Jee 2014 Booklet1 Hwt Trigo Ratio & Equation
Short Description
Jee 2014 Booklet1 Hwt Trigo Ratio & Equation...
Description
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [1]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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.
2.
3.
The value of 1 cos 56 cos 58 cos 66 is equal to : (A)
2 cos 28 cos 29 cos 33
(B)
4 cos 28 cos 29 sin 33
(C)
4 cos 28 cos 29 cos 33
(D)
2 cos 28 cos 29 sin 33
6.
(A)
sin 2
(B)
cos 2
(C)
tan 2
(D)
sec 2
7.
1 sinx 1 sin x 1 sinx 1 sin x
is
equal to :
4.
(A)
sin
x 2
(B)
tan
(C)
sec
x 2
(D)
cos ec
If tan x (A) (C)
5.
b , then a
ab ab
2 sin x sin 2 x 2 cos x sin 2 x
x 2
8. x 2
ab is equal to : ab
(B) (D)
9.
(A) (C)
VMC/Trigonometric Ratio & Equation
(C)
1 2 cos A cos B cos C
(D)
1 4 sin A sin B sin C
tan
is
2 2 tan 3 tan tan is equal to : 5 15 5 15
(A)
3
(B)
(C)
1
(D)
1 3 3
The period of sin 2 is : (A)
2
(B)
(C)
2
(D)
2
The value of (A)
2 sin x
(C)
cos 2 x 10.
(B) (D)
4 sin A sin B sin C
cos 2 x
sin 2 y 1 cos y sin y is equal to : 1 cos y sin y 1 cos y
0 sin y
3 , then cos 2 A cos 2 B cos 2C 2
(B)
2 cos x
The value of the expression
1
A BC
equal to : (A) 1 4 cos A cos B cos C
1 1 1 1 If cos x , then x 2 is equal to : 2 2 x x2
If x lies in IInd quadrant, then
If
1 tan 2 15 1 tan 2 15
1
is :
3
(B)
3 2
(D)
If sin 1, sin
2
1 , 2
then tan 2 tan 2 is equal to : (A) (C)
1 cos y
11
1 Zero
(B) (D)
1 None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [2]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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.
2.
The value of tan 1 tan 2 tan 3. . . tan 89 is : (A) 1 (B) 0 1 (C) (D) 2 If
sec tan 1 ,
then
root
of
the
a 2b c x 2 b 2c a x c 2a b 0 (A) (C) 3.
4.
5.
(B) (D)
7.
equation is :
tan cos
(C)
cos
1 p2
1 p 1 sec 2
2
under
the
restriction
1
None of these
The
value
cos A cos B sin A sin B sin A sin B cos A cos B
of
n
(where n is an even) is :
9.
(A)
2 tan n
(C)
0
A B 2
A B 2 None of these 2 cot n
(B) (D)
If tan
1 2
, tan
x x x 1
x 2
x x 1
and tan x 3 x 2 x 1 , then is :
, p 1
The maximum value of
(D)
n
8.
Which of the following relations is possible ? 5 sin (A) 3
tan 1002
2n
If 2 , then : tan tan tan tan tan tan (A) 2 2 2 2 2 2 tan tan tan tan tan tan 1 (B) 2 2 2 2 2 2 tan tan tan tan tan tan (C) 2 2 2 2 2 2 (D)
3 sin 4 3 The value of 3 sin 4 2 6 2 sin sin6 5 is equal to : 2 (A) 0 (B) 1 (C) 3 (D) None of these
(B)
1
(B)
2n 2 1 2n
(C)
If tan x cot x 2 , then sin 2n x cos 2n x is equal to : 1 (A) (B) 2n 2 1 (C) (D) None of these 2
(D) 6.
sec sin
1
(A)
10.
(A)
(B)
2
(D)
(D)
None of these
If 2230' , then 1 cos 1 cos 3 1 cos 5 1 cos 7 equals :
cos 1 cos 2 . . . cos n 0 1 , 2 , . . ., n
cot 1 cot 2 . . . cot n 1 , is :
VMC/Trigonometric Ratio & Equation
2
(A)
and (C)
12
1 8
1 2 2 2
(B) (D)
1 4
2 1 2 1
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [3]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 tan cos tan , then cot 2 is equal to : 2
(A) (C) 2.
sin sin
cos cos
6.
sin
(B)
sin cos
(D)
cos
7.
tan tan 2 tan 3 . . .tan 2n 2 tan 2n 1 is :
3.
0 1
(B) (D)
7 5 cot 2
9 4 sec 1 12 (A) 5 33 (C) 100 4.
8.
33 28 12 13
(B) (D)
3 and lies in the third quadrant, then the 5 value of cos is : 2 1 1 (A) (B) 5 10 1 5
9.
(B)
tan tan
(C)
tan 2 tan
(D)
2tan tan
If cos sin cos sin , then the (A)
cot
(B)
cot
(C)
cot
(D)
cot
1 cos 8
3 . 1 cos 8
5 . 1 cos 8
7 . 1 cos is 8
10
a 12
10.
, where a is a
(A)
x2 y 2 a2
(B)
x2 y 2 a2
(C)
x 2 4 y 2 4a 2
(D)
x = 2y
VMC/Trigonometric Ratio & Equation
1 2
(B)
cos
(C)
1 8
(D)
1 2 2 2
The value of
(C)
1
(D)
13
8
(A)
(A)
2a ,y 1 2 1 2 constant, is the parametric equation of the curve :
The equation x
2 tan tan
equal to :
is :
If sin
(C)
5.
1 None of these
If tan , 2 tan 2 , 3 tan 3 are in GP, then the value of
(A)
value of cot cot cot is :
If 4n , then the value of
(A) (C)
and , then tan equals : 2
If
1
1 tan 2 15 1 tan 2 15
is :
3
(B)
3 2
(D)
2
If A B C 180 , then sin 2 A sin 2 B sin 2C (A)
4 cos Acos B cos C (B)
4 sin A sin B sin C
(C)
2 sin A sin B sin C (D)
8 sin A sin B sin C
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [4]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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. 7
1.
The value of
sin
2n 1
n 1
(A) (C) 2.
1 32 1 128
14
6.
(B) (D)
Let
cos
0 ,
1 64
None of these
The function f given by x x x f x sin 2 cos tan 2 3 3
7.
3.
3 12
4 10
(B) (D)
8.
8 12
(C)
2
5
(B)
2
5 2
(D)
None of these
5
9.
Let A and B denote the statements A : cos cos cos 0 B : sin sin sin 0 If cos cos cos (A) (B) (C) (D)
10.
3 , then : 2
A is false and B is true Both A and B are true Both A and B are false A is true and B is false
VMC/Trigonometric Ratio & Equation
. Then tan 2 4
20/7
(B)
25/16
(C)
56/33
(D)
19/12
3 The expression 3 sin 4 sin 4 3 2
(A)
0
(B)
1
(C)
3
(D)
None of these
If , , , satisfy the equation tan x 3 tan 3 x , 4 then tan tan tan tan
If the angle is in the third quadrant and tan 2 , then sin is equal to : (A)
5.
(B) (D)
5 , where 13
1 2 sin6 sin6 5 is equal to : 2
The number of integral values of k for which the equation 7 cos x 5 sin x 2k 1 has a solution is : (A) (C)
4.
6 4
and let sin
(A)
is periodic with period : (A) (C)
4 5
14
(A)
1
(B)
1 3
(C)
0
(D)
2
If sin x cosec x 2 , then sin n x cosec n x is equal to : (A)
2
(B)
2n
(C)
2n 1
(D)
2n 2
In
any
triangle
ABC,
not
cos Acos ec B cos ec C
right
angled,
(A)
1
(B)
2
(C)
3
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [5]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 Pn cos n sin n then Pn Pn 2 kPn 4 , where
6.
k= (A) (C) 2.
3.
1 2
sin
2
sin cos
(D)
cos 2
If tan 2 x sec x a 0 has at least one solution, then complete set of values of a is : (A)
, 1
(B)
1,
(C)
9 4 ,
(D)
1,
Number
of
solutions
of
the
7.
4.
5.
0 2
(B) (D)
equation
(A)
, 4 4
(B)
3 , 8 8
(C)
, 3 6
(D)
None of these
8.
9.
(C)
x n 1
(D)
None of these
6
(B)
3
(C)
or 3 6
(D)
2 or 3 3
The period of function sin x 4 x 9 x . . . to n terms
(A)
4 n n 1
(B)
(C)
12 n n 1 2n 1
(D)
(B) n
x 2n
(A)
p 8 , q 4
(C)
p 4, q
10.
4 4
VMC/Trigonometric Ratio & Equation
15
None of these
9 2
9 2
(B)
p 8, q
(D)
None of these
tan 2 sec holds for some real if belongs to :
(C)
2
12 n n 1 n 2
If p cos 2 x 6 sin x 1 q , then :
(A)
The general solution of the trigonometrical equation sin x cos x 1 for n 0 , 1, . . . is given by :
x 2n
then = 2
(A)
1 3
In a right angled triangle, the hypotenuse is 2 2 times the length of perpendicular drawn from the opposite vertex on the hypotenuse, then the other two angles are :
(A)
4 2 3, 0 ,
to
is :
tan x sec x 2 cos x , lying in the interval 0, 2 is : (A) (C)
1 sin sin 2 . . .
0 ,
2
(B)
If
, 1 1,
(B) (D)
, 1 1,
1 1 1 1 tan tan tan . . . tan cot n 2 2 4 4 8 2 2 2n 1 1 (A) (B) tan cot n n n 2 2 2 2n 1 1 (C) (D) tan cot n 1 n n 1 2 2 2 2n
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [6]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 is a root of 25 cos 2 5 cos 12 0 , then sin 2 is equal to : 24 (A) 25 13 (C) 18
2.
, 2
6
5.
m0
(B) (D)
24 25 13 18
Let , be such that 3 . 6.
21 27 and cos cos , 65 65 then the value of cos is : 2 3 3 (A) (B) 130 130 6 6 (C) (D) 65 65
7.
8.
3 2 a , the triangle is right angled. 4 If tan A
1 cos B , then tan 2A = tan B sin B
9.
tan 3 x 1 never lies between and 3. tan x 3 Which of the statements given above are correct ? (A) I and II (B) II and III (C) III and I (D) I, II and III
(B)
C1 C3 C5 1
(C)
2C2 4C6 0
(D)
C4 2C6 0
The equation k sin x cos 2 x 2k 7 possesses a solution, if : (A) k>6 (B) 2k 6
k2
(D)
None of these
If sin x a, cos y b , then cos x y
1 b b 1 a
(A)
a 1 b2 b 1 a 2
(C)
a
2
2
(B)
ab
(D)
2ab
The equation sin 6 x cos 6 x , has a solution if : 1 1 (A) (B) , 1 , 1 2 4 1, 1
(D)
1 0, 2
If the value of the determinant
cos 10 sin 10 1 cos 20 sin 20 1 cos 30 sin 30 1 k 1 cos 10 sin 10 , then k =
Consider the following statements :
(A) (C)
I.
If sin A = sin B, then we have sin 2A = sin 2B always. 4 5 1 cos II. The value of cos cos , is . 7 7 7 4 Which of the statements given above is(are) correct ? (A) Only I (B) Only II (C) Both I and II (D) Neither I nor II
VMC/Trigonometric Ratio & Equation
C0 C2 C4 C6 0
(C)
III.
4.
(A)
(C)
Consider the following statements : I. If A 30 and area of the triangle ABC is
II.
Cm cosm x ,
where C0 , C1 , C2 , . . . . C6 are constant, then :
If sin sin
3.
If sin 3 x sin 3x
10.
16
2 8
(B) 4 (D) None of these A B C In a triangle ABC, tan , tan , tan are in H.P., then 2 2 2 A C cot . cot 2 2 (A) 2 (B) 3 (C) 4 (D) None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [7]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 One correct option. 1.
2.
3.
2
If
6
2
cos x sin y b ,
and
*8.
(C)
ab ab
The value of cos
ab
(D)
ab ab
1
3 3 4
(B) (D)
9.
(B)
(C)
1
(D)
None of these
sin
15 4
5 7 . sin . sin The numerical value of sin is equal 18 18 18 to : (A) 1 (B) 1/8 (C) 1/4 (D) 1/2
10.
1 15 8 2 cos 32 1 cosec 16 4 2
1
(B)
8 sin
1
(D)
8 2
32
cosec
32
The most general solutions of
7 4
(A)
n
(C)
2n
7 4
1 2
is : 7 4
(B)
n 1
(D)
None of these
n
The smallest positive root of the equation, tan x x 0 lies in : (A)
0, 2
(B)
2 ,
(C)
3 , 2
(D)
3 2 , 2
The maximum value of 1 sin 2 cos 4 4
1 2
15 7 3 . sin . sin is equal to : 32 16 8
tan 1, cos
1 2
5 None of these
1 2
(C)
2 4 6 cos cos is : 7 7 7
(B) (D)
(A)
(A) (B)
3 4
The value of sin 78 sin 66 sin 42 sin 6 is :
then
x y is equal to : 2
a+b
(C)
6.
sin x cos y a
(A)
(A)
5.
4
7.
If a cos 3 b cos 16 cos 9 cos is identity, then : (A) a = 1, b = 24 (B) a = 3, b = 24 (C) a = 4, b = 2 (D) a = 7, b = 18
tan
4.
(A) (C)
The ratio of the greatest value of 2 cos x sin 2 x is to its least value is : (A) 7/4 (B) 11/4 (C) 13/4 (D) None of these
for real values of is :
VMC/Trigonometric Ratio & Equation
17
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [8]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 One correct option. 1.
Let a cos A cos B cos A B
7.
A B A B sin cos . Then a b is equal to : 2 2 2 (A) 1 (B) 0 (C) (D) None of these 1 2 tan 4 is equal to : The value of tan 16 8 cot cot (A) (B) 8 16 cot 4 (C) (D) None of these 16
If xy + yz + zx = 1, then
and b 4 sin
2.
3.
5 cot Let f and . Then the value 1 cot 4 of f . f is : (A)
4.
5.
6.
2
8.
(B)
*9.
(B)
1
(C)
5
(D)
5
VMC/Trigonometric Ratio & Equation
1 x 1 y 2 1 z2
(C)
1 x 1 y 2 1 z2
(D)
None of these
2 xyz
2
4 xyz
2
If sin sin a and cos cos b then is equal to : 2
a b
a 2 b2
The set of all x in
,
b a
(B)
(D)
None of these
satisfying | 2 sin x|
3 is
given by :
If cos 2 x 2 cos x 1 then sin 2 x 2 cos 2 x is equal
1
(C)
(C)
If sin cos ec 2 then the value of sin8 cos ec8 is equal to : (A) 2 (B) 28 4 (C) 2 (D) None of these
to : (A)
1 x 1 y 2 1 z2 2
(A)
1 (C) (D) None of these 2 2 sin 1 sin cos then If is equal 1 sin cos 1 sin to : 1 (A) (B) (C) 1 (D) 1
xyz
(A)
tan
1 2
x y z 1 x2 1 y2 1 z2
10.
(A)
0, 3
(C)
, 3 3 ,
(D)
3 , 3
(B)
3 , 0
The number of distinct solutions of sin 5 . cos 3 sin 9 . cos 7 in 0, / 2 is :
(A) (C)
18
4 8
(B) (D)
5 9
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [9]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
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 One correct option. 1.
The number of solution of
6.
sin 2 3 cos 3 in
sin 3 x sin x cos x cos 3 x 1 in 2 , 7 are :
, is : (A) (C) 2.
4 0
(B) (D)
(A) (C)
2 1 cos
The number of solutions of
7.
3 sin 5,
0 5 , is :
(A) (C) 3.
4 5
(B) (D)
0 2
8.
0, 5
The number of value of x in
4.
5 8
The
most
6 10
general values 3 tan tan 2 are : 4
(C) (D) The
general
sec 2 x
(A) (C)
solutions
of
9.
satisfying
2n , n Z 3
of
the
equation
2 1 tan 2 x are given by :
(B) 8 n (D) 8 n
(B) (D)
9 11
The number of values of x for which sin2x + cos 4x = 2 is: (A) 0 (B) 1 (C) 2 (D) infinite If 2 sin x 1 0 and x 0, 2 then the exhaustive
(A)
7 0, 6 (B)
(C)
11 6 , 2
7 11 0, 6 6 , 2
(D)
If | tan x | 1 and x ,
None of these then the exhaustive
solution set for x is :
n , n Z (B) 3 2n ,n Z 3 n n 1 ,n Z 3
(A)
*5.
(B) (D)
8 10
solution set for x is :
satisfying the
equation 3 cos 2 x 10 cos x 7 0 is : (A) (C)
The number of solutions of
*10.
4 n 8 n
VMC/Trigonometric Ratio & Equation
(A)
3 3 , 4 4 , 4 4 ,
(B)
3 4 , 4 4 ,
(C)
4 , 4
(D)
None of these
7 If sin a for exactly one value of 0, then 3 the value of a is : 3 (A) (B) 1 2
(C)
19
0
(D)
1
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : TGM [10]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains 9 Objective Type Questions and 1 Subjective Type Question. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
sin x cos x
(A)
2
(B)
2
(C)
2
(D)
(A) (C)
2
2
2
sec
1 0
2
2
A cosec A 1 is equal to :
(B) (D)
–1 None of these
7.
2 4 z cos , then xy yz zx 3 3 –1 (B) 0 1 (D) 2
8.
The values of 0 360 satisfying cosec 2 0 are :
5.
If A B C
1 4 cos A cos B cos C
(B)
4 sin A sin B sin C
(C)
1 4 cos A cos B cos C
(D)
1 4 sin A sin B sin C
Maximum value of a cos b sin is : (A) a+b (B) ab
210 , 300
(B)
240 , 300
(C)
(C)
210 , 240
(D)
210 , 330
(D) 9.
(A) (C)
sin
0 2
sin 0 2
(B) (D)
VMC/Trigonometric Ratio & Equation
cos
0 2
cos 2
a b
and 2 r , r Z 2 None of these 2 r
The minimum value of 2 sin x 2cos x is : (A) 1 (B) 2
(C)
0
10.
20
a 2 b2
(D)
The general solution of tan sin cot cos is : 2 2 2 r , r Z (A) 2 (B) 2r , r Z
(A)
If sin sin and cos cos , then :
3 , then cos 2 A cos 2 B cos 2C 2
(A)
(C)
If x y cos (A) (C)
4.
1
The expression cosec 2 A cot 2 sec 2 Atan 2 A cot A tan A
3.
6.
2
1 2
1
(D)
2
1 2
If cosec x 1 cot x , then x = ________________.
HWT/Mathematics
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