1 . 2sin2Θ+3cosΘ−3=0 হলে, Θ এর মান কত? যেখানে Θ সুক্ষ্মকোণ? 

• A. 60°
• B. 0°
• C. 30°
• D. 45°

Answer: Option A

Explanation:

2 . θ এর মান নির্নয় করুন, যখন sinθ = √3/2 যদি 735°<825°.

• A. 785°
• B. 780°
• C. 760°
• D. 788°

Answer: Option B

Explanation:

3 . সমাধান করুনঃ tan2θ-(1+√3)tanθ+√3 = 0

• A. θ = 15°, 30°
• B. θ = 45°, 60°
• C. θ = 36°, 55°
• D. θ = 75°, 90°

Answer: Option B

Explanation:

4 . Sin θ = Cos θ হলে θ এর মান কত?

• A. ০°
• B. ৩০°
• C. ৪৫°
• D. ৯০°

Answer: Option C

Explanation:

5 . Sin θ এর সর্বনিম্ন মান কত?

• A. ০
• B. ১
• C. -১
• D. ৯০

Answer: Option A

Explanation:

6 . secθ = 2 হলে cotθ এর মান-

• A. 1/√5
• B. 1/√3
• C. √3
• D. √5

Answer: Option B

Explanation:

7 . cosecθ+cotθ=2 হলে cosecθ−cotθ= কত?

• A. -1
• B. 1/2
• C. 0
• D. 1

Answer: Option B

Explanation:

8 . tanθ=ab

• A. $\sin \theta =\frac{b}{a^2+b^2}$
• B. $\cos \theta =\frac{a}{\sqrt{a^{2+}}{b}^2}$
• C. $\sec \theta =\frac{a^2+b^2}{a}$
• D. $\csc \theta =\frac{a^2+b^2}{a}$

Answer: Option B

Explanation:

9 . secθ+tanθ=75,secθ-tanθ

• A. $\frac{5}{7}$
• B. $\frac{3}{7}$
• C. $\frac{3}{5}$
• D. $\frac{1}{5}$

Answer: Option A

Explanation:

10 . sinθ=45

• A. $\frac{5}{4}$
• B. $\frac{4}{9}$
• C. $\frac{3}{5}$
• D. $\frac{5}{3}$

Answer: Option D

Explanation:

11 . sinθ=45

• A. $4/3$
• B. $3/4$
• C. $3/5$
• D. $5/4$

Answer: Option A

Explanation:

12 . sinθ=513

• A. $\frac{5}{12}$
• B. $\frac{12}{5}$
• C. $\frac{13}{5}$
• D. $\frac{13}{5}$

Answer: Option C

Explanation:

13 . sin-θ

• A. $-\sin \theta$
• B. $\sin \theta$
• C. $\pm \sin \theta$
• D. কোনোটিই নয়

Answer: Option A

Explanation:

14 . secθ+tanθ=52

• A. $9/4$
• B. $2/5$
• C. $3$
• D. $25/4$

Answer: Option B

Explanation:

15 . sinθ=513

• A. $3/4$
• B. $5/12$
• C. $12/13$
• D. $5/13$

Answer: Option B

Explanation:

16 . secθ=2

• A. $0°$
• B. $30°$
• C. $45°$
• D. $60°$

Answer: Option D

Explanation:

17 . cscθ+cotθ=2

• A. $-1$
• B. $1/2$
• C. $0$
• D. $1$

Answer: Option B

Explanation:

18 . sinθ+cosθsinθ-cosθ=7

• A. $3/4$
• B. $4/3$
• C. $7/8$
• D. $8/7$

Answer: Option B

Explanation:

19 . θ

• A. $30°$
• B. $18°$
• C. $24°$
• D. $12°$

Answer: Option D

Explanation:

20 . 1+tan2θ=4

• A. $30°$
• B. $45°$
• C. $60°$
• D. $0°$

Answer: Option C

Explanation:

21 . sin-θ

• A. $-\sin \theta$
• B. $\sin \theta$
• C. $\pm \sin \theta$
• D. কোনোটিই নয়

Answer: Option A

Explanation:

22 . tanθ=8

• A. $\sqrt{8}$
• B. $3$
• C. $\sqrt{3}$
• D. $8$

Answer: Option B

Explanation:

23 . sin θ = cos θ  হলে  θ  এর মান কত?

• A. 0 °
• B. 30 °
• C. 45 °
• D. 90 °

Answer: Option C

Explanation:

24 . r = a sinθ সমীকরণটি নির্দেশ করে- 

• A. বৃত্ত
• B. পরাবৃত্ত
• C. উপবৃত্ত
• D. অধিবৃত্ত

Answer: Option A

Explanation:

25 . asinθ,bcosθ

• A. অধিবৃত্ত
• B. উপবৃত্ত
• C. বৃত্ত
• D. সরলরেখা

Answer: Option C

Explanation:

26 . n একটি পূর্ণ সংখ্যা হলে sinθ=0 এর সাধারন সমাধান-

• A. θ=nπ
• B. θ=(2n+1)π/2
• C. θ=2nπ
• D. θ=2nπ±α

Answer: Option A

Explanation:

27 .

• A. $\left(\frac{1}{2},0\right)\frac{1}{2}$
• B. $\left(0,2\right),\frac{1}{2}$
• C. $\left(0,\frac{1}{2}\right),2$
• D. $\left(0,\frac{1}{2}\right),\frac{1}{2}$

Answer: Option D

Explanation:

28 . cotα+cotβ=a,tanβ=B

• A. $\frac{1}{b}-\frac{1}{a}$
• B. $\frac{1}{a}-\frac{1}{b}$
• C. $\frac{1}{a}+\frac{1}{b}$
• D. $-\frac{1}{a}-\frac{1}{b}$

Answer: Option A

Explanation:

29 . tan2θtanθ=1

• A. 0°
• B. 30°
• C. 45°
• D. 60°

Answer: Option B

Explanation:

30 . x=2secθ

• A. $\frac{1}{2\sqrt{2}}$
• B. $2\sqrt{2}$
• C. $\frac{1}{2\sqrt{3}}$
• D. $2\sqrt{3}$

Answer: Option A

Explanation:

31 . cosθ=12x+1x

• A. $-\frac{1}{2}\left(x+\frac{1}{x^2}\right)$
• B. $\frac{1}{2}\left(x-\frac{1}{x^2}\right)$
• C. $\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)$
• D. $\frac{1}{2}\left(\frac{1}{x^2}-x\right)$

Answer: Option D

Explanation:

32 . sinθ-2=cos2θ,-π≤θ≤π

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer: Option C

Explanation:

33 . cosθ=1213

• A. $\frac{5}{12}$
• B. $\frac{25}{144}$
• C. $\frac{13}{12}$
• D. $\pm \frac{13}{12}$

Answer: Option A

Explanation:

34 . sinθ-cosθ=0 হলে, θ এর ক্ষুদ্রতম ধনাত্বক মান কোনটি?

• A. π/3
• B. π/2
• C. π/4
• D. π/6

Answer: Option C

Explanation:

35 . θ=cos-145

• A. $\frac{16}{25}$
• B. $\frac{9}{25}$
• C. $\frac{8}{25}$
• D. $\frac{7}{25}$

Answer: Option D

Explanation:

36 . sinθ+cosθ=2

• A. π/6
• B. π/4
• C. π/3
• D. π/2

Answer: Option B

Explanation:

37 . secθ=13123π2<θ<2π

• A. $\frac{5}{12}$
• B. $\frac{12}{5}$
• C. $-\frac{5}{12}$
• D. $-\frac{12}{5}$

Answer: Option A

Explanation:

38 . tanθ=512π<θ<3π2

• A. $-\frac{5}{13}$
• B. $-\frac{7}{13}$
• C. $\frac{5}{13}$
• D. $\frac{7}{13}$

Answer: Option B

Explanation:

39 . 5tan2θ-sec2θ=11n<θ<2pi

• A. $\frac{7\mathrm{\pi }}{3}$
• B. $\frac{2\mathrm{\pi }}{3}$
• C. $\frac{4\mathrm{\pi }}{3}$
• D. $\frac{\mathrm{\pi }}{3}$

Answer: Option D

Explanation:

40 . tanθ=340<θ<π2

• A. $7$
• B. $\frac{1}{7}$
• C. $-\frac{1}{7}$
• D. $-7$

Answer: Option C

Explanation:

41 . tanθ=13

• A. $\frac{3}{5}$
• B. $\frac{24}{26}$
• C. $\frac{24}{25}$
• D. $\frac{9}{10}$

Answer: Option C

Explanation:

42 . asinθ,bcosθ

• A. অধিবৃত্ত
• B. উপবৃত্ত
• C. বৃত্ত
• D. সরলরেখা

Answer: Option B

Explanation:

43 .

• A. $\left(\frac{1}{2},0\right),\frac{1}{2}$
• B. $\left(0,2\right),\frac{1}{2}$
• C. $\left(0,\frac{1}{2}\right),2$
• D. $\left(0,\frac{1}{2}\right),\frac{1}{2}$

Answer: Option D

Explanation:

44 . 2cos2x+3cosx=2 0<θ<2π

• A. $\left\{\frac{\pi }{3},\frac{5\pi }{3}\right\}$
• B. $\left\{\frac{\pi }{3},\pi \right\}$
• C. $\left\{\frac{\pi }{3},\frac{2\pi }{3}\right\}$
• D. $\left\{\frac{\pi }{2},\frac{5\pi }{3}\right\}$

Answer: Option A

Explanation:

45 . r=8cosθ+6sinθ

• A. 8
• B. 6
• C. 4
• D. 3

Answer: Option A

Explanation:

46 . cotα+cotβ=a,tanβ=b

• A. $\frac{1}{b}-\frac{1}{a}$
• B. $\frac{1}{a}-\frac{1}{b}$
• C. $\frac{1}{a}+\frac{1}{b}$
• D. $-\frac{1}{a}-\frac{1}{b}$

Answer: Option A

Explanation:

47 . tan2θtanθ=1

• A. 0°
• B. 30°
• C. 45°
• D. 60°

Answer: Option B

Explanation:

48 . cotθ-tanθ=65

• A. $\theta \frac{1}{2}{\cos }^{-1}\left(\frac{5}{\sqrt{34}}\right)$
• B. $\theta \frac{1}{2}{\cos }^{-1}\left(\frac{3}{\sqrt{34}}\right)$
• C. $\theta \frac{1}{2}{\cos }^{-1}\left(\frac{10}{\sqrt{34}}\right)$
• D. $\theta \frac{1}{2}{\cos }^{-1}\left(\frac{3}{\sqrt{34}}\right)$

Answer: Option B

Explanation:

49 . r2-43rcosθ-4rsinθ+15=0

• A. 4
• B. 3
• C. 2
• D. 1

Answer: Option B

Explanation:

50 . x=2secθ

• A. $\frac{1}{2\sqrt{2}}$
• B. $2\sqrt{2}$
• C. $\frac{1}{2\sqrt{3}}$
• D. $2\sqrt{3}$

Answer: Option A

Explanation:

51 . tanθ+secθ=x

• A. $\frac{x^2+1}{x^2-1}$
• B. $\frac{x^2-1}{x^2+1}$
• C. $\frac{1-x^2}{1+x^2}$
• D. $\frac{1+x^2}{1-x^2}$

Answer: Option A

Explanation:

52 . tanθ+cotθ=2cscθ,0≤θ≤π2

• A. $\frac{\pi }{4}$
• B. $\frac{5\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{3}$

Answer: Option D

Explanation:

53 . tanθ=yx

• A. $x$
• B. $y$
• C. $\frac{1}{x}$
• D. $\frac{1}{y}$

Answer: Option A

Explanation:

54 . 8sin4θ2-8sin2θ2+1

• A. $2{\sin }^2\theta$
• B. $2{\cos }^2\theta$
• C. $\sin 2\theta$
• D. $\cos 2\theta$

Answer: Option D

Explanation:

55 . 2cos22θ+22sinθ=3 হলে,θ

• A. 30°
• B. 45°
• C. 60°
• D. 120°

Answer: Option B

Explanation:

56 . r2-23r cosθ-8r sin θ+15=0

• A. 1
• B. 2
• C. 3
• D. 4

Answer: Option B

Explanation:

57 . x=3tanθ, y=2secθ

• A. $\frac{x^2}{9}-\frac{y^2}{4}=1$
• B. $\frac{x^2}{9}+\frac{y^2}{4}=1$
• C. $\frac{x^2}{4}-\frac{y^2}{9}=1$
• D. $\frac{y^2}{4}-\frac{x^2}{9}=1$

Answer: Option D

Explanation:

58 . cosθ+sinθ=2cosθ

• A. $\pm \sqrt{2}\sin \theta$
• B. $2\sin \theta$
• C. $\sqrt{2}\sin \theta$
• D. $\sqrt{2\sin \theta }$

Answer: Option A

Explanation:

59 . sinθ = 12/13 এবং π/2<θ<π হলে, cotθ+cosec(-θ) এর মান কত?

• A. 2/3
• B. 5/3
• C. -3/2
• D. 10/3

Answer: Option C

Explanation:

60 . sinθ = 12/13 এবং π/2<θ<π হলে, cotθ+cosec(-θ) এর মান কত?

• A. 2/3
• B. 5/3
• C. -3/2
• D. 10/3

Answer: Option C

Explanation:

61 . sinθ - cos2θ = 2 এর সাধারন সমাধান কোনটি ?

• A. (4n+1)π/2
• B. (2n+1)π/2
• C. (2n+1)π/3
• D.

Answer: Option A

Explanation:

62 . f(x)=1−x2/1+x2 then f(tanθ)=?

• A. cos2ϴ
• B. tan2ϴ
• C. sin 2ϴ
• D.

Answer: Option A

Explanation:

63 . θ হলে θ এর কোন মানের জন্য f(θ)=0 হবে ?

• A. π/4
• B. π/2
• C. π/3
• D.

Answer: Option A

Explanation:

64 . cosθ+3–√sinθ=2 সমীকরণটি বিশেষ সমাধান কোনটি ?

• A. θ=2nπ+π
• B. θ=2nπ±π3
• C. θ=π/3
• D.

Answer: Option A

Explanation:

65 . cos 2θ = 1/√2 সমীকরনের সাধারন সমাধান কোনটি?

• A. 2nπ±π/3
• B. nπ±π/3
• C. 2nπ±π/8
• D. nπ±π/8

Answer: Option D

Explanation:

66 . ভূমির সঙ্গে  θ  কোণে আনত কোন তল হতে একটি বস্তু পড়তে থাকলে বস্তুর ত্বরণের মান কত ?

• A. g
• B. g cos θ
• C. g sin θ
• D. g tan θ
• D. g cot θ

Answer: Option C

Explanation:

67 . cos θ = 12/13 হলে tanθ এর মান কত ?

• A. 13/12
• B. ±13/12
• C. 25/144
• D. ±5/12

Answer: Option D

Explanation:

68 . Cosθ+ √3 sinθ = 2 সমীকরণের সাধারণ সমাধান-

• A. θ=2nπ + π/3
• B. θ=2nπ + π/6
• C. θ=2nπ - π/3
• D.

Answer: Option A

Explanation:

69 . 〖sin² 2θ-3cos² θ=0 সমীকরণের সাধারণ সমাধান-

• A. nπ± π/3
• B. 2nπ± π/6
• C. 2nπ± π/3
• D.

Answer: Option A

Explanation:

70 . 2 cos²θ + 2√2 sinθ = 3 হলে θ এর মান-

• A. 30 ͦ
• B. 45 ͦ
• C. 60 ͦ
• D. 120 ͦ

Answer: Option B

Explanation:

71 . 2(cos²θ-sin²θ)=√3 হলে, θ এর মান কত?

• A. 2nπ±π/6
• B. nπ±π/6
• C. 2nπ±π/12
• D. nπ±π/12

Answer: Option D

Explanation:

72 . cosθ + sinθ = √2 হলে, θ এর মান-

• A. 2nπ
• B. (2n+1)π
• C. 2nπ + π/4
• D. (2n-1)π/4

Answer: Option C

Explanation:

73 . 4 ( sin2θ   +   cos θ ) = 5  সমীকরণের সাধারণ সমাধান -

• A. θ = 2 n π ± π / 2
• B. θ = 2 nπ ± π / 3
• C. θ = 2 nπ ± π / 4
• D. θ = 2 nπ ± π / 5

Answer: Option B

Explanation: