Trigonometric Functions Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If y = cos
2
x + sec
2
x, then
(a)
(b)
(c)
(d)
2. Period of  is
(a) 2 p
(b)
(c)
(d)
3. If an angle  is divided into 2 parts A and B such that A – B = k and A
+ B = ? and tan A : tan B = k : 1, then the value of sin k is :
Page 2


PART-I (Single Correct MCQs)
1. If y = cos
2
x + sec
2
x, then
(a)
(b)
(c)
(d)
2. Period of  is
(a) 2 p
(b)
(c)
(d)
3. If an angle  is divided into 2 parts A and B such that A – B = k and A
+ B = ? and tan A : tan B = k : 1, then the value of sin k is :
(a)
(b)
(c)
(d) None of these
4. The equation  has a solution for
(a) all of values of a
(b) a = –1
(c)
(d)
5. If for n ?N,
f
n
(?) = tan ?/2 (1 + sec ?) (1+sec 2?) (1 + sec 4?)....
(1 + sec 2
n
?), then correct statement is
(a) f
2
 (p/16) = 1
(b) f
3
 (p/32) = 1
(c) f
4
 (p/64) = 1
(d) All of these
6. The expression is equal to
(a) cos 2x
(b) 2cos x
(c) cos
2
x
(d) 1 + cos x.
7. If then  is
(a) < 1
(b) > 1
Page 3


PART-I (Single Correct MCQs)
1. If y = cos
2
x + sec
2
x, then
(a)
(b)
(c)
(d)
2. Period of  is
(a) 2 p
(b)
(c)
(d)
3. If an angle  is divided into 2 parts A and B such that A – B = k and A
+ B = ? and tan A : tan B = k : 1, then the value of sin k is :
(a)
(b)
(c)
(d) None of these
4. The equation  has a solution for
(a) all of values of a
(b) a = –1
(c)
(d)
5. If for n ?N,
f
n
(?) = tan ?/2 (1 + sec ?) (1+sec 2?) (1 + sec 4?)....
(1 + sec 2
n
?), then correct statement is
(a) f
2
 (p/16) = 1
(b) f
3
 (p/32) = 1
(c) f
4
 (p/64) = 1
(d) All of these
6. The expression is equal to
(a) cos 2x
(b) 2cos x
(c) cos
2
x
(d) 1 + cos x.
7. If then  is
(a) < 1
(b) > 1
(c) = 1
(d) None of these
8. If sin then
cos A +  sin A is equal to
(a)
(b)
(c)
(d)
9. General solution of the equation
  is
(a)
(b)
(c)
(d) None
10. The least positive non-integral solution of the equation 
 is
(a) rational
(b) irrational of the form 
(c) irrational of the form , where p is an odd integer
(d) irrational of the form , where p is an even integer
11. If A and B are positive acute angles satisfying
,
Then the value of A + 2B is equal to :
Page 4


PART-I (Single Correct MCQs)
1. If y = cos
2
x + sec
2
x, then
(a)
(b)
(c)
(d)
2. Period of  is
(a) 2 p
(b)
(c)
(d)
3. If an angle  is divided into 2 parts A and B such that A – B = k and A
+ B = ? and tan A : tan B = k : 1, then the value of sin k is :
(a)
(b)
(c)
(d) None of these
4. The equation  has a solution for
(a) all of values of a
(b) a = –1
(c)
(d)
5. If for n ?N,
f
n
(?) = tan ?/2 (1 + sec ?) (1+sec 2?) (1 + sec 4?)....
(1 + sec 2
n
?), then correct statement is
(a) f
2
 (p/16) = 1
(b) f
3
 (p/32) = 1
(c) f
4
 (p/64) = 1
(d) All of these
6. The expression is equal to
(a) cos 2x
(b) 2cos x
(c) cos
2
x
(d) 1 + cos x.
7. If then  is
(a) < 1
(b) > 1
(c) = 1
(d) None of these
8. If sin then
cos A +  sin A is equal to
(a)
(b)
(c)
(d)
9. General solution of the equation
  is
(a)
(b)
(c)
(d) None
10. The least positive non-integral solution of the equation 
 is
(a) rational
(b) irrational of the form 
(c) irrational of the form , where p is an odd integer
(d) irrational of the form , where p is an even integer
11. If A and B are positive acute angles satisfying
,
Then the value of A + 2B is equal to :
(a)
(b)
(c)
(d)
12. If tan (cot x) = cot (tan x), then
(a) sin 
(b) sin 
(c) sin 
(d) None of these
13. If f (x) = cos (log x) then
f (x)f (y)  is equal to :
(a) 0
(b) 1
(c) –1
(d) none of these
14. sin 12° sin 24° sin 48° sin 84° =
(a) cos 20° cos 40° cos 60° cos 80°
(b) sin 20° sin 40° sin 60° sin 80°
(c)
(d) None of these
15. The set of all x in  satisfying  is given by
Page 5


PART-I (Single Correct MCQs)
1. If y = cos
2
x + sec
2
x, then
(a)
(b)
(c)
(d)
2. Period of  is
(a) 2 p
(b)
(c)
(d)
3. If an angle  is divided into 2 parts A and B such that A – B = k and A
+ B = ? and tan A : tan B = k : 1, then the value of sin k is :
(a)
(b)
(c)
(d) None of these
4. The equation  has a solution for
(a) all of values of a
(b) a = –1
(c)
(d)
5. If for n ?N,
f
n
(?) = tan ?/2 (1 + sec ?) (1+sec 2?) (1 + sec 4?)....
(1 + sec 2
n
?), then correct statement is
(a) f
2
 (p/16) = 1
(b) f
3
 (p/32) = 1
(c) f
4
 (p/64) = 1
(d) All of these
6. The expression is equal to
(a) cos 2x
(b) 2cos x
(c) cos
2
x
(d) 1 + cos x.
7. If then  is
(a) < 1
(b) > 1
(c) = 1
(d) None of these
8. If sin then
cos A +  sin A is equal to
(a)
(b)
(c)
(d)
9. General solution of the equation
  is
(a)
(b)
(c)
(d) None
10. The least positive non-integral solution of the equation 
 is
(a) rational
(b) irrational of the form 
(c) irrational of the form , where p is an odd integer
(d) irrational of the form , where p is an even integer
11. If A and B are positive acute angles satisfying
,
Then the value of A + 2B is equal to :
(a)
(b)
(c)
(d)
12. If tan (cot x) = cot (tan x), then
(a) sin 
(b) sin 
(c) sin 
(d) None of these
13. If f (x) = cos (log x) then
f (x)f (y)  is equal to :
(a) 0
(b) 1
(c) –1
(d) none of these
14. sin 12° sin 24° sin 48° sin 84° =
(a) cos 20° cos 40° cos 60° cos 80°
(b) sin 20° sin 40° sin 60° sin 80°
(c)
(d) None of these
15. The set of all x in  satisfying  is given by
(a)
(b)
(c)
(d)
16. Let f (x) = then range of f(x) is
(a) [–1, 0]
(b) [0, 1]
(c) [–1, 1]
(d) none of these
17. If  then  is equal to
(a)
(b)
(c) ab
(d) None of these
18. If , then the general value of ? is :
(a)
(b)
(c)
(d)
19. The maximum value of sin is in the interval 
if the value of x is