MULTIPLE CHOICE QUESTIONS; (MCQ’s)
1.In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
The value of tan C is____
(a) 12/7
(b) 24/7
(c) 20/7
(d) 7/24
2. (Sin 30° + cos 60°) (sin 60° + cos 30°) is equal to____
(a) 0
(b) 1+ 2√3
(c) 1 − √3
(d) 1+√3
3. The value of (tan 60°)/(cot 30° ) is equal to____
(a) 0
(b) 1
(c) 2
(d) 3
4. 1− cos2A is equal to____
(a) sin2A
(b) tan2A
(c) 1− sin2A
(d) sec2A
5. Sin (90° – A) and cos A are____
(a) Different
(b) Same
(c) Not related
(d) None of the above
6. If cos x = 2/3 then tan x is equal to____
(a) 5/2
(b) √(5/2)
(c) √5/2
(d) 2/√5
7. If cos x = a/b, then sin x is equal to____
(a) b²− a2/b
(b) b − a/b
(c) √(b2 − a2 )/b
(d) √(b− a)/b
8. The value of sin 60° cos 30° + sin 30° cos 60° is___
(a) 0
(b) 1
(c) 2
(d) 4
9. The value of (2tan30°) /(1 + tan230°) is ____
(a) Sin 60°
(b) Cos 60°
(c) Tan 60°
(d) Sin 30°
10. Sin 2A = 2 sin A is true when A = ____
(a) 30°
(b) 45°
(c) 0°
(d) 60°
11. The triangle ABC is a right angled at B. the side opposite to angle A is ____
(a) AC
(b) CA
(c) BC
(d) None of the these
12. Given tan A = 4/3 then sin A = ____
(a) 4/5
(b) 4/7
(c) 4/3
(d) 3/4
13. The value of Cos 45° = _____
(a) 1
(b) 1/2
(c) √3/2
(d) 1/√2
14. Given 16 Cos A = 7 ∴ Cos A = ______
(a) 7/15
(b) 16/7
(c) 7/16
(d) 7/11
15. The value sin 30° cos 60° + cos 30° sin 60° =______ .
(a) 1
(b)−1
(c) 0
(d) 2
16. 2tan 60°/ 1− tan² 45°
(a) 1
(b) √2
(c) 2√3
(d) 3√2
17. sec (90 − A) =
(a) Sec A
(b) Cot A
(c) Sin A
(d) Cosec A
18. The value of tan 55°/cot 35° is ____
(a) 1
(b) 2
(c) 0
(d) ¼
19. The value of _____ or _____ never exceeds the value 1
(a) Sin A , cos A
(b) Sin A , tan A
(c) TanA , cot A
(d) Sec A , cos A
20. sec A + tan A = 1 for ___
(a) 0° < A ≤ 90°
(b) 0° ≤ A ≤ 90°
(c) 0° ≤A < 90°
(d) none of the above
21. If sin A = 3/5 then tan A=____
a) 2/3
b) 3/4
c) −3/4
d) 5/4
22. The value of sin 60° . cos 30° =____
a) 2/3
b) 3/4
c) 5/4
d)7/4
23. The value of sin2 45° + cos2 45° ____
a) 1
b) 0
c) 1/2
d)√3/2
24. Tan 3x = sin45°+ cos45°+ sin 30°. The value of x will be____
a) 60°
b) 45°
c) 30°
d) 15°
25.The solution of cos2 13°− sin2 77° is ___
a) 1
b) 2
c) 0
d) 3
26. If sin 5θ = cos4θ where 5θ and 4θ are acute angles.
Then value of θ =____
a) 50°
b) 100°
c) 10°
d) 60°
27. If 8 tanx = 15 then sinx – cosx = ____
a) 7/17
b) 12/17
c) 1/15
d) 2/15
28. If A, B, C are the interior angles of the ΔABC then sin (B + C )/2 =____
a) Sin A/3
b) Cos A/3
c) Cos A/2
d) Sin A/2
29. Given that sin θ = ab then cos θ is equal to ___
(a) bb²−a²/b
(b) ba
(c) √b²−a²/b
(d) ab²−a²/√a
30. Given that sin α = 1/2 and cos β = 1/2, then the value of (α + β) is ____
(a) 0°
(b) 30°
(c) 60°
(d) 90°
31. sin (45° + θ) – cos (45° – θ) is equal to ___
(a) 2 cos θ
(b) 0
(c) 2 sin θ
(d) 1
32. If cos (40° + A) = sin 30°, then value of A is ____
(a) 30°
(b) 40°
(c) 60°
(d) 20°
33. If sin 2θ = 1 then θ = ___
(a) 30°
(b) 40°
(c) 45°
(d) 20°
34. If tan A = cot 32° then measure of ∠A is ____
(a) 32°
(b) 40°
(c) 45°
(d) 58°
35.If Δ ABC is right angled at C then the value of sin (A + B) = ____
(a) 0
(b) 1
(c) ½
(d) ¼
Answers + Clues.
1 : (b) ⇒ AB = 24 cm and BC = 7 cm
Tan C = Opposite side/Adjacent side
Tan C = ( 24)/7
2 : (c) ⇒ sin 30° = 1/2 sin 60° = ( √3)/2, cos 30° = ( √3)/2, and cos 60° = 1/2
Put these values, to get the answer.
3 : (b) ⇒ tan 60° = √3 and cot 30° = √3
Put these values, to get the answer.
4 : (a) ⇒ We know, sin2A + cos2A = 1, then continue.
5 : (b) ⇒ Sin (90°− A) = cos A [comes in the first quadrant of unit circle]
6 : (c) ⇒ We know: 1 + tan²x = sec²x
And sec x = 1/cos x = 1/(⅔) = 3/2
Hence, we can get …….
7 : (c) ⇒ Cos x = a/b and sin²x + cos²x = 1
8 :(b) ⇒ sin 60° =√ 3/2, sin 30° = ½, cos 60° = ½ and cos 30° = /2
Put these values, to get the answer.
9 : (a) ⇒ tan 30° = 1
10 : (c) ⇒ sin 2A = sin 0° = 0.
11 : (c) ⇒ Side facing the angle
12 :(a) ⇒ Draw the figure and use Pythagoras theorem to get the 3rd side
13 : (d) ⇒ See table in Text.Book
14 : (c) ⇒ See table in Text.Book
15 : (a) ⇒ Put the value from the table & find the value.
16 : (b) ⇒ Put the value from the table & find the value.
17 : (d) ⇒ Text book (8.4)
18 : (a) ⇒ Text book example 9
19 : (a) ⇒ Summary
20 : (b) ⇒ Summary
21 : (b) ⇒ Draw the right angled triangle find value of third side. Then find cos A and tan A.
22 : (b) ⇒ Put the values from the table and solve
23 : (a) ⇒ sin2 θ+ cos2 θ =1
24 : (d) ⇒ Put the values and solve
25 : (c) ⇒ Use cos (90−θ) =sin θ
26 : (c) ⇒ cos 4θ = (sin 90°−4θ)
27 : (a) ⇒ tan x= 15/8. Find sin x, and cos x
28 : (c) ⇒ Use ∠A+∠B+∠C= 180° (angles of a triangle) and B + C = 180°/ ∠A and solve.
29: (c) ⇒ Draw the right angled triangle find value of third side. Then find cosθ
30: (d) ⇒ Find sin α = 1/2 and cos β = 1/2, in the trig. table
31: (b) ⇒ Use cos (90−θ) =sin θ
32: (d)⇒ Use Sin (90°− A) = cos A
33: (c) ⇒ Use sinθ = 90° = 1
34: (d)⇒ Use tan(90−θ) = cot θ
35: (b) ⇒ A + B will be 90°