Solve These Questions

Class 11th JEE
Basic Maths (Physics)
Trigonometry

1. Convert 18 degree into radians. 8. Find angle subtended by a circular arc of radius 6
  cm and length  cm at its centre
(A) rad (B) rad
10 180 (A) 60° (B) 15°
 18 (C) 30° (D) 45°
(C) rad (D) rad
18 
9. Finding the value of sin 15°.
2. Value of sin (37°) cos (53°) is 3 −1 3− 2
(A) (B)
9 12 2 2 2
(A) (B)
25 25 3 −1 1
16 3 (C) (D)
(C) (D) 2 2 2
25 5
10. Finding the value of sin 75°.
1 3 +1 3 −1
3. If sin  = , then cos  will be (A) (B)
3
2 2 2
8 4
(A) (B) 3− 2 1
9 3 (C) (D)
2 2 2
2 2 3
(C) (D)
3 4 11. Find the approximate value of sin 1°
 
4. sin (90° + ) is (A) (B)
90 180
(A) sin  (B) cos 
 
(C) – cos  (D) – sin  (C) (D)
60 30
5. cos (30°) is equal to
12. Find the approximate value of tan 2°
3 1
(A) (B)  
2 2 (A) (B)
90 180
1
(C) (D) None of these  
2 (C) (D)
60 30

1 13. Find the approximate value of cos 1°
6. If sin  = , then sec  will be
3 
(A) 1 (B)
8 4 60
(A) (B)
9 3  
(C) (D)
3 3 30 180
(C) (D)
2 2 4
14. Find the value of sin–1 1.
7. Find the value of sin (105°).  
(A) (B)
4 6
(A)
1
4
( 3+ 7 ) (B)
1
4
( 5+ 2 ) (C)

(D) 
2
(C)
1
4
( 3+ 2 ) (D)
1
4
( 6+ 2 )
15. Find the value of cos–1 (–1/2).

,  2 3 5
(A) (B) (A) (B)
3 3 5 2
 5 2
(C) (D)  (C) (D)
6 3 5

16. As  increases from 0° to 90°, the value of cos  4
24. If cos  = then find the value of tan 
(A) Increases 5
(B) Decreases 4 3
(A) (B)
(C) Remains constant 5 5
(D) First decreases then increases. 4 3
(C) (D)
3 4
17. The greatest value of the function – 5 sin + 12 cos
is 25. Find the value of sin (90 + )
(A) 12 (B) 13 (A) sin  (B) – sin 
(C) 7 (D) 17 (C) cos  (D) – cos 

1 26. Minimum value of cos  for –     
18. If tan  = and  lies in the first quadrant, the
5
value of cos  is (A) –1 (B) +1
5 5 1
(A) (B) − (C) 0 (D)
6 6 2
1 1
(C) (D) − 27. Find the value of P
6 6


19. Find the value of sin 75° + sin 15°
2
(A) 0 (B)
3
3
(C) 3 (D)
2
3
(A) (B) 8
8
20. Find the value of cos (330°) 8
(A) tan 60° (B) sin 30° (C) (D) 0
3
(C) cos 60° (D) sin 60°

28. Find the angle ABC
5
21. If tan  = ; then what is the value of 3 sin  + 2
12
cos .
(A) 3 (B) 4
C) –3 (D) 12

22. If y = sin 2 then find ‘’ where y will be maximum
(A) 90° (B) 60°
(A) 0° (B) 60°
(C) 45° (D) 32°
(C) 30° (D) 45°
29. If  is very small then find H.
sin  + cos  7
23. If = then find tan.
sin  − cos  3

, tan 
30. If y = , then find the value of y if  = 10°

(A) 10° (B) 0
(C) 1 (D) 3
3
(A) 3 (B)
5
4
(C) (D) 5
5

Graphs

31. The spring force is given by F = – kx, here k is a
constant and x is deformation of spring. The F–x
graph is
(C) (D)
(A) (B)

34. A stone is allowed to fall freely from a certain height.
Neglecting air resistance, which graph represents the
(C) (D) variation of velocity ‘v’ with time ‘t’?



32. A body is attached to a spring whose other end is (A) (B)
fixed if the spring is elongated by x, its potential
energy is U = 5x2, where x is in metre and U is in
joule. U–x graph is


(C) (D)
(A) (B)



35. If y = x2+ 2x – 3, y-x graph is
(C) (D)
(A) (B)


33. A particle starts moving with constant, velocity
v = 2 m/s, from position x = 5 m. The position time
(C) (D)
graph will be




(A) (B)
36. The velocity displacement graph of a particle
moving along a straight line is shown in figure.

, The velocity as function of x(0  x  1) is 39. A parallelogram ABCD is shown in figure
(A) – 10x (B) – 10x + 10
(B) 10x – 10 (D) – 10x2 + 10x + 10

37. Which of the following best represents the graph of
velocity (v) versus displacement (s) for a particle
travelling with an acceleration (uniform) and some
non zero initial velocity?


Column I Column II
(A) (B) i. Equation of side AB a. 2y + x = 2
ii. Equation of side BC b. 2y – x = 2
iii. Equation of side CD c. 2y + x = – 2
iv. Equation of side DA d. 2y – x = – 2
Correct matching is
(A) i → b; ii → a; iii → d; iv → c
(C) (D) (B) i → a; ii → b; iii → d; iv → c
(C) i → b; ii → d; iii → c; iv → a
(D) i → c; ii → a; iii → d; iv → b

38. Repeated same as question no. 31 40. Find the slope of a line whose coordinates are (1, 1)
and (3, 2)
1 1
(A) (B)
3 4
1
(C) 2 (D)
2
41. Which of the following statement is not correct for
following straight line graph:

Line (A)
Line (B)




(A) Line (B) has negative y intercept
(B) Line (A) has positive y intercept
(C) Line (B) has positive slope
(D) Line (A) has negative slope

42. If velocity v varies with time t as v = t2. then the plot
between v and t2 will be given as: