TRIGONOMETRY
1) 25° when measured in radians is
A) 5π/18 B) 5π/24 C) 6π/36 D) none
2) 162° when measured in radians is
A) 5π/10 B) 9π/10 C) 4π/3 D) 5π/4
3) (8π/5)ᶜ = ?
A) 272° B) 302° C) 288° D) 316°
4) 11ᶜ= ?
A) 315° B) 372° C) 418° D) 630°
5) 1ᶜ= ?
A) 56°27'22" B) 57°16'22" C) 55°18'32" D) 57°26'32"
6) 3°45' expressed in radians is
A) (π/36)ᶜ B) (π/54)ᶜ C) A) (π/48)ᶜ B) (5π/96)ᶜ
7) 50°37'30" =?
A) (5π/16)ᶜ B) (7π/18)ᶜ C) A) (9π/32)ᶜ B) (11π/36)ᶜ
8) In a right angled triangle, the difference between two angles is (π/15)ᶜ. The measure of the smallest angle is
A) 40° B) 45° C) 36° D) 39°
9) The angles of a triangle are in AP and the greatest angle is double the least. The largest angle measures?
A) 60° B) 80° C) 75° D) 90°
10) The angles of a triangle are in AP and the ratio of the number of degrees in the least two the number of radians in the greatest is 60:π. The smallest angle is
A) 15° B) 30° C) 45° D) 60°
11) In a circle, the central angle of 45° intercepts an arc of length 33 cm. The radius of the circle is
A) 21cm B) 35cm C) 42cm D) 14cm
12) In a circle of radius 14cm an arc subtends an angle of 36° at the centre.. The length of the arc is
A) 6.6cm B) 7.7cm C) 8.8cm D) 9.2cm
13) The minute hand of a watch is 1.4cm long. How far does its tip move in 45 minutes?
A) 6cm B) 6.3cm C) 6.6cm D) 7cm
14) If the arcs of the same length in two circles subtend angles of 60° and 75° at their respective centres, the ratio of their radii is
A) 4:5 B) 5:4 C) 3:5 D) 5:3
15) A wire of length 121cm is bent to form an arc of a circle of radius 180cm. The angle subtends at the centre by the arc is
A) 36°20' B) 34°49' C) 38°30' D) 39°10'
16) A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88m when it traces 72° at the centre, then the length of the rope is
A) 35m B) 70m C) 17.5m D) 22m
17) A pendulum swings through an angle of 42° in discribing an arc of length 55cm. The length of the pendulum is
A) 56cm B) 60cm C) 75cm D) 88cm
18) The radius of a circle is 30 cm. The length of the arc of the circle whose chood is 30 cm long, is
A) 9πcm B) 10πcm C) 12πcm 13.6πcm
19) A wheel makes 180 revolutions in 1 minute. How many radians does it turn in 1 second?
A) 3π B) 4π C) 6π D) 12π
20) A railway train is moving on a circular curve of radius 1500m at a speed of 90 km/hr. Through what angle has it turned in 11 seconds?
A) 10°30' B) 11°40' C) 12° D) 16°30'
21) When a clock shows the time 7:20, what is the angle between its minute hand and the hour hand ?
A) 60° B) 80° C) 100° D) 120°
22) the angle between the hour and the minute hand of a clock at half past three is
A) 54° B) 63° C) 72° D) 75°
23) The angle between the minute hand and the hour hand of a clock when the time is 8:25 a.m. is
A) 107°15' B) 105° C) 102°30' D) 92°45
24) The length of a pendulum is 60cm. The angle through which its swings when its tip describes an arc of length 16.5 cm is
A) 15°30' B) 15°45' C) 16°15' D) 16°30'
25) the angles of a quadrilateral in degrees are in AP and the greatest angle is 120°. The smallest angle is
A) π/4 B) π/3 C) π/5 D) π/6
26) The perimeter of a sector of a circle is equal to half the circumference of the circle. The angle of the sector is
A) π/4 B) π/2 C) π-2 D) π+2
27) sin (25π/3)=
A) 1/2 B) 1/√2 C) √3/2 D) -√3/2
28) cos (41π/4)=?
A) 1/√2 B) -1/√2 C) √3/2 D) -√3/2
29) tan(-16π/3)=?
A) √3 B) -√3 C) 1/√3 D) -1/√3
30) cot(29π/4)=?
A) -1 B) 1 C) √3 D) 1/√3
31) sec(-19π/3)=?
A) -2 B) -1/2 C) 2 D) 1/2
32) Cosec(-33π/4)=?
A) -√2 B) √2 C) 1/√2 D) -1/√2
33)cos 15π=?
A) 1 B) -1 C) 0 D) none
34) sec 6π
A) 1 B) -1 C) √2 D) -√2
35) tan 5π/4=?
A) √3 B) 1/√3 C) 1 D) -1
36) sin(765°)=?
A) √3/2 B) -√3/2 C) 1/√2 D) -1/√2
37) cot(-600°)=?
A) -1 B) -√3 C) -1/√3 D) none
38) If sinx =-2√6/5 and x lies in quadrant III, then cot x =?
A) 1/2√6 B) -1/2√6 C) 3/2√6 D) -3/2√6
39) If cos x =- √15/4 and π/2 < x< π, then sin x= ?
A) 3/4 B) -3/4 C) 1/4 D) -1/4
40) If sec x =- 2 and π < x< 3π/2, then sin x= ?
A) √3/2 B) -√3/2 C) 1/2 D) -1/2
41) If cosec x =- 2/√3 and x lies in quadrant IV, then tan x= ?
A) 1/√3 B) -1/√3 C) √3 D) -√3
42) if cot x=√5 and x does not lie in the quadrant I, then the value of cosec x and sec x are respectively.
A) √6,(√6/5) B) -√6,√(6/5) C) -√6,-(√6/5) D) -√6,(√6/5)
43) If cos x =- 1/2 and x lies in quadrant II, and then (2sin x+ tan x) = ?
A) 0 B) 3√3/2 C) -√3/2 D) none
44) If cos x =- 3/5 and π < x< 3π/2, then (cosec x + cot x)/(sec x - tan x) = ?
A) 1/6 B) 2/3 C) 3/2 D) 1/3
45) If sin x = 3/5 and π/2 < x< π, then (2 sec x- 3 cot x)= ?
A) 3/2 B) -3/2 C) 13/2 D) -13/2
46) If sec x =√2 and 3π/2 < x< 2π, then (1+ tan x + cosec x)/(1- cot x- cosec x)= ?
A) √3/2 B) -1 C) -3/8 D) 3/4
47) If cos x =- 12/13 and π < x< 3π/2, then (cot x + cosec x) = ?
A) 1/5 B) -1/5 C) 3/5 D) -3/5
48) If cot x =- 12/5 and π/2 < x< π, then (1+ sin x - cos x)/(1- sin x + cos x)= ?
A) 13/4 B) -13/4 C) 15/2 D) -15/2
49) If sin x =4/5 and π/2 < x< π, then (5 cos x+ 4 cosec x + 3 tan x)/(4 cotx + 3 sec x + 5 sin x) = ?
A) -1/2 B) 1 C) 1/2 D) -1
50) If sec x = 13/5 and x is acute, then (4- 3cot x)/(3+ 4 tanx) = ?
A) 55/252 B) 44/305 C) 54/255 D) 33/215
51) cos 135 = ?
A) 1/√2 B) -1/√2 C) 1/2 D) -1/2
52) sec 120 = ?
A) √2 B) -√2 C) 2 D) -2
53) cosec 150 = ?
A) -2 B) 2 C) √2 D) -√2
54) sin 315 = ?
A) 1/√2 B) -1/√2 C) √2 D) -√2
55) cos 405 = ?
A) √2 B) 1/√2 C) -√2 D) -1/√2
56) tan(11π/6) = ?
A) -1/√3 B) 1/√3 C) √3 D) -√3
57) cot 675 = ?
A) -1 B) 1 C) -√3 D) √3
58) sin(31π/3) = ?
A) 1/2 B) -1/2 C) √3/2 D) -√3/2
59) cot (-600) = ?
A) -√3 B) 1/√3 C) -1/√3 D) √3
60) cosec(-1100) = ?
A) 2/√3 B) -2/√3 C) 2 D) -2
61) sec(-33π/4) = ?
A) -√2 B) √2 C) -√3/2 D) √3/2
62) Tan (-25π/3) = ?
A) -√3 B) √3 C) -1/√3 D) 1/√3
63) The value of Cot (π/3), Cot (π/4), Cot (π/6) are in
A) AP B) GP C) HP D) none
64) Which is smaller, sin 64° or cos 64°?
A) sin 64° B) cos 64° C) both are equal D) can not be compared
65) Which is larger, sin 24° or cos 24°?
A) sin 24° B) cos 24° C) both are equal D) can not be compared
66) The extremum values of sin x are
A) 0 and 1 B) -1 and 0 C) -1 and 1 D) -√3/2 and 1/√2
67) The extremum values of cos x are
A) 0 and 1 B) -1 and 0 C) -1 and 1 D) -√3/2 and √2
68) The values of sec x can
A) never be greater than 1 B) never be less than 1 C) never be equal to 1 D) never lie between -1 and 1
69) tan(150) = ?
A) 1/√3 B) -1/√3 C) √3 D) -√3
70) sec(150) = ?
A) 2/√3 B) -2/√3 C) 2 D) -2
71) cot(120) = ?
A) -1/√3 B) 1/√3 C) -√3 D) √3
72) sin 105 + cos 105 = ?
A) √2 B) 1/√2 C) 1/√3 D) 2/√3
73) sin 15 = ?
A) √3/2√2 B) (√3+1)/2√2 C) (√3-1)/2√2 D) (√2-1)/√2
74) cos 15 = ?
A) (√3+1)/√2 B) (√3+1)/2√2 C) (√3-1)/2√2 D) (√3-1)/√2
75) tan 15 = ?
A) (√3+1)/(√3-1) B) (√3-1)/(√3+1) C) (√2+1)/(√2-1) D) (√2-1)/(√2+1)
76) sin 75 = ?
A) (√3+1)/2√2 B) (√3-1)/2√2 C) (√2+1)/2√2 D) (√2-1)/2√2
77) cos 75=?
A) (√3+1)/2√2 B) (√3-1)/2√2 C) (√2-1)/2√2 D) (√2+1)/2√2
78) tan(13π/12)=?
A) (2+ √3) B) (1+ √2) C) (2 - √3) D) (√2-1)
78) (sin70 cos 10 - cos 70 sin 10)=?
A) 1/√2 B) 1/2 C) √3/2 D) -√3/2
80) (sin36 cos 9 - cos 36 sin 9)=?
A) 1/√2 B) 1/2 C) √3/2 D) 1
81) (cos 80 cos 20 + sin 80 sin 20)=?
A) 1/√2 B) 1/2 C) √3/2 D) 1
82) (cos 50 cos 10 - sin 50 sin 10)=?
A) 1/√2 B) 1/2 C) √3/2 D) 1
83) sin(40 +x) cos(10 + x) - cos(40 +x) sin (10 + x) =?
A) √2 B) 1/2 C) √3/2 D) none
84) sin 7π/12 cos π/4 - cos 7π/12 sin π/4 =?
A) 1/√2 B) √2 C) √3/2 D) none
85) sin π/4 cos π/12 - cos π/4 sin π/12 =?
A) 1/2 B) √2 C) √3/2 D) none
86) cos 2π/3 cos π/4 - sin 2π/3 sin π/4 =?
A) (√3+1)/√2 B) -(√3+1)/√2 C) (√3+1)/2√2 D) -(√3+1)/2√2
87) sin π/12 =?
A) (√3-1)/2√2 B) -(√3+1)/2√2 C) (√3+1)/2√2 D) none
88) sin 5π/12 =?
A) (√3-1)/2√2 B) (√3+1)/2√2 C) - (√3-1)/2√2 D) -(√3+1)/2√2
89) If sin x =15/17 and cos y= 12/13, where x and y both lie in quadrant I, then sin(x+ y)=?
A) 171/221 B) 180/221 C) 220/221 D) 181/221
90) If sin x =3/5 and cos y= -12/13, where x and y both lie in quadrant II, then sin(x- y)=?
A) 16/65 B) -16/65 C) 33/65 D) -33/65
91) If cos x =4/5 and cos y= 12/13, where x and y both lie in quadrant IV, then cos(x+ y)=?
A) 33/65 B) -33/65 C) 16/65 D) -16/65
92) If cot x =1/2 and sec y= -5/3, where x lie in quadrant III, and y lies quadrant II then tan(x+ y)=?
A) 5/11 B) 211 C) -6/11 D) 10/11
93) cos 15 - sin 15 = ?
A) 1/2 B) 1/√2 C) (√2-1)/√2 D) (√2+1)/√2
94) cot 105 - tan 105 = ?
A) √3 B) 2√3 C) √3/2 D) (√3+1)/(√3-1)
95) 2 sin 5π/12 sin π/12 = ?
A) √2 B) 1/√2 C) 1/2 D) √3/2
96) 2 cos 5π/12 cos π/12 = ?
A) √2 B) 1/√2 C) 1/2 D) √3/2
97) 2 sin 5π/12 cos π/12 = ?
A) √3/2 B) (2+√3)/2 C) 1/2 D) (√3+1)/2
98) {sin(180+x) cos(90+x) tan(270-x) cot(360- x)}/{sin(360-x) cos(360+x) cosec(-x) sin(270+x)} = ?
A) √2 B) √3/2 C) 3/2 D) 1
99) {sin(40+x) cos(10+x) - cos(40 +x) sin(10-+x)} = ?
A) 2 B) √3/2 C) 1/2 D) none
100) {cos(90+x) sec(270+x) sin(180+x)}/{cosec(-x) cos(270- x) tan(180+x)} = ?
A) cos x B) sec x C) cot x D) none
101) cosx+ sin(270+x) - sin(270-x)+ cos(180+x) = ?
A) 2cos x B) 2sin x C) 0 D) none
102) (cos8 - sin 8)/(cos8 + sin 8) = ?
A) tan 8 B) tan 37 C) tan 52 D) none
103) {cos(π+x) cos(-x)}/{ cos(π-x) cos(π/2 + x) = ?
A) -cot x B) cot x C) -tan x D) tan x
104) cos(π/4 +x) + cos(π/4 -x) = ?
A) 2cos x B) √2 cos x C) 2 sin x D) √2 sin x
105) cos(3π/4 +x) - cos(3π/4 - x) = ?
A) √2 sin x B) 2 sin x C) -√2 sin x D) 1/√2 sin x
106) (sin 3x - sin x)/(cosx - cos 3x) = ?
A) tan 2x B) cot 2x C) - tan 2x D) - cot 2x
107) (cos 6x + cos 4x)/(sin6x - sin4x)= ?
A) cot x B) - tan x C) - tan x D) - cot x
108) (cos4x +cos3x+ cos2x)/(sin4x + sin 3x + sin2x) = ?
A) tan 2x B) cot 2x C) tan 3x D) cot 3x
109) (sin 7x - sin 5x)/(cos7x + cos5x)= ?
A) tan x B) cot x C) tan 2x D) cot 2x
110) (sin²6x - sin²4x)= ?
A) sin10x B) sin 2x C) sin10x sin 2x D) n
111) cos20 cos40 cos80 = ?
A) 1/16 B) 1/8 C) √3/8 D) √3/16
112) sin 10 sin 50 sin 70 = ?
A) 1/16 B) 1/8 C) √3/8 D) √3/4
113) 2cos 45 cos 15 = ?
A) 3/2 B) (√3+1)/2 C) (√3-2)/2 D) √3/2
114) 2 sin 75 sin 15 = ?
A) 1/2 B) (√3+1)/2 C) √3/2 D) n
115) cos 15 - sin 15 = ?
A) 1/2 B) 1/√2 C) 1/2√2 D) √3/2
116) If sinx =-1/2 and x lies in quadrant III, then sin 2x = ?
A) 1/2 B) 1/2√3 C) √3 D) √3/2
117) If sec x =-13/12 and π/2< x<π, then cos 2x = ?
A) -120/169 B) 119/169 C) -120/119 D)n
118) If tan x =-3/4 and 3π/2< x<2π, then tan 2x = ?
A) -24/25 B) 7/25 C) 24/7 D) -24/7
119) If sin x = 1/3 then sin 3x = ?
A) 1 B) 1/9 C) 7/9 D) 23/27
120) If cos x = 1/2 then cos 3x = ?
A) 3/2 B) 1/6 C) -1 D) 2/3
121) cos² π/12 - sin²π/12 = ?
A) 1/2 B) √3/2 C) 3/2 D) -1/2
122) (1+sin 2x - cos2x)/(1+ sin2x+ cos2x) = ?
A) tan 2x B) tan x C) cot2x D) cot x
123) If cos x =-3/5 and π/2< x<π, then sin(x/2) = ?
A) -2/√5 B) 2/√5 C) -2/√5 D) 1/√5
124) If cos x =-3/5 and π/2< x<π, then cos(x/2) = ?
A) 1/√5 B) -1/√5 C) 2/√5 D) -2/√5
125) If cos x =-4/5 and π< x<3π/2, then cos(x/2) = ?
A) 1/√10 B) -1/√10 C) 3/√10 D) -3/√10
126) If tan x =3/4 and π < x<3π/3, then tan(x/2) = ?
A) 3 B) 1/3 C) -3 D) -1/3
127) If cos x =-1/3 and x lies in quadrant III, then tan(x/2) = ?
A) √2 B) -√2 C) √3 D) -√3
128) If sin x =-1/2 and x lies in quadrant IV then sin(x/2) = ?
A) √{2 +√3}/2 B) {√3+ √2}/2 C) √(2- √3)/2 D) none
129) (1+ cosx)/((1- cosx)=?
A) tan²(x/2) B) cot²(x/2) C) sec²(x/2) D) cosec²(x/2)
130) √{(1+ sinx)/((1- sinx)} =?
A) tan(x/2) B) cot(x/2) C) tan(π/4+ x/2) D) cot(π/4 + x/2)
131) sinx/((1+ cos x) =?
A) tan(x/2) B) cot(x/2) C) tan(π/4+ x/2) D) n
132) cot(x/2) - tan(x/2) =?
A) 2tanx B) 2cot x C) 2 sin x D) 2cos x
133) sin 18°=?
A) (√5-1)/4 B) (√5+1)/4 C) (√3+ 1)/2 D) (√3 -1)/2
134) cos 18°=?
A) √(10- 2√5)/4 B) √(10+2√5)/4 C) (√5+ 1)/4 D) none
135) cos 36°=?
A) (√5-1)/4 B) (√5+1)/4 C) (√3+ 1)/2 D)
(√3- 1)/2
136) sin 36°=?
A) (√5 -1)/4 B) √(10+2√5)/4 C) √(10- 2√5)/4 D) none
137) sin 54°=?
A) (√5+1)/4 B) (√5-1)/4 C) √(10+2√5)/4 D) √(10-2√5)/4
138) cos 72°=?
A) (√5+1)/4 B) (√5-1)/4 C) (2+√5)/3 D) (2 - √5)/3
139) cos 54°=?
A) (√5+1)/4 B) (√5-1)/4 C) √(10+2√5)/4 D) √(10-2√5)/4
140) sin 72°=?
A) (√5+1)/4 B) (√5-1)/4 C) √(10+2√5)/4 D) √(10-2√5)/4
141) 2sin 45/2 cos 45/2 =?
A) 1 B) 1/2 C) 1/√2 D) √2
142) (2 cos² 15 - 1) =?
A) 3/2 B) √3/2 C) 2√3 D) √3/√2
143) 3sin 40- 4 sin² 40 =?
A) 3√3 B) 3/2 C) none D) √3/2
144) 8cos³20- 6 cos 20 =?
A) 5/2 B) 5/3 C) 1 D) √3/2
145) If tan x= a/b, then a sin2x+ b cos2x = ?
A) a B) b C) a+ b D) a-- b
146) cotx - 2 cot 2x =?
A) tanx B) cosx C) sinx D) cos2x
147) cos 2x+ 2 sin²x =?
A) 2 B) 1/2 C) 1 D) 3/2
148) sin2x/(1- cos 2x) =?
A) tanx B) cot x C) sec x D) cosec x
149) sin2x/(1+ cos 2x) =?
A) tanx B) cot x C) sec x D) cosec x
150) tan 2x/(1+ sec 2x) =?
A) tanx B) cot x C) sin x D) cos x
151) (1- cos 2x+ sinx)/(sin2x+ cosx) =?
A) tanx B) cot x C) sec x D) cosec x
152) cosx/(1- sinx) =?
A) tan(x/2) B) tan(π/4+ x/2) C) tan(π/4- x/2) D) none
153)
PERMUTATION AND COMBINATIONS
EXERCISE -1
A) 32 B) 48 C) 56 D) 64
2) If ⁿ⁻¹P₃ : ⁿP₄ = 1:9, then n=?
A) 12 B) 11 C) 9 D) 10
3) ⁿPₙ/ⁿPₙ₋₂ =?
A) 1/2 B) 2 C) 1/(n-2) D) n(n-1)
4) ¹⁵Pₙ =2730, then n=?
A) 3 B) 4 C) 5 D) 6
5) ⁷P₃ =?
A) 105 B) 140 C) 210 D) 175
6) ⁿP₅ = 20. ⁿP₃, then n=?
A) 8 B) 9 C) 10 D) 11
7) ¹⁵Pₙ₋₁ : ¹⁶Pₙ₋₂= 3:4, then n= ?
A) 8 B) 10 C) 12 D) 14
8) ⁿC₁₀ =ⁿC₁₄ , then n=?
A) 4 B) 24 C) 14 D) 10
9) If ⁿC₃ = 220, then n=?
A) 9 B) 10 C) 11 D) 12
10) ⁿCₐ + ⁿCₐ₊₁ = ⁿ⁺¹Cₓ , then x=?
A) a-1 B) a C) a+1 D) n
11) ³⁶C₃₄ = ?
A) 1224 B) 612 C) 630 D) none
12) ⁿCₐ/ⁿCₐ₋₁ =?
A) (n-r)/r B) (n-r -1)/r C) (n-r +1)/r D) none
13) ⁿC₁₈= ⁿC₁₂ , then ¹²Cₙ=?
A) 248 B) 496 C) 992 D) none
14) ⁶⁰C₆₀ =?
A) 60! B) 1 C) 1/60 D) none
15) In how many ways can 5 persons occupy 3 seats ?
A) 15 B) 20 C) 30 D) 60
16) In how many ways can 5 children stand in a queue ?
A) 5 B) 25 C) 60 D) 120
17) In how many ways can 4 different books be arranged in a self ?
A) 4 B) 8 C) 24 D) 16
18) 10 students are participating in a race. In how many different ways can the first prize be own ?
A) 30 B) 60 B) 120 D) 720
19) three different rings are to be worn in four fingers. In how many ways can this be done ?
A) 12 B) 24 C) 64 D) 81
20) There are 6 periods on each working day of a school. In how many ways can one arrange 5 subjects such that each subject is allowed at least one period.
A) 360 B) 720 C) 3600 D) 1800
21) How many words with or without meaning can be formed by using all the letters of the word, DELHI, using each letter exactly once ?
A) 20 B) 60 C) 120 D) 5
22) It is required to seat 5 man and 4 Women in a row so that the women occupied the even places. How many such arrangements are possible ?
A) 24 B)120 C) 720 D) 2880
23) How many three-digit numbers are there ?
A) 648 B) 729 C) 900 D) 1000
24) How many 3-digit numbers are there with no digit repeated ?
A) 648 B) 720 C) 729 D) none
25) How many four-digit numbers can be formed with no digital repeated by using the digit 3,4,5,6,7,8 and 0?
A) 280 B) 560 C) 720 D) 840
26) How many 3-digits even numbers can be formed with no digit repeated by using the digit 0, 1, 2, 3, 4 and 5 ?
A) 50 B) 52 C) 54 D) 56
27) The number of positive integers greater than 6000 less than 7000 which are divisible by 5 with no digit repeated is
A) 28 B) 56 C) 84 D) 112
28) How many 10 digit numbers can be formed by using the digit 1 and 2 ?
A) ¹⁰P₂ B) ¹⁰C₂ C) 2¹⁰ D) 10!
29) How many words beginning with T and ending with E can be made with no letter repeated out of the letters of the word TRIANGLE?
A) ⁸P₆ B) 720 C) 722 D) 1440
30) How many words can be formed from the letters of the word DAUGHTER so that the vowels always come together ?
A) 720 B) 2160 C) 4320 D) none
31) How many words can be found from the letters of the word LAUGHTER so that the vowels are never together ?
A) 3600 B) 4320 C) 36000 D) 40320
32) In how many ways can the letters of the word MACHINE be arranged so that the vowels may occupy only odd positions ?
A) 288 B) 576 C) 5040 D) none
33) in how many ways can the letter of the word PENCIL be arranged so that N is always next to E?
A) 120 B) 240 C) 720 D) 1440
34) In how many ways can the letters of the word APPLE be arranged?
A) 6 B) 60 C) 90 D) 120
35) How many words can be formed by using all the letter of the word ALLAHABAD?
A) 9! B) 1890 C) 3780 D) 7560
36) How many words can be formed using the letter A thrice, the letter B twice and the letter C once ?
A) 6 B) 60 C) 90 D) 120
37) In how many ways can the 10 books be arranged in a self so that a particular pair of books shall be always together ?
A) 8! B) 9! C) 2 . 8! D) 2 . 9!
38) In how many ways can 10 books be arranged in a shelf so that a particular pair of books shall be never together ?
A) 8! B) 9! C) 2. 9! D) 8.9.
39) How many 4 digit numbers are there where a digit may be repeated any number of times in each number ?
A) 5040 B) 9000 C) 10000 D) 4500
40) How many ways can 6 boys be arranged in a row?
A) 5! B) 6! C) 6 D) 2.6!
41) In how many ways can 6 girls be seated in a circle ?
A) 6 B) 6! C) 5! D) 2.5!
42) How many diagonals are there in a polygon of n sides?
A) n(n-1)/2 B) n(n-2)/2 C) n(n-3)/2 D) n(n+1)/2
43) How many diagonals are there in an octagon ?
A) 28 B) 24 C) 20 D) 36
44) A polygon as 54 diagonals. Number of sides in this polygon is.
A) 9 B) 12 C) 15 D) 16
45) There are 10 points in a plane, out of which 4 points are collinear. The number of line segments obtained from the pairs of these points is
A) 39 B) 40 C) 41 D) 45
46) There are 10 points in a plane, out of which 4 points are collinear. The number of triangles formed with the vertices as these points is
A) 20 B) 120 C) 116 D) none
47) Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A) 330 B) 1050 C) 6300 D) 25200
48) In how many ways can a committee of 5 member be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
A) 25 B) 50 C) 100 D) 200
49) Out of 5 men and 2 women, a committee of 3 is to be formed. In how many ways it be formed if at least one woman is included in each committee ?
A) 21 B) 25 C) 32 D) 50
50) A committee of five is to be formed out of six gents and four ladies. In how many ways can this be done when each committee may have atmost 2 ladies ?
A) 120 B) 160 C) 180 D) 186
51) How many different teams of 7 players can be chosen out of 10 players?
A) 720 B) 70 C) 120 D) none
52) 12 persons meet in a room and each shakes hands with all the others. How many handshakes are there ?
A) 144 B) 132 C) 72 D) 66
53) In how many ways can we select 9 balls out of 6 red balls, 5 white balls and five blue balls if 3 balls if each colour are selected
A) 40 B) 200 C) 2000 D) 400
54) How many ways can a cricket team be chosen out of a batch of 15 players, if a particular player is always chosen?
A) 1364 B) 364 C) 1001 D) none
55) In how many ways can a cricket team be chosen out of a batch of 15 players, if a particular player is never chosen ?
A) 364 B) 1001 C) 1364 D) none
56) For the post of 5 teachers, there are 23 applicants. 2 posts are reserved for SC candidates and there are 7 SC candidates among the applicants. In how many ways can the selection be made?
A) 5880 B) 11760 C) 3920 D) none
57) In how many ways can 5 white balls and 3 black balls be arranged in a row so that no two black balls are together
A) 192 B) 40 C) 20 D) 120
58) In an examination a candidate has to pass in each of the five subjects. In how many ways he fail ?
A) 5 B) 10 C) 21 D) 31
59) An examination paper content 12 questions consisting of two parts, A and B. Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions, selecting at least three from each part. In how many ways can the candidate select the questions ?
A)210 B) 175 C) 420 D) none
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