Karnataka 2nd PUC Mathematics Inverse Trigonometric Functions MCQ with Answers

GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION (PRE-UNIVERSITY)
18TH CROSS, MALLESHWARAM, BENGALURU – 560 012
CHAPTERWISE MULTIPLE CHOICE QUESTIONS FOR COMPETATIVE EXAM
SUBJECT: MATHEMATICS – II PUC
NAME OF THE CHAPTER: INVERSE TRIGONOMETRIC FUNCTIONS

Inverse Function: If f is a function from A to B i.e. 𝑓: 𝐴 → 𝐵, then the inverse function 𝑓 −1 : 𝐵 → 𝐴 exists iff 𝑓
is one-one and onto (Bijective)
The inverse of a function f  x  can be discussed only when f  x  is bijective

The inverse of the function f  x  is denoted by f 1  x  and is unique

In general, trigonometric functions are not bijective functions.
We make them bijective functions by selecting appropriate domain, so that the inverse of each function can be
discussed
Example: sin x : R   1,1 is not one-one

  
By taking domain as   ,  in the place of R, we can make sin x as bijective function.
 2 2
Now inverse of sin x exists, denoted by arc sinx or sin1 x .
Numerically least angle is called the principal value

DEFINITION: The inverse sine function, denoted by sin−1x (or arcsinx), is defined to be the inverse of the
restricted sine function

Graph of y  sin x Graph of y  sin 1 x
Domain:  R   ,  Domain:  1,1
  
Range:  1,1 Range:   , 
 2 2

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DEFINITION: The inverse cosine function, denoted by cos−1x (or arccosx), is defined to be the inverse of
the restricted cosine function

Graph of y  cos x Graph of y  cos 1 x
Domain:  R   ,  Domain:  1,1
Range:  1,1 Range:  0, 

DEFINITION: The inverse tangent function, denoted by tan−1x (or arctanx), is defined to be the inverse of
the restricted tangent function

Graph of y  tan x Graph of y  tan 1 x
  
Domain:  R   x : x   2n  1 ,n  Z  Domain:  , 
 2 
  
Range:  ,  Range:   , 
 2 2
−1
DEFINITION: The inverse cotangent function, denoted by cot x (or arccotx), is defined to be the inverse
of the restricted cotangent function

Graph of y  cot x Graph of y  cot 1 x
Domain:  R   x : x  n ,n  Z  Domain:  , 
Range:  ,  Range:  0, 

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DEFINITION: The inverse secant function, denoted by sec−1x (or arcsecx), is defined to be the inverse of
the restricted secant function

Graph of y  sec x Graph of y  sec 1 x
  
Domain:  R   x : x   2n  1 ,n  Z  Domain:  R   1,1    , 1  1, 
 2 
       
Range:  R   1,1    , 1  1,  Range:  0 ,       0 ,    , 
2  2   2 
−1
DEFINITION: The inverse cosecant function, denoted by csc x (or arccscx), is defined to be the inverse of
the restricted cosecant function

Graph of y  co sec x Graph of y  co sec 1 x
Domain:  R   x : x  n ,n  Z  Domain:  R   1,1    , 1  1, 
       
Range:  R   1,1    , 1  1,  Range:   ,   0    , 0    0, 
 2 2  2   2

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Domain And Range Of The Inverse Trigonometric Functions Are As Follows

Functions Domain Range ( PVB ) x>0 x<0
 
     0 y   y0
y  sin 1 x  1,1 (or) 1  x  1   2 , 2  (or)  2  y  2 2 2


0 y 
1
y  cos x  1,1 (or) 1  x  1 0,   (or) 0  y   2  y 
2

 
y  cos ec 1 x R – (-1, 1) (or) , 1  1,         0 y   y0
      2 , 2   0 (or)   2 , 0    0 , 2  2 2


   
1
y  sec x R – (-1, 1) (or)   , 1  1,   0,      (or) 0,    ,  0 y
2  y 
2  2 2  2

 
     0 y   y0
y  tan 1 x R (or)   ,     ,  (or)   y  2 2
 2 2 2 2


0 y 
1
y  cot x R (or)   ,    0,   (or) 0  y   2  y 
2

Properties of inverse trigonometric functions
 
I (i) sin 1 (sin  )   ,    (ii) cos 1 (cos  )   , 0    
2 2
 
(iii) tan 1 (tan  )   ,    (iv) cot 1 (cot  )   , 0    
2 2
   
(v) sec 1 (sec  )   , 0    or   (vi) cosec 1 (cosec )   ,     0 or 0   
2 2 2 2
II (i) sin(sin 1 x)  x, 1  x  1 (ii) cos(cos 1 x)  x, 1  x  1

(iii) tan(tan 1 x)  x,   x   (iv) cot(cot 1 x)  x,   x  

(v) sec(sec1 x)  x,   x  1 or 1  x   (vi) cosec (cosec –1 x)  x,   x  1 or 1  x  

III (i) sin 1 (  x)   sin 1 x (ii) cos 1 ( x)    cos 1 x

(iii) tan 1 ( x)   tan 1 x (iv) cot 1 ( x)    cot 1 x

(v) cosec 1 ( x)  cosec –1 x (vi) sec 1 ( x)    sec 1 x

IV (i) sin 1 x  cos 1 x  , x  [1,1]
2
 
(ii) tan 1 x  cot 1 x  , xR (iii) sec1 x  cosec-1 x  , x  (,  1]  [1, )
2 2
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Conversion property:

x 1 1  x2  1  –1  1 

1
sin x  cos 1
1  x  tan
2 1
 cot  sec 1    cosec  
1  x2 x  1 x 
2
x
 1  x2  1 1  1   x 

1
cos x  sin 1
1  x  tan 
2 1
  sec  cosec –1    cot 1  
 x  x  1 x 
2
 1 x 
2
 
 x  1  1  1  1 
 1  x2 
 tan 1 x  sin 1    cos    cot    sec 1
1  x 2
 cosec 1
 
  2
   2
  x   x 
1 x 1 x  
1
 sin 1    cosec 1 x , for all x  (,1]  [1, )
x
1
1
 cos    sec 1 x, for all x  (,1] [1, )
1 x
x

 1   cot x,
1
1 for x  0
 tan     1– x2
 x    cot x, for x  0
1

Formulae for sum, difference of inverse trigonometric function
 x y 
(1) tan 1 x  tan 1 y  tan 1   ; If x  0, y  0 and xy  1
 1  xy 
 x y 
(2) tan 1 x  tan 1 y    tan 1   ; If x  0, y  0 and xy  1
 1  xy 
 x y 
(3) tan 1 x  tan 1 y  tan 1   ; If xy  1
 1  xy 

(4) sin 1 x  sin 1 y  sin 1{ x 1  y 2  y 1  x 2 } ; If 1  x, y  1 and x 2  y 2  1 or if xy  0 and x 2  y 2  1

(5) sin 1 x  sin 1 y  sin 1{ x 1  y 2  y 1  x 2 }, If 1  x; y  1 and x 2  y 2  1 if or xy  0 and x 2  y 2  1 .

(6) cos 1 x  cos 1 y  cos 1{ xy  1  x 2 . 1  y 2 } , If 1  x, y  1 and x  y  0 .

(7) cos 1 x  cos 1 y  cos 1{ xy  1  x 2 1  y 2 }, If 1  x, y  1, and x  y .

Inverse trigonometric ratios of multiple angles
1 1 1 1
(1) 2sin 1 x  sin 1 (2 x 1  x 2 ) , If  x (2) 3sin 1 x  sin 1 (3 x  4 x3 ), If x
2 2 2 2
1
(3) 2 cos 1 x  cos 1 (2 x 2  1) , If 0  x  1 (4) 3cos 1 x  cos 1 (4 x3  3 x) , If  x 1
2
 2x   2x 
(5) 2 tan 1 x  tan 1  2 
, If 1  x  1 (6) 2 tan 1 x  sin 1  2 
, If 1  x  1
 1 x   1 x 

 1  x2   3x  x3  1 1
(7) 2 tan 1 x  cos 1  2 
, If 0  x   (8) 3 tan 1 x  tan 1  2 
, If x
 1 x   1  3x  3 3

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CLASSROOM CHALLENGE
1. The range of 𝒔𝒆𝒄−𝟏 𝒙 is (Easy) (CET2017)
𝜋 −𝜋 𝜋 −𝜋 𝜋
1) [0, 𝜋] 2) [0, 𝜋] − { } 3) ( , ) 4) [ , ]
2 2 2 2 2

2. Which of the following corresponds to the principal value branch of 𝐭𝐚𝐧−𝟏 𝒙? (Easy)
𝜋 𝜋 𝜋 𝜋
1) (− 2 , 2 ) 2) [− 2 , 2 ] 3) [0, 𝜋] 4) (0, 𝜋)

3. Which of the following is the principal value branch of 𝐜𝐨𝐬 −𝟏 𝒙 ? (Easy)
𝜋 𝜋 𝜋
1) [− 2 , 2 ] 2) (0, 𝜋) 3) [0, 𝜋] 4) (0, 𝜋) − { 2 }

4. Which of the following is the principal value branch of 𝒄𝒐𝒔𝒆𝒄−𝟏 𝒙? (Easy)
𝜋 𝜋 𝜋 𝜋 𝜋 𝜋 𝜋
1) (− 2 , 2 ) 2) [0, 𝜋], − {2 } 3) [− 2 , 2 ] 4) [− 2 , 2 ] − {0}

5. One branch of cos 1 x other than the principal value branch corresponds to (Easy)
𝜋 3𝜋 3𝜋
1) [ 2 , 2 ] 2) [𝜋, 2𝜋] − { 2 } 3) (0, 𝜋) 4) [2𝜋, 3𝜋]

6. The principal value of the expression 𝐜𝐨𝐬 −𝟏 [𝐜𝐨𝐬(−𝟔𝟖𝟎𝟎 )] is (Easy)
2𝜋 2𝜋 34𝜋 𝜋
1) 9 2) − 9 3) 9 4) 9

7. The value of 𝐜𝐨𝐭(𝒔𝒊𝒏−𝟏 𝒙) 𝒊𝒔 (Easy)
√1+𝑥2 𝑥 1 √1−𝑥 2
1) 2) √1+𝑥 2 3) 𝑥 4)
𝑥 𝑥
𝝅
8. If 𝐭𝐚𝐧−𝟏 𝒙 = 𝟏𝟎 for some 𝒙 ∈ 𝑹 then the value of 𝐜𝐨𝐭 −𝟏 𝒙 𝒊𝒔 (Easy)
𝜋 2𝜋 3𝜋 4𝜋
1) 5 2) 5 3) 4) 5
5
−𝟏
9. The domain of 𝐬𝐢𝐧 𝟐𝒙 𝒊𝒔 (Easy)
1 1
1) [0,1] 2) [−1, 1] 3) [− 2 , 2] 4) [−2, 2]

10. The domain of the function 𝒇(𝒙) = 𝐜𝐨𝐬 −𝟏 (√𝒙 − 𝟏) 𝒊𝒔 (Average)(CET2020)
1) [1,2] 2) [−1,1] 3) [0,1] 4) [0,2]
11. The domain of the function 𝒚 = 𝐬𝐢𝐧−𝟏 (−𝒙𝟐 ) 𝒊𝒔 (Average)
1) [0,1] 2) (0,1) 3) [−1,1] 4) φ
12. The domain of 𝒚 = 𝒄𝒐𝒔−𝟏 ( 𝒙𝟐 − 𝟒) is (Average)
1) [3,5] 2) [0, 𝜋]
3) [−√5, −√3] ∩ [−√5, √3] 4) [−√5, −√3] ∪ [√3, √5]
13. The domain of the function defined by 𝒇(𝒙) = 𝐬𝐢𝐧−𝟏 𝒙 + 𝐜𝐨𝐬 𝒙 (Easy)
1) [−1, 1] 2) [−1, 𝜋 + 1] 3) (−∞, ∞) 4) ∅
14. The domain of the function 𝐜𝐨𝐬 −𝟏 (𝟐𝒙 − 𝟏) 𝒊𝒔 (Easy)
1) [0,1] 2) [−1,1] 3) (−1, 1) 4) [0, 𝜋]

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15. Which of the following is not true for all real values of 𝒙 ? (Easy)
𝜋 𝑥
1) 0 ≤ 𝑡𝑎𝑛−1 𝑥 2 < 2)𝑠𝑖𝑛(𝑡𝑎𝑛−1 𝑥) = √1+𝑥 2
2

3) 𝑡𝑎𝑛(𝑡𝑎𝑛−1 𝑥) = 𝑥 4) 𝑠𝑖𝑛(𝑠𝑖𝑛−1 𝑥) = 𝑥
16. If ‘x’ takes negative permissible value, then sin-1x = (Easy)(CET2009)
1) − 𝑐𝑜𝑠 −1 √1 − 𝑥 2 2)𝑐𝑜𝑠 −1 √𝑥 2 − 1
3) π− 𝑐𝑜𝑠 −1 √1 − 𝑥 2 4) 𝑐𝑜𝑠 −1 √1 − 𝑥 2
17. The graph of the function 𝒚 = 𝒄𝒐𝒔−𝟏 𝒙 is the mirror image of the graph of the function y= 𝒄𝒐𝒔𝒙 along
the line (Easy)
1) x=0 2) y=x 3) y=1 4) y=0
18. Match Column I with Column II (Easy)

Column I Column II
a) Range of 𝑠𝑒𝑐 −1 𝑥 i) 𝑅 − (−1,1 )
b) Range of 𝑐𝑜𝑠𝑒𝑐 −1 𝑥 𝜋
ii) [0, 𝜋] − {2 }

c) Domain of 𝑐𝑜𝑠𝑒𝑐 −1 𝑥 𝜋 𝜋
iii) [− 2 , 2 ] − {0}

Choose the correct answer from the options given below:
1) a-i, b-ii, c-iii 2) a-iii, b-ii, c-i 3) a-ii, b-iii, c-i 4) a-iii, b-i, c-ii
𝝅
19. If 𝒔𝒊𝒏−𝟏 𝒙 = 𝟓 , for some 𝒙 ∈ (−𝟏, 𝟏) then the value of 𝒄𝒐𝒔−𝟏 𝒙 = (Easy)
3𝜋 5𝜋 7𝜋 9𝜋
1) 10 2) 10 3) 10 4) 10

20. 𝟐 𝒄𝒐𝒔−𝟏 𝒙 = 𝒔𝒊𝒏−𝟏 (𝟐𝒙√𝟏 − 𝒙𝟐 ) is valid for all values of x satisfying (Easy)(CET2012,25)
1 1
1) 0 ≤ 𝑥 ≤ 2) −1 ≤ 𝑥 ≤ 1 3) 0 ≤ 𝑥 ≤ 1 4) ≤𝑥≤1
√2 √2

𝟏−𝒙𝟐
21. The formula 𝐜𝐨𝐬 −𝟏 𝟏+𝒙𝟐 = 𝟐 𝐭𝐚𝐧−𝟏 𝒙 𝒊𝒔 𝒗𝒂𝒍𝒊𝒅 𝒇𝒐𝒓 (Average)

1) 𝑥 𝜖 𝑅 2) |𝑥| ≤ 1 3) 𝑥 𝜖 [−1,1] 4) 𝑥 𝜖 [0, ∞)
22. 𝐬𝐢𝐧(𝐭𝐚𝐧−𝟏 𝒙), |𝐱| < 𝟏 is equal to (Easy)
𝑥 1 1 𝑥
1) √1−𝑥2 2) √1−𝑥 2 3) √1+𝑥 2 4) √1+𝑥 2

 π π   3 
23. Statement 1: The range of f  x  = sin-1x in 0, 2π other than - ,  is  , 
 2 2 2 2 
Statement 2: Domain of f(x) = sin1 x  cos 1 x is [-1, 1] (Easy)
1) Statement 1 is true and Statement 2 is false. 2) Statement 1 is true and Statement 2 is true.

3) Statement 1 is false and Statement 2 is true. 4) Statement 1 is false and Statement 2 is false.

2026-27 MATHEMATICS CET MATERIAL Page 7 of 18

𝟏 𝟏𝟐
24. 𝒕𝒂𝒏 (𝟐 𝒕𝒂𝒏−𝟏 𝟓 ) = (Average)
5 11 2 3
1) 3 2) 3 3) 3 4) 5
𝟓𝟑𝝅
25. The value of 𝒔𝒊𝒏−𝟏 (𝒄𝒐𝒔 𝟓 ) is (Average)(CET2016)
−3𝜋 −𝜋 3𝜋 𝜋
1) 2) 10 3) 5 4) 10
5

26. The value of sin(2 sin-1 0.8) is (Average)(CET2014)
1) sin 1.60 2) 0.48 3) 0.96 4) sin1.20
27. 𝒔𝒆𝒄𝟐 (𝒕𝒂𝒏−𝟏 𝟐) + 𝒄𝒐𝒔 𝒆 𝒄𝟐 (𝒄𝒐𝒕−𝟏 𝟑) = (Average)(CET2025)
1) 5 2) 10 3) 15 4) 20
𝟏 𝟐
28. The value of the expression 𝒕𝒂𝒏 (𝟐 𝒄𝒐𝒔−𝟏 ) is (Average) (CET2018)
√𝟓

√5−2
1) 2 − √5 2) √5 − 2 3) 4) 5 − √2
2

𝟔𝟑
29. 𝐬𝐢𝐧 (𝟐𝐬𝐢𝐧−𝟏 √𝟔𝟓) = (Average) (CET2008)

63 8√63 4√63 2√126
1) √65 2) 65 3) 65 4) 65

𝟐 𝟐
30. 𝐜𝐨𝐬 −𝟏 [𝐬𝐢𝐧 (𝐜𝐨𝐬 −𝟏 𝟑 + 𝐬𝐢𝐧−𝟏 𝟑)] = (Easy)
𝜋 𝜋 𝜋
1) 4 2) 0 3) 2 4) 3
𝟐 𝟐
31. 𝒔𝒊𝒏 [𝐬𝐢𝐧−𝟏 ( ) + 𝟐 𝐜𝐨𝐬 −𝟏 ( )] = (Easy)
𝟑 𝟑
3 1 2 1
1) 2 2) 3 3) 3 4) 4

32. If 𝒄𝒐𝒔−𝟏 𝒑 + 𝒄𝒐𝒔−𝟏 𝒒 + 𝒄𝒐𝒔−𝟏 𝒓 = 𝝅, then 𝒑𝟐 + 𝒒𝟐 + 𝒓𝟐 + 𝟐𝒑𝒒𝒓 = (Easy) (CET2004)
1) 2 2) -1 3) 1 4) 3
33. If 𝒄𝒐𝒔−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 𝒚+ 𝒄𝒐𝒔−𝟏 𝒛= 3π, then 𝒙𝒚 + 𝒚𝒛 + 𝒛𝒙 = (Easy)
1) 0 2) 1 3) 3 4) -3
𝟐𝝅
34. If 𝒔𝒊𝒏−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝒚 = 𝟑 then 𝒄𝒐𝒔−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 𝒚 = (Easy)
2𝜋 𝜋 𝜋
1) 3 2) 3 3) 6 4) 𝜋

35. If 𝐜𝐨𝐬 −𝟏  + 𝐜𝐨𝐬 −𝟏  + 𝐜𝐨𝐬 −𝟏  = 𝟑𝝅 then ( + ) + ( + ) + ( + ) = (Average) (CET2024)
1) 0 2) 1 3) 6 4) 12
𝟑𝝅
36. If 𝒔𝒊𝒏−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝒚 + 𝒔𝒊𝒏−𝟏 𝒛 = 𝟐 , then 𝒙𝟏𝟎𝟎 + 𝒚𝟏𝟎𝟎 + 𝒛𝟏𝟎𝟎 − (𝒙𝟏𝟎𝟏 + 𝒚𝟏𝟎𝟏 + 𝒛𝟏𝟎𝟏 )= (Easy)
1) 1 2) 0 3) 4 4) 2
𝟓 𝟓 𝝅
37. If 𝒄𝒐𝒔−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝒙 = 𝟐 , then (Easy)

1) x is any real number 2) x > 5
3) -5 < x < 5 4) x ≤ -5 or x ≥ 5
2026-27 MATHEMATICS CET MATERIAL Page 8 of 18

38. If 𝐜𝐨𝐬 −𝟏 𝒙 > 𝐬𝐢𝐧−𝟏 𝒙 then (Average)
1 1 1
1) <𝑥≤1 2) 0 ≤ 𝑥 < 3) −1 ≤ 𝑥 < 4) 𝑥 > 0
√2 √2 √2

39. The value of the expression 𝐬𝐢𝐧[𝐜𝐨𝐭 −𝟏 (𝐜𝐨𝐬(𝐭𝐚𝐧−𝟏 𝟏))] is (Average)
1 2
1) 0 2) 1 3) 4) √3
√3

𝟑𝝅
40. The value of 𝐜𝐨𝐬 −𝟏 (𝐜𝐨𝐬 𝟐 ) 𝒊𝒔 (Easy)
𝜋 3𝜋 5𝜋 7𝜋
1) 2 2) 2 3) 2 4) 2
𝟏
41. The value of the expression 𝟐 𝐬𝐞𝐜 −𝟏 𝟐 + 𝐬𝐢𝐧−𝟏 𝟐 𝒊𝒔 (Easy)
𝜋 5𝜋 7𝜋
1) 6 2) 6 3) 6 4) 1
𝟕
42. The value of 𝐜𝐨𝐭 [𝐜𝐨𝐬−𝟏 (𝟐𝟓)] is (Easy)
25 25 24 7
1) 24 2) 7 3) 25 4) 24
√𝟑
43. The principal value of 𝒔𝒊𝒏−𝟏 [𝒄𝒐𝒔 (𝐬𝐢𝐧−𝟏 𝟐 )] 𝒊𝒔 (Easy)
𝜋 𝜋 𝜋 𝜋
1) 6 2) 3 3) − 3 4) 4
𝟒 𝟐
44. The value of 𝒕𝒂𝒏 [𝒄𝒐𝒔−𝟏 𝟓 + 𝐬𝐢𝐧−𝟏 ] 𝒊𝒔 (Average)
√𝟏𝟑
7 17 6 4
1) 16 2) 6 3) 17 4) 17
𝟒 𝟐
45. The value of [𝒄𝒐𝒔−𝟏 ( ) + 𝐭𝐚𝐧−𝟏 ( )] 𝒊𝒔 (Average)
𝟓 𝟑
17 6 16 7
1) tan−1 6 2) tan−1 17 3)tan−1 7 4)tan−1 6
𝝅
46. The value of 𝒄𝒐𝒔 [𝒄𝒐𝒕−𝟏 (−√𝟑) + 𝟔 ] 𝒊𝒔 (Easy)(CET2021)
1
1) 0 2)1 3) 4) -1
√2

𝟏 𝟓𝝅 √𝟑
47. The value of 𝒕𝒂𝒏−𝟏 ( 𝐬𝐢𝐧 𝟐 ) + 𝐬𝐢𝐧−𝟏 (𝐜𝐨𝐬(𝐬𝐢𝐧−𝟏 𝟐 ) 𝒊𝒔 (Average) (CET2021)
√𝟑
𝜋 𝜋
1) 0 2) 6 3) 3 4) 𝜋
𝝅 𝝅
48. The value of 𝒄𝒐𝒔 [𝒔𝒊𝒏−𝟏 + 𝒄𝒐𝒔−𝟏 ] 𝒊𝒔 (Easy)(CET2020)
𝟑 𝟑

1) Does not exist 2) 0 3) 1 4) -1
𝟑 𝟑
49. The value of 𝐜𝐨𝐬 [𝟐 𝒔𝒊𝒏−𝟏 (𝟒) + 𝒄𝒐𝒔−𝟏 (𝟒)] is (Average) (CET2019)
3 3 −3
1) Does not exist 2) 5 3) 4 4) 4
𝟒𝟑𝝅
50. The value of 𝐬𝐢𝐧−𝟏 (𝐜𝐨𝐬 ( 𝟓 )) 𝒊𝒔 (Easy)
3𝜋 7𝜋 𝜋 𝜋
1) 5 2) − 5 3) 10 4) − 10

2026-27 MATHEMATICS CET MATERIAL Page 9 of 18

𝟑 𝟏
51. The value of 𝐭𝐚𝐧 (𝒄𝒐𝒔−𝟏 𝟓 + 𝒕𝒂𝒏−𝟏 𝟒) 𝒊𝒔 (Average)
19 8 19 3
1) 8 2) 19 3) 12 4) 4
𝟏 𝟏
52. If 𝒄𝒐𝒔 [𝟐 𝐜𝐨𝐬 −𝟏 𝟓 + 𝐬𝐢𝐧−𝟏 𝟓] = (Average) (CET2013)
1 2√6 1 √6
1) 5 2) − 5 3) − 5 4) 5
𝟏 𝟏
53. 𝐜𝐨𝐬 −𝟏 (𝟐) + 𝟐𝐬𝐢𝐧−𝟏 (𝟐) 𝐢𝐬 𝐞𝐪𝐮𝐚𝐥 𝐭𝐨 (Easy)
𝜋 𝜋 𝜋 2𝜋
1) 4 2) 6 3) 3 4) 3
𝟏 √𝟓
54. 𝒕𝒂𝒏 [𝟐 𝒄𝒐𝒔−𝟏 𝟑 ] = (Average)
3−√5 √5− 3 3+√5 2+√5
1) 2) 3) 4)
2 2 2 2
𝟐𝝅
55. If 𝒔𝒊𝒏−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 𝒚 = 𝟓 then 𝒄𝒐𝒔−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝒚 is (Average)(CET2018)
2𝜋 3𝜋 4𝜋 3𝜋
1) 5 2) 3) 4) 10
5 5
𝝅
56. If 𝒔𝒊𝒏−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝒚 = 𝟐 , then 𝒙𝟐 = (Average)(CET2016,26)

1) 𝑦 2 2) √1 − 𝑦 3) 1 − 𝑦 2 4) 0
57. If 𝟑 𝒕𝒂𝒏−𝟏 𝒙 + 𝒄𝒐𝒕−𝟏 𝒙 = 𝝅, then (Easy)(CET2016)
1
1) 1 2) 2 3) 0 4) -1
𝝅
58. If 𝐬𝐞𝐜 −𝟏 𝒙 − 𝐜𝐨𝐬𝐞𝐜 −𝟏 𝒙 = 𝟔 ,then x= (Easy)
1 √3 2
1) 2 2) 2 3) 4)
2 √3
𝟑𝝅
59. 𝒕𝒂𝒏−𝟏 (𝒕𝒂𝒏 𝟒 ) 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 = (Easy)
𝜋 𝜋 3𝜋 5𝜋
1) 4 2) − 4 3) 4) 4
4
60. If 𝟒 𝒔𝒊𝒏−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 𝒙 = 𝝅 , then x = (Easy)
2 1 1
1) 3 2) 3 3) 2 4) 2
CLASSROOM CHALLENGE
1 2 3 4 5 6 7 8 9 10
2 1 3 4 4 1 4 2 3 1
11 12 13 14 15 16 17 18 19 20
3 4 1 1 4 1 2 3 1 4
21 22 23 24 25 26 27 28 29 30
4 4 2 3 2 3 3 2 4 2
31 32 33 34 35 36 37 38 39 40
3 3 3 2 3 2 4 3 4 1
41 42 43 44 45 46 47 48 49 50
2 4 1 2 1 4 3 1 4 4
51 52 53 54 55 56 57 58 59 60
1 2 4 1 2 3 1 1 2 3

2026-27 MATHEMATICS CET MATERIAL Page 10 of 18

ADDITIONAL PROBLEMS
1. Domain of the function 𝒄𝒐𝒔−𝟏 [𝒙], where [. ] denotes the greatest integer function, is
(Easy)(CET2022)
1) (−1,2] 2) [−1,2] 3) (−1, 2) 4) [−1,2)
2. The value of sin (𝟐 𝐬𝐢𝐧−𝟏 (𝟎. 𝟔)) 𝒊𝒔 (Easy)
1) 0.48 2) 0.96 3) 1.2 4) sin(1.2)
𝒙
3. The domain of 𝒇(𝒙) = 𝒔𝒊𝒏−𝟏 [𝒍𝒐𝒈𝟐 (𝟐)] is (Average)(CET2011)

1) 4 ≤ 𝑥 ≤ 6 2) 1 ≤ 𝑥 ≤ 4 3) 0 ≤ 𝑥 ≤ 4 4) 0 ≤ 𝑥 ≤ 1
𝟐𝝅
4. If 𝒕𝒂𝒏−𝟏 𝒙 + 𝟐 𝒄𝒐𝒕−𝟏 𝒙= 𝟑 , then x = (Average)
√3−1
1) 3 2) √3 3) √2 4)
√3+1

𝟐√𝟐 𝟏
5. 𝒔𝒊𝒏−𝟏 ( ) + 𝒔𝒊𝒏−𝟏 = (Average) (CET2015)
𝟑 𝟑
2𝜋 𝜋 𝜋 𝜋
1) 3 2) 4 3) 2 4) 6
𝟐𝒙
6. If |𝒙| ≤ 𝟏, then 2 𝐭𝐚𝐧−𝟏 𝒙 + 𝐬𝐢𝐧−𝟏 (𝟏+𝒙𝟐 )is equal to (Easy)
𝜋
1) 4 tan−1 𝑥 2) 0 3) 2 4) 𝜋
𝒙 𝒙−𝒚
7. The simplified form of 𝒕𝒂𝒏−𝟏 (𝒚) − 𝒕𝒂𝒏−𝟏 (𝒙+𝒚) is equal to (Average)(CET2013,16)
𝜋 𝜋
1) 4 2) 𝜋 3) 0 4) 2

𝟏 𝒙 √𝟑−𝟑𝒙𝟐
8. If 𝟐 ≤ 𝒙 ≤ 𝟏 then 𝒄𝒐𝒔−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 (𝟐 + )= (Easy)
𝟐
𝜋 𝜋 𝜋 𝜋
1) 4 2) 2 3) 3 4) 5
𝟏−𝒙𝟐 𝟏−𝒙𝟐
9. 𝒔𝒊𝒏 [𝒕𝒂𝒏−𝟏 ( 𝟐𝒙 ) + 𝒄𝒐𝒔−𝟏 (𝟏+𝒙𝟐 )] = (Average)

1) 1/2 2) 0 3) 1/3 4) 1
10. The value of 𝒔𝒊𝒏−𝟏 (𝒄𝒐𝒔 𝒙) − 𝒔𝒊𝒏−𝟏 (𝒄𝒐𝒔 𝟑 𝒙) = (Average)
1) 2x 2) 3x 3) x 4) 4x
𝟏
11. The equation 𝐭𝐚𝐧−𝟏 𝒙 − 𝐜𝐨𝐭 −𝟏 𝒙 = 𝐭𝐚𝐧−𝟏 ( ) has (Average)
√𝟑

1) no solution 2) unique solution
3) infinite number of solutions 4) two solutions

   1  2π
12. If cos-1x = α,  0 < x < 1 and sin -1 2x 1 - x 2 + sec-1  2  =
 2x - 1  3
then tan-1  2x  =

(Difficult)(CET2006)
𝜋 𝜋 𝜋 𝜋
1) 2 2) 6 3) 3 4) 4

2026-27 MATHEMATICS CET MATERIAL Page 11 of 18

𝝅
13. If 𝒕𝒂𝒏−𝟏 𝒙 + 𝒕𝒂𝒏−𝟏 𝒚 = 𝟒 then (Easy)(CET2005)

1) x + y + xy + 1 = 0 2) x + y –xy + 1 = 0 3) x + y + xy = 1 4) x + y -xy =1
𝟒𝝅
14. If 𝒕𝒂𝒏−𝟏 𝒙 + 𝒕𝒂𝒏−𝟏 𝒚 = 𝟓 then 𝒄𝒐𝒕−𝟏 𝒙 + 𝒄𝒐𝒕−𝟏 𝒚 is equal to (Average)(CET2017)
2𝜋 𝜋 3𝜋
1) 5 2) 𝜋 3) 5 4) 5
𝟏 𝝅
15. 𝑰𝒇 𝟐 𝐭𝐚𝐧−𝟏 𝟐 + 𝐬𝐢𝐧−𝟏 𝒙 = 𝟐 , 𝒕𝒉𝒆𝒏 𝒙 = (Difficult)
3 3 4 3
1) 5 2) 4 3) 5 4) 7
𝟏−𝒙 𝟏
16. Solve for x: 𝒕𝒂𝒏−𝟏 (𝟏+𝒙) = 𝟐 𝒕𝒂𝒏−𝟏 𝒙 , x >0 (Average)
1
1) 2) -1 3) 1 4) √3
√3
𝝅
17. 𝐬𝐢𝐧−𝟏 (𝟏 − 𝒙) − 𝟐 𝐬𝐢𝐧−𝟏 𝒙 = , 𝒕𝒉𝒆𝒏 𝒙 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 (Average)
𝟐
1 1 1
1) 0, 2 2) 1, 2 3) 0 4) 2

5 12 π
18. If sin-1 + sin-1 = , then x = (Average)
x x 2
1) 10 2) 12 3) 13 4) 14
𝒙 𝝅
19. If 𝒄𝒐𝒔−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝟐= 𝟔 , then x = (Easy)
1
1) ±√3 2) 1 3) 4) 0
√2

√𝟏+𝒙𝟐 −𝟏
20. If 𝐭𝐚𝐧−𝟏 = 𝟒 𝒕𝒉𝒆𝒏 𝒙 = (Difficult)
𝒙
1
1) 𝑡𝑎𝑛2 2) 𝑡𝑎𝑛4 3) 𝑡𝑎𝑛 (4) 4) 𝑡𝑎𝑛8
𝟏 𝟏 𝟏
21. The value of 𝐜𝐨𝐬 −𝟏 (− 𝟐) − 𝟐 𝐬𝐢𝐧−𝟏 𝟐 + 𝟑 𝐜𝐨𝐬 −𝟏 (− ) + 𝟒 𝐭𝐚𝐧−𝟏 (−𝟏) is (Average)
√𝟐
43𝜋 19𝜋 𝜋 25𝜋
1) 12 2) 12 3) 12 4) 12
𝒙 𝟓 𝝅
22. If 𝒔𝒊𝒏−𝟏 𝟓 + 𝒄𝒐𝒔 𝒆 𝒄−𝟏 𝟒 = 𝟐 , then x = (Average) (CET2004)

1) 5 2) 3 3) 4 4) 1
𝟐𝒙 𝟏−𝒙𝟐 𝟐𝒙
23. 𝐈𝐟 𝟑𝐬𝐢𝐧−𝟏 𝟏+𝒙𝟐 + 𝟐 𝐜𝐨𝐬 −𝟏 𝟏+𝒙𝟐 = 𝐭𝐚𝐧−𝟏 𝟏−𝒙𝟐 , 𝒕𝒉𝒆𝒏 𝒙 = (Average)

1) 1 2) −1 3) 0 4) 2
𝟏 𝟓
24. If 𝒙 + 𝒙 = 𝟐, then the principal value 𝒐𝒇 𝐬𝐢𝐧−𝟏 𝒙 𝒊𝒔 (Average)
𝜋 𝜋 𝜋 5𝜋
1) 6 2) 4 3) 3 4) 4
𝟐√𝟐
25. When 𝒙 = , the value of 𝐬𝐢𝐧𝟐 (𝟓 𝐬𝐢𝐧−𝟏 𝒙 + 𝟒 𝐜𝐨𝐬 −𝟏 𝒙) = (Average)
𝟑
8 2√2 8 2
1) 9 2) 3 3) 3 4) 3

2026-27 MATHEMATICS CET MATERIAL Page 12 of 18

𝟐𝝅
26. If 𝒔𝒊𝒏−𝟏 𝒙 + 𝒔𝒊𝒏−𝟏 𝟐 𝒙 = 𝟑 , then 𝟒𝒙𝟐 − 𝟒𝒙= (Average)

1) 1 2) 0 3) -1 4) -2
𝟏+𝒙𝟐 𝝅 𝟏−𝒙𝟐
27. If 𝟐 𝒄𝒐𝒔 𝒆 𝒄−𝟏 ( 𝟐𝒙 ) = 𝟐 − 𝒄𝒐𝒕−𝟏 ( 𝟐𝒙 ), x= (Difficult)
1 √3−1
1) 1 2) 3) √3 4)
√3 √3+1

𝟐𝒙 𝟏−𝒙𝟐 𝟐𝒙 𝝅
28. If 𝟑 𝒔𝒊𝒏−𝟏 (𝟏+𝒙𝟐 ) − 𝟒 𝒄𝒐𝒔−𝟏 (𝟏+𝒙𝟐 ) + 𝟐 𝒕𝒂𝒏−𝟏 (𝟏−𝒙𝟐 ) = 𝟑 , then x = (Average)
1 1
1) 1 2) 2 3) 4)
√3 √2
−𝟏
29. If 𝒕𝒂𝒏(𝒙 + 𝒚) = 𝟑𝟑 and 𝒙 = 𝒕𝒂𝒏 𝟑 then y is (Difficult)
3
1) 3/10 2) 33/10 3) 1/3 4) 𝑡𝑎𝑛−1 10

30. If 𝜶 ≤ 𝟐 𝒔𝒊𝒏−𝟏 𝒙 + 𝒄𝒐𝒔−𝟏 𝒙 ≤ 𝜷 , then (Average)(CET2015)
−𝜋 3𝜋 −𝜋 𝜋
1) 𝛼 = 0, 𝛽 = 2𝜋 2) 𝛼 = 0, 𝛽 = 𝜋 3) 𝛼 = 2 , 𝛽 = 2 4) 𝛼 = 2 , 𝛽 = 2
𝝅
31. If 𝒂 + 𝟐 < 𝟐 𝒕𝒂𝒏−𝟏 𝒙 + 𝟑 𝒄𝒐𝒕−𝟏 𝒙 < 𝒃 then a and b are respectively (Average) (CET2019)
𝜋 𝜋 𝜋
1) − 2 𝑎𝑛𝑑 2 2) 0 and 2𝜋 3) 2 𝑎𝑛𝑑 2𝜋 4) 0 and 𝜋
𝟏 𝟐𝒙 𝟏 𝟏−𝒙𝟐
32. 𝒕𝒂𝒏 [𝟐 𝒔𝒊𝒏−𝟏 (𝟏+𝒙𝟐 ) + 𝟐 𝒄𝒐𝒔−𝟏 (𝟏+𝒙𝟐 )] = (Average)
2𝑥 2𝑥
1) ∞ 2) 1 3) 1−𝑥 2 4) 1+𝑥 2

33. The value of 𝐬𝐢𝐧(𝐜𝐨𝐭 −𝟏 (𝐜𝐨𝐬(𝐭𝐚𝐧−𝟏 𝒙))) is (Average)
𝑥 2 +2 𝑥 2 +1 𝑥 1
1)√𝑥 2 +1 2) √𝑥 2 +2 3) √𝑥 2 4) √𝑥 2
+2 +2

34. If 𝟐 𝒔𝒊𝒏−𝟏 𝒙 − 𝟑 𝐜𝐨𝐬 −𝟏 𝒙 = 𝟒 , 𝒙 ∊ [−𝟏, 𝟏] then 𝟐 𝒔𝒊𝒏−𝟏 𝒙 + 𝟑 𝐜𝐨𝐬 −𝟏 𝒙= (Difficult)(CET2024)
4−6𝜋 6𝜋−4 3𝜋
1) 2) 3) 4) 0
5 5 2
𝟐𝒂 𝟏−𝒂𝟐 𝟐𝒙
35. If 𝒔𝒊𝒏−𝟏 (𝟏+𝒂𝟐 ) + 𝒄𝒐𝒔−𝟏 (𝟏+𝒂𝟐 ) = 𝒕𝒂𝒏−𝟏 (𝟏−𝒙𝟐 ) 𝒘𝒉𝒆𝒓𝒆 𝒂, 𝒙 ∊ (𝒐, 𝟏), then 𝒙= (Difficult)(CET2023)
2𝑎 2𝑎 𝑎
1) 1+𝑎2 2) 0 3) 1−𝑎2 4) 2

36. The value of 𝒄𝒐𝒔𝟐 [𝒕𝒂𝒏−𝟏 {𝒔𝒊𝒏( 𝒄𝒐𝒕−𝟏 𝒙)}] = (Difficult)
𝑥 2 +1 𝑥 2 −1 𝑥 2 +1 𝑥 2 −1
1) 2) 2 3) 2 4) 2
𝑥 2 +2 𝑥 −2 𝑥 −2 𝑥 +2
𝟏 𝟏 𝟏 𝟏
37. If 𝐭𝐚𝐧−𝟏 (𝟏+𝟐) + 𝐭𝐚𝐧−𝟏 (𝟏+𝟐(𝟑)) + 𝐭𝐚𝐧−𝟏 (𝟏+𝟑(𝟒)) + . . . 𝐭𝐚𝐧−𝟏 (𝟏+𝒏(𝒏+𝟏)) = (Average)(CET2026)
𝑛 𝑛+1 𝑛 𝑛+2
1) tan−1 ( 𝑛+2) 2)tan−1 ( 𝑛 ) 3)tan−1 ( 𝑛+1) 4) tan−1 ( 𝑛 )
√𝟏+𝒔𝒊𝒏 𝒙+√𝟏−𝒔𝒊𝒏 𝒙 𝝅
38. The value of cot−𝟏 ( ) , 𝒘𝒉𝒆𝒓𝒆 𝒙 ∈ (𝟎 𝟒 ) is (Difficult) (CET2023)
√𝟏+𝒔𝒊𝒏 𝒙−√𝟏−𝒔𝒊𝒏 𝒙
𝑥 𝑥 𝑥 𝑥
1) 𝜋 − 3 2) 2 3) 𝜋 − 2 4) 2 − 𝜋

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𝒙𝟐 𝒙𝟑 𝒙𝟒 𝒙𝟔 𝝅
39. If 𝒔𝒊𝒏−𝟏 (𝒙 − 𝟐 + 𝟒 − +. . ∞) + 𝒄𝒐𝒔−𝟏 (𝒙𝟐 − 𝟐 + 𝟒 − +. . ∞) = 𝟐 for 0 < |𝒙| <√𝟐 then x =(Easy )
1 1 1
1) 1 2) 2 3) 3 4) − 2

40. The angles of a triangle are cot-12 and cot-13. Then the third angle is (Average)
1) π/4 2) 3π/4 3) π/3 4) π/2

CLASSROOM CHALLENGE
1 2 3 4 5 6 7 8 9 10
2 2 1 3 4 4 1 1 2 4
11 12 13 14 15 16 17 18 19 20
2 3 4 2 1 3 1 1 2 4
21 22 23 24 25 26 27 28 29 30
4 2 1 3 1 2 1 3 3 4
31 32 33 34 35 36 37 38 39 40
3 1 2 4 2 4 3 1 2 1

PRACTICE ZONE
1. If y  sin 1 x , 1  x  0 , then the range of y is

          
(1)   , 0  (2)   ,  (3)   , 0  (4) 0 , 
 2   2 2  2   2
2. If y  cos 1 x , 0  x  1 , then the range of y is
   
(1)  0,  (2)  0,  (3) 0 ,  (4)  , 
 2 2 

sin 1  x  3
3. The domain of the function f  x   is
9  x2
(1) 1, 2 (2)  2,3 (3)  2,3 (4) 1, 2 

4. In which of the following the inverse of the function y=sinx does not exist.
𝜋 𝜋 𝜋 3𝜋 3𝜋 𝜋
(1) [0,π] (2)[− 2 , 2 ] (3)[ 2 , 2 ] (4)[− 2 , − 2 ]

 1  1
5. The value of tan -1 1 + cos -1  -  + sin -1  -  is equal to
2   2  
(1) 3π/2 (2) 3π/4 (3) π/2 (4) π
6. 𝑇ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 tan 2  sec-1  2   + cot 2  cosec-1  3   𝑖𝑠

(1) 5 (2) 11 (3) 13 (4) 16
7. Evaluate sin -1  sin1000  + cos-1  cos1000 

(1) 0 (2) 1800 (3) 1000 (4) 2000

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𝟏 𝟏𝟒𝝅
8. Which of the following value of 𝐜𝐨𝐬 [𝟐 𝐜𝐨𝐬 −𝟏 (𝐜𝐨𝐬 (− 𝟓 )] is wrong
7𝜋 𝜋 2𝜋 3𝜋
(1) cos (− 5 ) (2) sin 10 (3) cos ( 5 ) (4) −cos 5

 3 1  1 
cos 1  0   sin 1    cos  
 2  2
9. 
 3   1 
sin 1 1  cos 1  1
  sin  
 2   2
(1)7/11 (2)11/12 (3)7/10 (4)14/11
  3  π
10. Find the value of k, sin-1 ktan  2cos-1  = .
  2   3

1 1
(1)2 (2) 3 (3) (4)
2 3
 1  -1  1  -1   π 
11. Find the value of, tan-1  -  + cot   + tan sin  - 2   .
 3  3   
   
(1)  (2) (3) (4)
12 12 6 2
  
12. Evaluate sin 1  sin   cos 1  cos    tan 1 1
 4 
  3 3
(1) (2)  (3)  (4)
4 4 2 2
    3 
13. Evaluate sin 1  sin   cos 1  cos   tan 1 1
 4   4 
  5 5
(1) (2)  (3)  (4)
4 4 4 4
x 5 π
14. If sin -1   + cosec-1   = , then x is
5 4 2
(1)4 (2)5 (3)1 (4)3
  π 
cos-1 sin x+  
 8π 
15. Let f  x  = e   3 
. Then, f   =
 9 
5 13 2 2
18 18 18 18
(1) e (2) e (3) e (4) e
16. Consider the following statements
1 
1. tan 1 x  tan 1     2. There exist x, y   1,1 , where x  y such that sin 1 x  cos 1 y 
x 2
Which of the above statements is/are correct?
(1) 1 Only (2) 2 Only (3) Both 1& 2 (4) Neither 1 nor 2

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 3 1
17. Find the value of x if x  y  sin1   & x  y  sin 1  
 2  2

(1) 300 (2) 900 (3) 150 (4) 450
18. The angle of a triangle are cot 1 2 and cot 1 3 ,then the third angle is
 3  
(1) (2) (3) (4)
4 4 6 3
19. If 𝐜𝐨𝐬 −𝟏 (𝒙 − 𝟐) = 𝐬𝐢𝐧−𝟏 (𝒚 + 𝟏) then the variables 𝒙 and 𝒚 satisfy the equation
(1) 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 + 4 = 0 (2) 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 + 5 = 0
(3) 𝑥 2 + 𝑦 2 − 4𝑥 + 2𝑦 + 6 = 0 (4) 𝑥 2 + 𝑦 2 − 2𝑥 + 𝑦 + 4 = 0
20. If 𝟓𝝅 − 𝟔𝐜𝐨𝐬 −𝟏 (√𝟑(𝟐𝒙 − 𝟏)) = 𝟎, then the value of 𝒙 is equal to
1 1
(1) 2 (2) 2 (3) 4 (4) 4
𝟓𝝅 𝝅 𝝅 𝟓𝝅
21. The value of 𝐬𝐢𝐧−𝟏 (𝐬𝐢𝐧 𝟗 𝐜𝐨𝐬 𝟗 + 𝐬𝐢𝐧 𝟗 𝐜𝐨𝐬 𝟗 ) is equal to
2𝜋 𝜋 𝜋 𝜋
(1) 3 (2) 2 (3) 6 (4) 3
𝟐𝝅 𝟐𝝅
22. The value of 𝐜𝐨𝐬 −𝟏 (𝐜𝐨𝐬 𝟑 ) + 𝐬𝐢𝐧−𝟏 (𝐬𝐢𝐧 𝟑 ) is equal to
𝜋 2𝜋 𝜋
(1) − 2 (2) − 2 (3) 2 (4) 𝜋
𝐜𝐨𝐬 𝒙−√𝟑𝐬𝐢𝐧 𝒙 𝝅
23. The value of 𝐭𝐚𝐧−𝟏 ( ), where 𝟎 < 𝒙 < 𝟐 is
√𝟑𝐜𝐨𝐬 𝒙+𝐬𝐢𝐧 𝒙
𝜋 𝜋 𝜋 𝜋
(1) − 𝑥 (2) − 𝑥 (3) − 𝑥 (4) − 𝑥
6 4 3 2

24. Identify the domain from the following graph

(1)  , 1  1,   (2)  1,1 (3) R   1,1 (4)  ,  

25. Identify the range from the following graph

   
(1) 0  y   (2)   y (3) 0  y   (4)   y
2 2 2 2

2026-27 MATHEMATICS CET MATERIAL Page 16 of 18

26. The graph shown below depicts:

(1) y  cot x (2) y  cot 1 x (3) y  tan 1 x (4) y  tan x

27. Identify the graph of cos 1 x , where x   1,0

28. The graph of a trigonometric function is as shown. Which of the following will represent graph of its
inverse?

PRACTICE ZONE
1 2 3 4 5 6 7 8 9 10
3 3 3 1 2 2 2 1 4 3
11 12 13 14 15 16 17 18 19 20
1 4 4 4 2 4 4 2 1 3

2026-27 MATHEMATICS CET MATERIAL Page 17 of 18

21 22 23 24 25 26 27 28 29 30
4 4 1 3 4 2 C C

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