Download Jee-2014-Booklet4-Hwt-Inverse Trigo & Prop of Triangle PDF

TitleJee-2014-Booklet4-Hwt-Inverse Trigo & Prop of Triangle
Tags Triangle Trigonometric Functions Sine Classical Geometry
File Size181.2 KB
Total Pages11
Document Text Contents
Page 1

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 46 HWT/Mathematics

DATE : IITJEE : MARKS :
 
 
 10 TIME : 25 MINUTES

NAME : TEST CODE : INVTG & PROP  [1]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.
 Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. If
1

5
x  , the value of  1 12cos cos x sin x  is :

(A)
24

25
 (B)

24

25
(C)

1

5
 (D)

1

5

2. The value of  1 10sin sin is :
(A) 10 (B) 3 10  (C) 10 3 (D) None of these

3. If 1 1
2

3
sin x sin y

   , then 1 1cos x cos y  is equal to :

(A)
2

3


(B)

3


(C)

6


(D) 

4. 1 1
2

2
2

1

x
sin tan x

x

    
 

for :

(A) 1x  (B) 0x  (C) 1x  (D) all x R

5. If 0 1x  and 1 1 1sin x cos x tan x      , then :

(A)
2


  (B)

2


  (C)

4


  (D)

4 2

 
 

6. The principal value of 1 1
3 7

2 6
sin cos cos

               
, is :

(A)
5

6


(B)

2


(C)

3

2


(D) None of these

7. Sides of a triangle are in ratio 1: 3 : 2 , then angles of triangle are in ratio :

(A) 1 : 3 : 5 (B) 2 : 3 : 4 (C) 3 : 2 : 1 (D) 1 : 2 : 3

8. If
2

A b c
cot

a


 then the ABC is :

(A) isosceles (B) equilateral (C) right angled (D) None of these

9. Which of the following pieces of data does not uniquely determine an acute-angled triangle ABC (R being the circumradius) ?

(A) a, sin A, sin B (B) a, b, c (C) a, sin B, R (D) a, sin A, R

10. The angles of a  are in the ratio 4 : 1 : 1, then the ratio of the largest side to the perimeter is :

(A) 1:1 3 (B) 2 : 3 (C) 3 : 2 3 (D) 1: 2 3

Page 2

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 47 HWT/Mathematics

DATE : IITJEE : MARKS :
 
 
 10 TIME : 25 MINUTES

NAME : TEST CODE : INVTG & PROP  [2]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.
 Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1.  1tan cos x is equal to :
(A)

21 x

x


(B)

21

x

x
(C)

21 x

x


(D) 21 x

2. If x y z xyz   , then 1 1 1tan x tan y tan z    

(A)  (B)
2


(C) 1 (D) None of these

3.
1

1
2 1

1

2

1 2

n r

r
r

tan







 
   

 is equal to :

(A)  1 2ntan (B)  1 2
4

ntan
  (C)  1 12ntan  (D)  1 12

4
ntan

  

4. Range of the function     1f x cos x  , where { } is fractional part function, is :

(A)
2

,



 
 
 

(B)
2

,



 
 
 

(C)
2

,



 


 

(D) 0
2

,
 

 
 

5. Incircle of radius 4 of a ABC touches the side BC at D. If BD = 6, DC = 8 and  be the area of triangle then 3  
(A) 2 (B) 3 (C) 4 (D) 5

6. The sides a, b, c of ABC are in G.P. where 2 2 3log a log b, log b log c  and 3log c log a are in A.P., then ABC is :
(A) acute angled (B) right angled (C) obtuse angled (D) None of these

7. If
cos A cos B cosC

a b c
  and the side a = 2, then area of triangle is :

(A) 1 (B) 2 (C)
3

2
(D) 3

8. If the angles A, B, C of the triangle ABC be in A.P., then
2 2

a c

a ac c




 

(A) 2
2

A C
cos

 
 
 

(B) 2
2

A C
sin

 
 
 

(C) 2
2

A C
cos

 
 
 

(D) 2
2

A C
sin

 
 
 

9. If 2x   then  1cos cos x 
(A) x (B) x (C) 2 x  (D) 2 x 

10. If 1 1 1a sin x cos x tan x b      , then :

(A) 0a , b   (B) 0
2

a , b


  (C)
2

a , b


  (D) None of these

Page 5

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 50 HWT/Mathematics

DATE : IITJEE : MARKS :
 
 
 10 TIME : 25 MINUTES

NAME : TEST CODE : INVTG & PROP  [5]
ROLL NO. START TIME : END TIME : TIME TAKEN:
STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.
 Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct. However, questions marked with '*' may have more than
correct option.

1. If 1 1
4

tan x tan y
   , then 1 1cot x cot y  

(A)
2


(B)

3

4


(C)  (D)

5

4



2. The domain of the function    1 1
4

f x sin x log x
    is :

(A)
1

1
2

x ,
 
  
 

(B)
1

1
2

x ,
 
  
 

(C)
1

1
2

x ,
 
 
 

(D)
1

1
2

x ,
 
  
 

3. If 1 2 3 4x , x , x , x are roots of the equation
4 3 22 2 0x x sin x cos sin x cos        , then

1 1 1 1
1 2 3 4tan x tan x tan x tan x

      

(A)  (B)
2


 (C)   (D) –

4. In a right angled 2 2 2ABC, sin A sin B sin C   
(A) 0 (B) 1 (C) 2 (D) 3

5. If in a triangle
11 12 13

b c c a a b
ABC,

  
  then cos A is equal to :

(A) 1/5 (B) 5/7 (C) 19/35 (D) None of these

6. If in a 2 2 2 28ABC, R a b c    , then the triangle ABC is :
(A) right angled (B) isosceles (C) equilateral (D) None of these

7. If in a
2

sin B
ABC, cos A

sinC
  then the ABC is :

(A) equilateral (B) isosceles (C) right angled (D) None of these

*8. The area of a regular polygon of n sides is :

(A)
2 2

2

nR
sin

n

 
 
 

(B) 2nr tan
n

 
 
 

(C)
2 2

2

nr
sin

n

 
 
 

(D) 2nR tan
n

 
 
 

9. Angles A, B and C of a triangle ABC are in A.P. If
3

2

b

c
 , the angle A is equal to :

(A)
6


(B)

4


(C)

3


(D) None of these

10. 1 1
1 1

2
2 2

cos sin 
   
   

   
is equal to :

(A)
4


(B)

6


(C)

3


(D)

2

3



Page 6

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 51 HWT/Mathematics

DATE : IITJEE : MARKS :
 
 
 10 TIME : 25 MINUTES

NAME : TEST CODE : INVTG & PROP  [6]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.
 Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. The value of 1 1
1 1

2 3
tan tan 

   
   

   
is :

(A) 0 (B) 3 (C) 6 (D) 4

2. If 1 1 1
3

2
sin x sin y sin z

     , the value of 100 100 100
101 101 101

9
x y z

x y z
  

 
is :

(A) 0 (B) 1 (C) 2 (D) 3

3. The value of 1
1 5

2 3
tan cos
  
      

is :

(A)
3 5

2


(B) 3 5 (C)

3 5

2


(D) None of these

4. The numerical value of 1
1

2
5 4

tan tan
  

 
is :

(A) 1 (B) 0 (C) 7/17 (D) –7/17

5. If
1

2x
x
  , the principal value of 1sin x is :

(A)
4


(B)

2


(C)  (D)

3

2



6. The equation 1 1 1
3

2
sin x cos x cos  

 
    

 
has :

(A) no solution (B) unique solution (C) infinite no. of solution (D) None of these

7. The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60 . If the third side is 3, the remaining
fourth side is :
(A) 2 (B) 3 (C) 4 (D) 5

8. If in a triangle ABC, b + c = 3a then
2 2

B C
cot . cot
   
   
   

is equal to :

(A) 1 (B) –1 (C) 2 (D) –2

9. If in a     3ABC, sin A sin B sinC sin A sin B sinC sin A . sin B      then :
(A) 60A   (B) 60B   (C) 60C   (D) None of these

10. If the angles A, B, C of a triangle ABC are in AP and sides a, b, c are in G.P. then 2 2 2a , b , c are in :

(A) AP (B) GP (C) HP (D) None of these

Page 10

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 55 HWT/Mathematics

DATE : IITJEE : MARKS :
 
 
 10 TIME : 25 MINUTES

NAME : TEST CODE : INVTG & PROP  [10]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

 This test contains a total of 10 Objective Type Questions.
 Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. The principal value of 1
3

2
sin

 
  
 

is :

(A)
2

3


(B)

3


(C)

4

3


(D)

5

3



2. Two angles of a triangle are  1 2cot and  1 3cot . Then the third angle is :

(A)
4


(B)

3

4


(C)

6


(D)

3



3. If 1 2 3 na , a , a , . . . . ., a is an AP with common difference d, then :

1 1 1

1 2 2 3 11 1 1 n n

d d d
tan tan tan . . . . . tan

a a a a a a
  



    
                  

(A)
 

1

1

n

n d

a a




(B)

 
1

1

1 n

n d

a a




(C)

11 n

nd

a a
(D) 1

1

n

n

a a

a a




*4. The value of 1
1 1

1 1

sin x sin x
tan

sin x sin x
    
 
   

is :
2

x



 
  

 

(A)
2

x
  (B) 2 x  (C)

2

x
(D) 2

2

x
 

5. If 0a b c   , then 1 1 1
1 1 1ab bc ca

cot cot cot
a b b c c a

                       

(A) 0 (B)
2


(C)  (D) 2

6. 12 3
4

cot cot
   
 

is equal to :

(A) 1 (B) 7 (C) –1 (D) None of these

7. The sides of a triangle are 17, 25, 28. The greatest altitude is of length :

(A)
420

17
(B)

84

5
(C) 15 (D) None of these

8. If 1 1 1
2

cot x cot y cot z
     , then x y z  

(A) xy z (B) x yz (C) xz y (D) xyz

Page 11

Vidyamandir Classes

VMC/Inverse Trigonometry & Properties of Triangle 56 HWT/Mathematics

Paragraph for Q.9 - 10

The vertices of a ABC are A(1, 1), B(5, 1) and C(5, –4).

9. The orthocenter of ABC has coordinates :

(A) (5, 1) (B)
3

3
2

,
 
 

 
(C)

3
5

2
,

 
 

 
(D) (3, 1)

10. The circumcentre of ABC has coordinates :

(A) (3, 1) (B)
3

5
2

,
 
 

 
(C)

3
3

2
,
 
 

 
(D)

11 2

3 3
,

 
 

 

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