10\sqrt{3}$ metre

In circular measure,the value of angle $11^{0}15'$ is1). $\frac{\pi^{c}}{16}$2). $\frac{\pi^{c}}{8}$3). $\frac{\pi^{c}}{4}$4). $\frac{\pi^{c}}{12}$

If $sin\theta + sin^{2}\theta$ = 1 then $cos^{2}\theta + cos^{4}\theta$ is equal to1). None2). 13). $\frac{sin\theta}{cos^{2}\theta}$4). $\frac{cos^{2}\theta}{sin\theta}$

If $7sin\alpha$ = $24cos\alpha$ : $0 < \alpha < \frac{\pi}{2}$, then the value $14tan\alpha-75cos\alpha - 7sec\alpha$ is equal to1). 32). 43). 14). 2

If $cos\theta + sec\theta$ = 2, the value of $cos^{6}\theta + sec^{6}\theta $ is1). 42). 83). 14). 2

If x = $a (sin\theta + cos\theta)$ and y = $b (sin\theta - cos\theta)$, then the value of $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$ is:1). 42). 33). 14). 2

If $tan\theta + cot\theta$ = 2, then the value of $tan^{100}\theta + cot^{100}\theta$ is1). 22). 03). 14). $\sqrt{3}$

If a $\triangle ABC$ ,$\angle B$ = $\frac{\pi}{3}$ ,$\angle C$ = $\frac{\pi}{4}$ ,and D divides BC internally in the ratio 1 : 3 then $\frac{sin\angle BAD}{sin\angle CAD}$ to equal to1). $\frac{1}{\sqrt{2}}$2). $\frac{1}{\sqrt{3}}$3). $\frac{1}{\sqrt{6}}$4). $\sqrt{6}$

The minimum value of $4 tan^{2}\theta + 9 cot^{2}\theta$is equal to1). 02). 53). 124). 13

If sin(A + B) = sin A cos B + cos A sin B, then the value of $sin 75^{0}$is1). $\frac{\sqrt{3}+1}{\sqrt{2}}$2). $\frac{\sqrt{2}+1}{2\sqrt{2}}$3). $\frac{\sqrt{3}+1}{2\sqrt{2}}$4). $\frac{\sqrt{3}+1}{2}$

If $2cos\theta - sin\theta$ = $\frac{1}{\sqrt{2}}$ , $(0^{0} < \theta

The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from $45^{0}$ to $30^{0}$ . Then the height of the tower is1). $5(\sqrt{3}+ 1)$ metres2). $5(\sqrt{3}- 1)$ metres3). $5\sqrt{3}$ metres4). $\frac{3}{\sqrt{3}}$ metres

If $sin\theta + cosec\theta$= 2, then the value of $sin^{5}\theta + cosec^{5}\theta$ when $0^{0}\theta \theta \theta 90^{0}$, to1). 02). 13). 104). 2

The value of $(2cos^{2}\theta-1)\left(\frac{1 + tan\theta}{1 - tan\theta}+\frac{1 - tan\theta}{1 + tan\theta}\right)$1). 42). 13). 34). 2

If $sin\theta + cos\theta$ = $\sqrt{2}sin(90^{0} - 0)$, then the value of $cot\theta$ is1). $-\sqrt{2}-1$2). $\sqrt{2}-1$3). $\sqrt{2}+1$4). $-\sqrt{2}+1$

If tan x = $sin 45^{0}.cos 45^{0} + sin 30^{0}$ ,then the value of x is1). $30^{0}$2). $45^{0}$3). $60^{0}$4). $90^{0}$

If $sin\theta - cos\theta$ = $\frac{7}{13}$ and $0 < \theta < 90^{0} $, then the value of $sin\theta + cos\theta$ is1). $\frac{17}{13}$2). $\frac{13}{17}$3). $\frac{1}{13}$4). $\frac{1}{17}$

The valueof $\frac{cot30^{0} - cot75^{0}}{tan15^{0} - tan60^{0}}$is equal to1). -12). 03). 14). 2

If $7sin^{2}\theta + 3cos^{2}\theta$ = 4, then the value of $tan\theta$ is ($\theta$ is acute)1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{\sqrt{2}}$3). $\sqrt{3}$4). 1

The value of $\theta$, which satisfies the equation $tan^{2}\theta + 3$ = $3 sec\theta$,$0^{0} < \theta < 90^{0}$ is1). $15^{0}$or $0^{0}$2). $30^{0}$or $0^{0}$3). $45^{0}$or $0^{0}$4). $60^{0}$or $0^{0}$

The simplified value of $(sec x sec y + tan x tan y)^{2} - (sec x tan y + tan x sec y)^{2}$ is :1). -12). 03). $sec^{2}x$4). 1

The value of $(cosec\alpha - sin\alpha ) (sec\alpha- cos\alpha) (tan\alpha + cot\alpha)$ is1). 12). 63). 24). 4

The value of the expression $sin^{2}1^{0}+sin^{2}11^{0}+sin^{2}21^{0}+sin^{2}31^{0}+sin^{2}41^{0}+sin^{2}45^{0}+sin^{2}49^{0}+sin^{2}59^{0}+sin^{2}69^{0}+sin^{2}79^{0}+sin^{2}89^{0}$is :1). 02). $5\frac{1}{2}$3). 54). $4\frac{1}{2}$

The minimum value of $2sin^{2}\theta + 3cos^{2}\theta$ is1). 32). 43). 24). 1

If $0^{0} < A < 90^{0}$, the value of $\frac{tan A - sec A -1}{tan A + sec A +1}$ is1). $\frac{sin A -1}{cos A}$2). $\frac{1- sin A}{cos A}$3). $\frac{1-cos A}{sin A}$4). $\frac{sinA + 1}{cos A}$

The value of $tan 11^{0} tan 17^{0} tan 79^{0} tan 73^{0}$is1). $\frac{1}{2}$2). 03). 14). $\frac{1}{\sqrt{2}}$

If $cos^{4}\theta - sin^{4}\theta$= $\frac{2}{3}$, then the value of $1 - 2 sin^{2}\theta$ is1). $\frac{2}{3}$2). $\frac{3}{2}$3). 14). 0

If $sin\alpha sec(30^{0}+ \alpha)$ = 1, $(0 < \alpha < 60^{0})$, then the value of $sin\alpha + cos2\alpha$ is1). 12). $\frac{2+\sqrt{3}}{2\sqrt{3}}$3). 04). $\sqrt{2}$

$\left(\frac{3\pi}{5}\right)$ radians is equal to1). $100^{0}$2). $120^{0}$3). $108^{0}$4). $180^{0}$

If $sin\theta + coses\theta$ = 2, then the value of $sin^{9}\theta + cosec^{9}\theta$ is :1). 32). 23). 44). 1

The ratio of the length of a rod and its shadow is 1 :$\sqrt{2}$. The angle of elevation of the sun is :1). $90^{0}$2). $30^{0}$3). $45^{0}$4). $60^{0}$

The shadow of a tower is $\sqrt{3}$ times its height. Then the angle of elevation of the top of the tower is1). $45^{0}$2). $30^{0}$3). $60^{0}$4). $90^{0}$

If $x cos^{2}30^{0}. sin 60^{0}$ = $\frac{tan^{2}45^{0}. sec 60^{0}}{cosec60^{0}}$ then the value of x is1). $\frac{1}{\sqrt{3}}$2). $\frac{1}{\sqrt{2}}$3). $2\frac{2}{3}$4). $\frac{1}{2}$

If $tan(5x - 10^{0})$ = $cot(5y + 20^{0})$, the value of (x +y ) is1). $15^{0}$2). $16^{0}$3). $24^{0}$4). $20^{0}$

The angle of elevation of sun changes from $30^{0}$ to $45^{0}$, the length of the shadow of a pole decreases by 4 metres, the height of the pole is (Assume $\sqrt{3}$ = 1.732)1). 1.464 m2). 9.464 m3). 3.648 cm4). 5.464 m

The numerical value of $\left(\frac{1}{cos\theta}+\frac{1}{cot\theta}\right)\left(\frac{1}{cos\theta}-\frac{1}{cot\theta}\right)$1). 02). -13). +14). 2