Jee-2014-Booklet4-Hwt-Inverse Trigo & Prop of Triangle
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Jee-2014-Booklet4-Hwt-Inverse Trigo & Prop of Triangle...
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Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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.
If x (A)
2.
4.
5.
6.
7.
8.
24 25
(B)
(D)
1 5
10 3
(D)
None of these
6
(D)
x 1
(D)
all x R
4
(D)
4 2
(D)
None of these
(D)
1:2:3
(D)
None of these
24 25
(C)
3 10
(C)
1 5
The value of sin 1 sin10 is : (A)
3.
1 , the value of cos cos 1 x 2 sin 1 x is : 5
10
(B)
2 If sin 1 x sin 1 y , then cos 1 x cos 1 y is equal to : 3 2 (A) (B) (C) 3 3
2x sin 1 1 x2 (A) x
1 2 tan x for : (B) 1
x0
If 0 x 1 and sin 1 x cos 1 x tan 1 x , then : (A) (B) 2 2 3 7 The principal value of sin 1 cos 1 cos 2 6 5 (A) (B) 6 2
(C)
(C)
, is :
(C)
3 2
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 If cot (A)
A bc then the ABC is : 2 a isosceles (B)
equilateral
(C)
right angled
9.
Which of the following pieces of data does not uniquely determine an acute-angled triangle ABC (R being the circumradius) ? (A) (B) a, b, c (C) (D) a, sin A, sin B a, sin B, R 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
VMC/Inverse Trigonometry & Properties of Triangle
(C)
3 :2 3
46
(D)
1: 2 3
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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.
tan cos 1 x is equal to :
1 x2 x
(A) 2.
3.
1 x
1 x2 x
(C)
2
If x y z xyz , then tan 1 x tan 1 y tan 1 z (A) (B) 2 n r 1 2 tan 1 is equal to : 1 22 r 1 r 1
(C)
1
(C)
tan 1 2n 1
(D)
1 x2
(D)
None of these
(D)
tan 1 2n 1
(D)
0, 2
(A) 4.
x
(B)
tan 1 2n
tan 1 2n
(B)
4
4
Range of the function f x cos 1 x , where { } is fractional part function, is : (A)
2 ,
(B)
2 ,
(C)
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 (A) 2 (B) 3 (C) 4 (D) 5
6.
The sides a, b, c of ABC are in G.P. where log a log 2b, log 2b log 3c and log 3c 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 cos C and the side a = 2, then area of triangle is : a b c
(A) 8.
(B)
2
AC 2 cos 2
(B)
3 2
(C)
ac a ac c 2 2
(D)
3
AC 2 sin 2
(C)
AC 2 cos 2
(D)
AC 2 sin 2
x
(C)
2 x
(D)
2 x
(C)
a
(D)
None of these
If x 2 then cos 1 cos x (A)
10.
1
If the angles A, B, C of the triangle ABC be in A.P., then (A)
9.
3
x
(B)
If a sin 1 x cos 1 x tan 1 x b , then : (A)
a 0, b
(B)
a 0, b
2
VMC/Inverse Trigonometry & Properties of Triangle
47
,b 2
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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.
2.
For which value of x, sin cot 1 x 1 cos tan 1 x 1 (A) (B) 0 2
x
7.
8.
9.
2
1
(D)
1 2
12
1
x
(C)
x 1 x2
(D)
1 x2
0.96
(C)
0.6
(D)
None of these
0.48
(B)
If cos 1 cos 1 cos 1 3 , then the value of is : 0
(B)
3
(C)
3
(D)
1
(C)
0
(D)
None of these
In a triangle ABC, a b cos C ccosB is : (A)
6.
(B)
1 x2
(A) 5.
(C)
The value of cos 2 cos 1 0.8 is : (A)
4.
1 x 2 x cos cot 1 x sin cot 1 x
If 0 < x < 1, then (A)
3.
a2
(B)
b2 c2
If the lengths of the sides of a triangle are 5, 12 and 13 units, the circumradius of triangle is : (A) 2.5 (B) 6 (C) 6.5 (D) The in-radius of the triangle formed by the axes and the line 4 x 3 y 12 0 is : 1 (A) (B) r (C) r2 r 1 2 2 2 5 2 If tan 1 x cot 1 x , then x = 8 (A) (B) 1 (C) 0 1
7
1 4
(D)
r
(D)
None of these
A man from the top of a 100m high tower sees car moving towards the tower at an angle of depression of 30 . After some time, the angle of depression becomes 60 . The distance (in metres) travelled by the car during this time is : (A)
10.
100 3
(B)
The area of an equilateral triangle is 1 (A) (B) 3
200 3 3
(C)
100 3 3
(D)
3 square units. The circumradius of equilateral triangle is : 2 (C) 1 (D) 3
VMC/Inverse Trigonometry & Properties of Triangle
48
200 3
3
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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. 1.
2a 1 2b 1 If sin 1 sin 2 tan x , then x is equal to : 1 a2 1 b2 a b b (A) (B) (C) ab 1 ab 2n
2.
If
sin 1 xi n then find the value of
i 1
(A) 3.
4.
5.
6.
7.
9.
x cos
1
x , then tan sin
(D)
None of these
(D)
1/3
(D)
1
(D)
4
x . i
2n
(C)
1
(C)
n n 1 2
2/3
x =
3 1 (C) 2 2 In a ABC , a b c b c a bc , where I , the greatest value of is : 0
(B)
(A)
1
(B)
2
(C)
3
3 If x , 2 , then the value of the expression sin 1 cos 1 cos x sin 1 sin x is : 2 (A) (B) (C) 0 (D) 2 2
In ABC a 2 cos 2 B cos 2 C b 2 cos 2 C cos 2 A c 2 cos 2 A cos 2 B is equal to :
1
(C)
a b2 c2
(D)
2 a 2 b2 c2
B C If b c 3a , the cot . cot 2 2 (A) 1 (B) 2
(C)
3
(D)
4
0
(B)
2
In any triangle the ratio of angles is 1 : 2 : 3, the ratio of corresponding sides is : (A)
10.
(B)
(A)
(A) 8.
ab 1 ab
2n
2 If sin sin 1 cos 1 x 1 , then x = 3 (A) 1 (B) 0 If sin
(D)
i 1
n
1
b 1 ab
1:2:3
(B)
1: 2 : 2
(C)
1: 3 : 2
(D)
1: 2 : 3
(C)
5 4
(D)
2
tan 1 1 tan 1 2 tan 1 3 (A)
3 4
(B)
VMC/Inverse Trigonometry & Properties of Triangle
49
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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. However, questions marked with '*' may have more than correct option. 1.
2.
, then cot 1 x cot 1 y 4 3 (A) (B) (C) 2 4 The domain of the function f x sin 1 x log 1 x is : 4
If tan 1 x tan 1 y
(A) 3.
1 x , 1 2
(B)
1 x , 1 2
(C)
(D)
5 4
1 x , 1 2
(D)
1 x , 1 2
If x1 , x2 , x3 , x4 are roots of the equation x 4 x 3 sin 2 x 2 cos 2 sin x cos 0 , then
tan 1 x1 tan 1 x2 tan 1 x3 tan 1 x4
4.
5.
(D)
–
(C)
2
(D)
3
19/35
(D)
None of these
If in a ABC, 8 R a b c , then the triangle ABC is : (A) right angled (B) isosceles (C)
equilateral
(D)
None of these
sin B If in a ABC , cos A then the ABC is : 2 sinC (A) equilateral (B) isosceles
7.
right angled
(D)
None of these
*8.
(D)
nR 2 tan n
(D)
None of these
1/5 2
bc ca ab then cos A is equal to : 11 12 13 (B) 5/7 (C) 2
2
2
(C)
The area of a regular polygon of n sides is : nR 2 2 sin 2 n
(B)
nr 2 tan n
Angles A, B and C of a triangle ABC are in A.P. If (A)
10.
(B)
If in a triangle ABC ,
(A) 9.
In a right angled ABC, sin 2 A sin 2 B sin 2 C (A) 0 (B) 1
(A) 6.
2
(C)
(A)
6
(B)
1 1 cos 1 2 sin 1 is equal to : 2 2 (A) (B) 4
b c
4
6
VMC/Inverse Trigonometry & Properties of Triangle
(C)
nr 2 2 sin 2 n
3 , the angle A is equal to : 2 (C) 3
(C)
3
50
(D)
2 3
HWT/Mathematics
Vidyamandir Classes DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [6]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
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.
1 1 The value of tan 1 tan 1 is : 2 3 (A) 0 (B) 3
5.
6.
7.
8.
9.
4
(D)
3 9 , the value of x100 y100 z100 101 101 101 is : 2 x y z (B) 1 (C) 2 (D) 5 is : 3
3 5 2
(B)
3 5
1 The numerical value of tan 2 tan 1 is : 5 4 (A) 1 (B) 0 1 1 If x 2 , the principal value of sin x is : x (A) (B) 4 2 3 The equation sin 1 x cos 1 x cos 1 has : 2 (A) no solution (B) unique solution
3
(C)
3 5 2
(D)
None of these
(C)
7/17
(D)
–7/17
(C)
(D)
3 2
(C)
infinite no. of solution
(D)
None of these
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
B C If in a triangle ABC, b + c = 3a then cot . cot is equal to : 2 2 (A) 1 (B) –1 (C) 2
(D)
–2
(D)
None of these
If in a ABC , sin A sin B sin C sin A sin B sin C 3 sin A . sin B then : (A)
10.
0
1 The value of tan cos 1 2 (A)
4.
6
If sin 1 x sin 1 y sin 1 z (A)
3.
(C)
A 60
(B)
B 60
(C)
C 60 2
2
2
If the angles A, B, C of a triangle ABC are in AP and sides a, b, c are in G.P. then a , b , c are in : (A)
AP
(B)
GP
VMC/Inverse Trigonometry & Properties of Triangle
(C)
HP
51
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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 correct option. 1.
2.
3.
If the sides of a triangle are in the ratio 3 : 7 : 8, the R : r is equal to : (A) 2:7 (B) 7:2 (C) 3:7
(D)
7:3
If in a ABC, sin 2 A sin 2 B sin 2 C then the triangle is : (A) acute angled (B) right angled (C)
(D)
None of these
c 2 3c 7 0
(D)
c 2 3c 7 0
(C)
4
(D)
24
(C)
equilateral
(D)
None of these
In a ABC , a 4 , b 3, A 60 . Then c is the root of the equation :
c 2 3c 7 0
(A) 4.
67 8
If sin (A)
7.
65 4
isosceles 1
(B)
right angled
x , for some x 1, 1 , then the value of cos 1 x is : 5 3 10
(B)
5 10
(C)
7 10
(D)
9 10
1 3 cos 1 2 5
(B)
1 1 3 sin 2 5
(C)
1 3 tan 1 2 5
(D)
1 tan 1 2
0
1
(D)
2
2
(D)
3
(B)
1 2
(C)
If cos 1 x cos 1 y cos 1 z , then x 2 y 2 z 2 2 xyz (A)
10.
(B)
If tan 1 x 1 tan 1 x tan 1 x 1 tan 1 3x , then x = (A)
9.
(C)
1 2 tan 1 tan 1 4 9 (A)
*8.
c 2 3c 7 0
If in a ABC , a sin A b sin B , then the triangle is : (A)
6.
(B)
The sides of a triangle are 13, 14, 15. The radius of its incircle is : (A)
5.
obtuse angled
0
(B)
1
(C)
3 The value of cos tan 1 is : 4 (A)
3 5
(B)
4 5
VMC/Inverse Trigonometry & Properties of Triangle
(C)
1 2
52
(D)
2 3
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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. 1.
1 1 sin sin 1 cos 1 2 2 (A)
2.
2 tan 5 (A)
4.
5.
7.
4tan 1 x
(B)
0
(C)
1
(D)
None of these
(C)
2
(D)
1
(D)
(C)
17/6
(D)
None of these
(C)
tan 1 0.3
(D)
1 tan 1 18
(D)
None of these
(D)
30
2 tan 15 3 tan 5 . tan 15 is equal to : 1 3 (B) (C) 3
4 2 The value of tan cos 1 tan 1 : 5 3 (A) 6/17 (B) 7/16
3
If tan x y 33 and x tan 1 3 , then y will be : (A)
6.
1 2
(B)
2x If x 1 , then 2 tan 1 x sin 1 is equal to : 1 x2
(A) 3.
0
tan 1 2.3
(B)
tan 1 1.3
If tan tan tan k tan 3 , then the value of k is : 3 3 1 (A) 1 (B) (C) 3 3 x 3 2x k If A tan 1 and B tan 1 , then the value of A B is : 2k x k 3 (A) 0 (B) 45 (C) 60
8.
If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ(= PR), then the angle P is : (A) (B) (C) (D) 6 3 2 2 3
9.
Two straight roads intersect at an angle of 60. A bus on one road is 2km away from the intersection and a car on the other road is 3km away from the intersection. Then the direct distance between the two vehicles is : (A)
10.
1 km
(B)
2 km
(B)
s b tan
(C)
4 km
(C)
s b tan
(D)
7 km
In a triangle ABC, r = (A)
s a tan
B 2
B 2
VMC/Inverse Trigonometry & Properties of Triangle
53
C 2
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [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 correct option. 1.
In an equilateral triangle the in-radius and the circum-radius are connected by :
r 4R
(A) 2.
s4
(D)
None of these
b2c2
(C)
c2a2
(D)
a 2b 2
2
(C)
3
(D)
4
(B)
1
(C)
tan nA . tan nB . tan nC (D)
None of these
2, 3
(B)
3, 4
A 5 C 2 , tan , then : 2 6 2 5 a, c, b are in AP (B) a, b, c are in AP
(C)
4, 3
(D)
6, 8
(C)
b, a, c are in AP
(D)
a, b, c are in GP
(C)
x3
(D)
x4
(C)
tan 1 n
(D)
tan 1 n 1
(B) (D)
Geometric mean of a and b None of these
(C)
0,
6 sin 1 x 2 6 x 8.5 if :
sin r 1
(A)
10.
R 3
In a ABC , tan
n
9.
r
If in a ABC, right angled at B, s a 3, s c 2 , then the values of a and c are respectively :
(A) 8.
(B)
0
(A) *7.
(C)
If A B C , n Z , then tan nA tan nB tan nC is equal to :
(A) 6.
(B)
(A) 5.
R 2
In any ABC, b 2 sin 2C c 2 sin 2 B (A)
4.
r
If c 2 a 2 b 2 , 2s a b c , then 4s s a s b s c : (A)
3.
(B)
x 1
(B)
x2
r r 1 is equal to : r r 1
1
tan 1 n
4
(B)
tan 1 n 1
4
a b If tan 1 tan 1 , then x is : x x 2 (A) Arithmetic mean of a and b (C) Harmonic mean of a and b If sin 1 x sin 1 1 x cos 1 x , then x equals : (A)
1, 1
(B)
1, 0
VMC/Inverse Trigonometry & Properties of Triangle
1 2
54
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : INVTG & PROP [10]
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.
3 The principal value of sin 1 is : 2
(A) 2.
(B)
4
(B)
(A)
7.
3 4
n 1 d a1 an
d 1 tan 1 a 2 a3 (B)
x 2
(B)
0
(B)
cot 2 cot 1 3 is equal to : 4 (A) 1 (B)
5 3
(C)
(D)
3
nd 1 a1an
(D)
an a1 a1 an
x 2
(D)
2
6
d 1 . . . . . tan 1 a n 1an
n 1 d 1 a1an
(C)
2 x
(C)
x 2
2
(C)
(D)
2
7
(C)
–1
(D)
None of these
The sides of a triangle are 17, 25, 28. The greatest altitude is of length : (A)
8.
(D)
ab 1 1 bc 1 1 ca 1 If a b c 0 , then cot 1 cot b c cot c a a b (A)
6.
4 3
1 sin x 1 sin x The value of tan 1 is : x 2 1 sin x 1 sin x
(A)
5.
(C)
If a1 , a2 , a3 , . . . . ., an is an AP with common difference d, then :
d tan tan 1 1 a1a2
*4.
3
Two angles of a triangle are cot 1 2 and cot 1 3 . Then the third angle is : (A)
3.
2 3
420 17
(B)
84 5
, then x y z 2 x yz (B)
(C)
15
(D)
None of these
(C)
xz y
(D)
xyz
If cot 1 x cot 1 y cot 1 z (A)
xy z
VMC/Inverse Trigonometry & Properties of Triangle
55
HWT/Mathematics
Vidyamandir Classes 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)
10.
(5, 1)
(B)
3 3, 2
(C)
3 5, 2
(D)
(3, 1)
(C)
3 3, 2
(D)
11 2 3 , 3
The circumcentre of ABC has coordinates : (A)
(3, 1)
(B)
3 5, 2
VMC/Inverse Trigonometry & Properties of Triangle
56
HWT/Mathematics
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