Mathematics :
10. If A and B are coefficient of xn in the expansion
(1+x)2n and (1+x)2n-1 respectively, then :
a) A = 2B
b) A=B
c) 2A = B
d) none of these
1. If arg(z) = 𝜃 then arg(𝑧) is equal to :
a) θ − π
b) π − θ
c) θ
d) – θ
𝑛
2. If 𝑖 2 = -1,then the value of ∑200
𝑛=1 𝑖 is :
a) 0
3.
b) 50
c) -50
d) 100
If sin 𝛼 𝑎𝑛𝑑 cos 𝛼 are roots of the equation
px2 + qx + r = 0, then :
a) p2 + q2 -2pr = 0
b) p2 – q2 + 2pr = 0
c) p2 – q2 - 2pr = 0
d) p2 + q2 - 2pr = 0
4. The equation whose roots are
2
a) 7x -6x + 1 = 0
c) x2 – 6x + 7 = 0
1
1
and
is:
3+√2
3−√2
2
b) 6x – 7x + 1=0
d) x2 – 7x +6 = 0
𝑥−𝑚
5. If the roots of the quadratic equation 𝑚𝑥+1 =
𝑥+𝑛
𝑛𝑥+1
b) n = 0
d) m + n = 1
6. HM between the roots of the equation x2- 10x +
11 = 0 is :
c)
6𝑖 −3𝑖
12. If | 4
3𝑖
20
3
a)(1,3)
c) (3,1)
11
5
21
20
1 4
20
13. The roots of the equation |1 −2
5 |=0
1 2𝑥 5𝑥 2
are:
a) -1,-2
b) -1,2
c) 1,-2
d) 1,2
14. For what value of 𝜆, the system of equations
x + y +z =6, x + 2y +3z = 10, x +2y + 𝜆z =10 is
consistent?
a) 1
b) 2
c) -1
d) 3
5
b) 21
1
d) 5
7. If arithmetic mean of a and b is ( an+1 + bn+1)/(an +
bn )then n is equal to :
a) 0
b) 2
c) 1
d) -1
1
15. [−1] [21 −1] is equal to :
2
2
2
1 −1
a) [−1]
b) [−2 −1 1 ]
−2
4
2 −2
c) [−1]
d) not defined
16. If A = [
8. The value of 2
a) 3⁄2
c) 2
1
1
1
1⁄
4 .4 ⁄8 .8 ⁄16 .16 ⁄32
..., :
b) 5⁄2
d) 1
9. In a geometric progression, if the (p+q)th term is
m and (p-q)th is n, then its pth term is :
a) mn
c)
1
−1| = x + 𝑖y , then (x,y) is:
𝑖
b) (0,3)
d) (0,0)
are reciprocal to each other, then :
a) m2 + n2 = 1
c) m = n
a)
11. Coefficient of x19 in the polynomial (x-1) (x-2)
.......... (x-20) is equal to :
a) 210
b) -210
c) 20!
d) none of these
1
(m+n)
2
b) √𝑚𝑛
d) 0
:
a) 2
c) 4
1 2
] and A2 –kA- Ι2 = 0,then value of k is
2 3
b) -4
d) 1
x
1 1
1 x
0
17. If [1 −2 −2] [y] = [3] , then [y] is equal to :
z
1 3
1 z
4
0
1
a) [1]
b) [ 2 ]
1
−3
5
c) [−2]
1
1
d) [−2]
3
18. A polygon has 44 diagonals, the number of its
sides is :
a) 7
b) 11
c) 8
d) none of these
3
2
a) 1
b)
c) 0
d) 2
28. The value of tan(-9450 )is :
a) -1
b) -2
c) -3
d) -4
𝑐𝑜𝑠170 +sin 170
𝑐𝑜𝑠170 −sin 170
0
19. If nCr-1 = 36, nCr = 84 and nCr+1 = 126, then :
a) n = 6, r = 2
b) n = 9, r = 6
c) n = 9, r = 3
d) n = 6, r = 3
29.
20. A coin is tossed and a dice is rolled. The
probability that the coin shows the head and the
die shows 6 :
30. sin 1630 cos 3470 + sin 730 sin 1670 is equal
to :
1
1
a) 12
b) 24
1
1
c) 2
d) 6
13
a) 20
7
c) 20
12
b) 20
2
d) 5
22. The probability that the three cards drawn from
a pack of 52 cards are all red :
a)
c)
1
12
b) 17
17
2
19
d)
3
19
23. Cos2 𝛼 + Cos2 (𝛼 + 1200 ) + Cos2 (𝛼 - 1200 ) is
equal to :
a) 3/2
b) 1
c) 1/2
d) 0
24. The value of cos 150 - sin 150 is :
1
b) 2
√
1
d) - 2
√
a) 0
c)
1
2
25. Sin6A + cos6A + 3sin2Acos2A is equal to :
a) 3
b) 2
c) 1
d) 0
26. If tan x
a) a
c) a + b
𝑏
=𝑎,
b) tan 540
d) tan 620
a) tan 73
c) tan 560
a) ½
c) 1
b) 0
d) none of these
tan 3𝜃−1
=
tan 3𝜃+1
𝑛𝜋
𝜋
a) 3 − 12
𝑛𝜋
7𝜋
c) 3 + 36
31. If
21. If A speaks truth in 75% cases and B in 80%
cases, then the probability that they contradict
each other in during the same statement, is :
is equal to :
√3, then the general value of 𝜃 is :
b) n𝜋 +
d) n𝜋 +
7𝜋
12
𝜋
12
32. If angles of triangle are in the ratio of 2:3:7, then
the sides are in the ratio of :
a) 2:(√3 + 1) : √2
b) √2 : 2:(√3 + 1)
c) 2: √2 :(√3 + 1)
d) √2 :(√3 + 1):2
33. In a ∆𝐴𝐵𝐶 , if a =2x, b = 2y, and ∠𝑐 = 1200 , then
the area of the triangle is :
a) xy
c) 3xy
b) √3xy
d) 2xy
34. If tan -1 a + tan -1 b = sin-1 1 – tan -1 c, then :
a) a+b+c = abc
c)
1
𝑎
+
1
𝑏
+
1
𝑐
−
b) ab + bc + ca = abc
1
𝑎𝑏𝑐
= 0 d) ab + bc + ca =
a+b+c
35. The locus of a point whose difference of distance
from points (3,0) and (-3,0) is 4, is :
a)
c)
𝑥2
−
4
2
𝑥
−
2
𝑦2
5
𝑦2
3
=1
b)
=1
d)
𝑥2
−
5
2
𝑥
−
3
𝑦2
4
𝑦2
2
=1
=1
then the value of acos2x + bsin2x is :
b) a - b
d) b
27. The value of cos 520 + cos 680 + cos 1720 is :
36. The perpendicular distance of the straight line
12x + 5y = 7 from the origin (0,0) is given by :
1
12
a) 13
5
b) 13
c) 13
d)
7
13
37. The lines y = 2x, and x = -2y are :
a) Perpendicular
b) parallel
c) equally inclined to axes
d) coincident
38. 2x2 + 7xy + 3y2 + 8x + 14y + 𝜆 = 0 will represent a
pair of straight lines when 𝜆 is equal to :
a) 8
b) 6
c) 4
d) 2
39. A straight line makes an angle of 1350 with the x
– axis and cuts y – axis at a distance -5 from the
origin. The equation of the line is :
a) x+2y+3=0
b) x+y+3=0
c) 2x+y+5=0
d) x+y+5=0
40. If we reduce 3x+3y+7=0 to the form xcos𝛼 +
ysin𝛼 = p, then the value of p is :
3√7
a)
2
7
c)3 2
√
41. If the equation
b)
d)
7
2√3
7
3
𝑘(𝑥+1)2
3
+
a) a,b,c are in HP
c) a,b,c are in AP
b) a,b,c are in GP
d) none of these
46. If the line y = mx + c touches the ellipse
𝑦2
𝑎2
𝑥2
𝑏2
+
= 1, then c is equal to:
a) ±√𝑏 2 𝑚2 − 𝑎2
b) ±√𝑏 2 𝑚2 + 𝑎2
c) ±√𝑎2 𝑚2 − 𝑏 2
d) ±√𝑎2 𝑚2 + 𝑏 2
47. The equation of the normal at the point (2,3) on
the ellipse 9x2 + 16y2 = 180, is :
a) 3x + 2y + 7 = 0
b) 3y = 8x – 10
c) 3y – 8x + 7 = 0
d) 8y + 3x + 7 = 0
48. The foci of the hyperbola 9x2 – 16y2 =144 are :
a) (0, ±5)
b) (±5, 0)
c) (±4, 0)
d) (0, ±4)
49. The eccentricity o the hyperbola 5x2 - 4y2 +20x +
8y = 4 is :
3
a) √2
b) 2
c) 2
d) 3
1−𝑥
(𝑦−2)2
4
50. If f(x) = 1+𝑥, then f[f(cos 2𝜃)] is equal to :
= 1 represents
a circle, then k is equal to :
a) 12
b) 4/3
c) 1
d) 3/4
42. The gradient of the radical axis of the circles
x2+y2-3x-4y+5 = 0,
a) cot 2𝜃
c) sec 2𝜃
51. If f(x) =
b) cos 2𝜃
d) tan 2𝜃
𝑥
,then
𝑥−1
𝑓(𝑎)
the value of 𝑓(𝑎+1) is equal to :
1
a) f(a2)
b) f(𝑎)
c) f(-a)
d) f[𝑎−1]
−𝑎
3x2+3y2-7x+8y+11 = 0, is :
1
a) − 10
2
c) − 3
1
b) − 2
1
d) 3
43. The equation of the tangent to the circle x2+y2 =
4, which are parallel to x+2y+3=0, are :
a) x-2y= 2
b) x+2y= ± 2√3
c) x+2y= ± 2√5
d) x-2y= ± 2√5
44. The line y =mx + c touches the parabola x2 = 4ay
if :
a) c = a/m
b) c = am2
c) c = am
d) c = - am2
45. If ‘a’ and ‘c’ are the segment of a chord of a
parabola and ‘b’ the semi latusrectum, then :
52. Suppose that g(x) = 1 + √𝑥 and f(g(x)) = 3 + 2√𝑥
+ x, then f(x) is :
a) 1+ x
b) 1 + 2x2
c) 2 + x
d) 2 + x2
𝑥 + 𝜆, 𝑥 < 3
53. If f(x) = { 4,
𝑥 = 3 is continuous at x = 3,
3𝑥 − 5, 𝑥 > 3
then 𝜆 is equal to :
a) 3
b) 2
c) 1
d) 4
(1−cos 2𝑥) sin 5𝑥
𝑥 2 sin 3𝑥
𝑥→0
54. The value of lim
a) 10/3
c) 3/10
b) 5/6
d) 6/5
is :
55. The first derivative of the function [ cos-1
1+𝑥
)
2
1
a) −
2
(sin√
𝑥
+ x2 ] with respect to x at x = 1 is :
:
a) -1/3
c) 1/5
7
4
1
d) 2
b)
c) 0
64. The maximum value of f(x) = 4+𝑥+𝑥 2 on [ 1, -1] is
56. Let 3f(x) – 2 f(1/x) = x, then f ‘(2) is equal to :
a) 7/2
b) 2
c) 1/2
d) 2/7
𝑥 𝑒𝑥
65. Correct evaluation of ∫ (𝑥+1)2 𝑑𝑥 is :
𝑒𝑥
a) (𝑥+1)3 + 𝑐
c) −
57. The adjacent sides of a rectangle with given
perimeter as 100 cm and enclosing maximum
area are :
a) 20 cm and 30 cm b) 25 cm and 25 cm
c) 15 cm and 35 cm
d) 10 cm and 40 cm
b) -1/4
d) 1/6
𝑒𝑥
(𝑥+1)2
b)
+ 𝑐
d)
𝑒𝑥
+ 𝑐
𝑥+1
𝑒𝑥
- 𝑥+1 + 𝑐
𝑒 tan
−1 𝑥
66. Correct evaluation of ∫ (1+ 𝑥2 ) 𝑑𝑥 is :
−1
a)
c)
2𝑥𝑒 tan 𝑥
+
(1+ 𝑥 2 )2
1
+ 𝑝
1+ 𝑥 2
−1 𝑥
b) 𝑒 tan
𝑝
+ 𝑝
d) tan−1 𝑥 + 𝑝
( where 𝑝 is arbitrary constant )
5
4
3
58. The function x – 5x + 5x - 1 is :
a) neither maximum or minimum at x = 0
b) maximum at x = 0
c) maximum at x = 1 and minimum at x = 3
d) minimum at x = 0
67. ∫ √1 + sin 𝑥 𝑑𝑥 is equal to :
1
𝑥
𝑥
1
2
𝑥
2
𝑥
2
a) 2 (sin 2 + cos 2) + 𝑐
b) (sin − cos ) + 𝑐
c) 2√(1 + sin 𝑥) + 𝑐
59. The least value of the sum of any positive real
number and its reciprocal is :
a) 2
b) 3
c) 1
d) 4
d) − 2√(1 − sin 𝑥) + 𝑐
1
68. ∫
𝑑𝑥 is equal to :
𝑥− 𝑥 3
𝜋
60. If f(x) = cos x, 0 ≤ x ≤ 2 , then the real number ‘c’
c) log
of the mean value theorem is :
2
a) cos-1(𝜋 )
c)
π
6
2
b) sin-1 (𝜋)
π
d) 4
61. If the distance travelled by a point in time t is s=
180t – 16t2 , then the rate of change in velocity is
:
a) 48 unit
b) -32 unit
c) -16t unit
d) none of these
62. If sum of two numbers is 3, then maximum value
of the product of first and the square of second
is :
a) 4
b) 3
c) 2
d) 1
1
63. Maximum value of 𝑥 𝑥 is :
a) e
b)0
c) 1/e
d) e1/e
𝑥2
1
b) log 𝑥 (1 − 𝑥 2 ) + 𝑐
a) 2 log (1− 𝑥2 ) + 𝑐
(1−𝑥)
𝑥(1+ 𝑥)
1
69. If ∫ (1+𝑥)
√𝑥
1
2
+ 𝑐
d) log
1−𝑥 2
𝑥2
+ 𝑐
𝑑𝑥 = f(𝑥) + A, where A is any arbitrary
constant, then the function 𝑓(𝑥) is :
a) 2tan−1 √𝑥
b) 2tan−1 𝑥
c) log 𝑒 (1 + 𝑥)
d) 2cot −1 √𝑥
cos 2𝑥−1
70. ∫
𝑑𝑥 is equal to :
cos 2𝑥+1
a) 𝑥 − tan 𝑥 + 𝑐
c) 𝑥 + tan 𝑥 + 𝑐
b) − 𝑥 − cot 𝑥 + 𝑐
d)tan 𝑥 − 𝑥 + 𝑐
𝑑𝑥
71. ∫ sin 𝑥−cos 𝑥+ 2 is equal to :
√
1
𝑥
𝜋
𝑡𝑎𝑛 (2 + 8 ) + 𝑐
√2
1
𝑥
𝜋
b) − 2 𝑡𝑎𝑛 (2 + 8 ) + 𝑐
√
1
𝑥
𝜋
c) 2 𝑐𝑜𝑡 (2 + 8 ) + 𝑐
√
1
𝑥
𝜋
d) − 2 𝑐𝑜𝑡 (2 + 8 ) + 𝑐
√
a)
𝑥
𝑎 ⁄2
72. ∫ −𝑥 𝑥 𝑑𝑥 is equal to :
√𝑎 − 𝑎
1
1
a) log 𝑎 sin−1 (𝑎 𝑥 ) + 𝑐
b) log 𝑎 tan−1 (𝑎 𝑥 ) +
𝑐
c) 2√𝑎−𝑥 − 𝑎 𝑥 + 𝑐
log(𝑎 𝑥 − 1) + 𝑐
d)
73. An integrating factor for the differential equal
(1 + y2)𝑑𝑥 - (tan-1 y - x)𝑑𝑦 = 0, is :
a) tan−1 𝑥
c)
b) 𝑒
1
1+𝑦 2
tan−1 𝑦
1
𝑑𝑦
2𝑥𝑦 𝑑𝑥 = 𝑥 2 + 3𝑦 2 is :
𝑥2
𝑦3
+
=
2
2
2
2
𝑦2 + 𝑝
b) 𝑥 2 + 𝑦 3 = 𝑝𝑥 2
c) 𝑥 + 𝑦 = 𝑝𝑥 3
d) 𝑥 3 + 𝑦 2 = 𝑝𝑥 2
75. Te differential equation of all straight lines
passing through the point (1,-1) is :
𝑑𝑦
a) 𝑦 = (𝑥 − 1) 𝑑𝑥 − 1
𝑑𝑦
b) 𝑦 = (𝑥 − 1) 𝑑𝑥 +
𝑑𝑦
1
c) 𝑦 = (𝑥 + 1) 𝑑𝑥 − 1
(𝑥 +
𝑑𝑦
1) 𝑑𝑥
d) 𝑦 =
+ 1
𝑦
𝑑𝑦
𝑦
a) 𝑑𝑥 = (𝑥 ) log 𝑥
𝑑𝑦
𝑥
𝑑𝑦
𝑥
b) 𝑑𝑥 = (𝑦) log 𝑦
c) 𝑑𝑥 = (𝑥 ) log 𝑦
d) 𝑑𝑥 = (𝑦) log 𝑥
77. If the gradient of the tangent at any point (x,y) of
𝜋
a curve which passes through the point (1, 4 ) is
𝑦
{𝑥
−
𝑦
sin2 ( )},
𝑥
⃗⃗⃗ | = 1, |𝑐⃗⃗ | = 4 and 𝑎 + 𝑏⃗ + 𝑐⃗⃗ = 0,
80. If |𝑎
⃗⃗⃗ | = 3, |𝑏
then 𝑎. 𝑏⃗ + 𝑏⃗. 𝑐⃗⃗ + 𝑐⃗⃗ . 𝑎 is equal to :
b) -10
d) -13
81. Force 3𝑖̂ + 2𝑗̂ + 5𝑘̂ and 2𝑖̂ + 𝑗̂ - 3𝑘̂ are acting on
particle and displace it form point 2𝑖̂ - 𝑗̂ - 3𝑘̂ to
the point 4𝑖̂ - 3𝑗̂ + 7𝑘̂, then work done by the
forces is :
a) 18 unit
b) 24 unit
c) 30 unit
d) 36 unit
82. The angle between the vectors (2𝑖̂ + 6𝑗̂ + 3𝑘̂) and
(12𝑖̂ − 4𝑗̂ + 3𝑘̂) is :
a) cos-1(9)
1
b) cos-1(11)
9
d) cos-1(10)
c) cos-1(91)
76. The elimination of the arbitrary constant m from
the equation 𝑦 = 𝑒 𝑚𝑥 gives the differential
equation :
𝑑𝑦
y2= 2k(x+√𝑘) (where k is a positive parameter )
are respectively :
a) 1 and 2
b) 2 and 4
c) 1 and 4
d) 1 and 3
a) 10
c) 13
d) 𝑥(1+𝑦2 )
74. Solution of the differential equation
a)
79. The order and the degree of the differential
equation representing the family of curves
9
1
83. If the equation of a line through a point 𝑎 and
parallel to vector 𝑏⃗ is 𝑟 = 𝑎 + 𝑡𝑏⃗, where t is a
parameter , then perpendicular distance from
the point 𝑐 is :
a) |(𝑎 − 𝑏⃗) × 𝑐 | ÷ |𝑐|
b) |(𝑎 − 𝑏⃗) × 𝑐| ÷ |𝑎 + 𝑐|
c) |(𝑐 − 𝑏⃗) × 𝑎| ÷ |𝑎|
d) |(𝑐 − 𝑎) × 𝑏⃗| ÷ |𝑏⃗|
then the equation of curve is :
𝑥
a) 𝑦 = cot −1 (log 𝑒 𝑒 )
𝑒
𝑥
b) 𝑦 = cot −1 (log 𝑒 )
c) 𝑦 = 𝑥 cot −1 (log e 𝑒𝑥)
d) 𝑦 = cot −1(log 𝑒 𝑥)
78. Solution of (𝑥 + 𝑦 − 1)𝑑𝑥 + (2𝑥 + 2𝑦 −
3) 𝑑𝑦 = 0 is :
a) 2𝑦 + 2𝑥 + 𝑙𝑜𝑔(𝑥 + 𝑦 − 2) = 𝑐
b) 𝑦 + 2𝑥 + 𝑙𝑜𝑔(𝑥 + 𝑦 − 2) = 𝑐
c) 2𝑦 + 𝑥 + 𝑙𝑜𝑔(𝑥 + 𝑦 − 2) = 𝑐
d) 𝑦 + 𝑥 + 𝑙𝑜𝑔(𝑥 + 𝑦 − 2) = 𝑐
84. If 𝐴 = 𝑖̂ − 2 𝑗̂ − 3 𝑘̂, ⃗B = 2𝑖̂ + 𝑗̂ − 𝑘̂, 𝐶 = 𝑖̂ +3
⃗ )× 𝐶 is :
𝑗̂ − 2 𝑘̂ , then (𝐴 × 𝐵
a) 4(-𝑖̂+3 𝑗̂ + 4 𝑘̂)
b) 5(-𝑖̂+3 𝑗̂ + 4 𝑘̂)
c) 4(𝑖̂+3 𝑗̂ + 4 𝑘̂)
d) 5(−𝑖̂ − 3𝑗̂ − 4 𝑘̂)
85. The value of 𝜆, for which the four points (2𝑖̂+3
𝑗̂ − 𝑘̂ ), (𝑖̂+2 𝑗̂ + 3 𝑘̂), (3𝑖̂+4 𝑗̂ − 2 𝑘̂), (𝑖̂-𝜆 𝑗̂ + 6𝑘̂)
are coplanar, is :
a) -2
b) 8
c) 6
d)
0
86. If the planes ax + by + cz + d = 0 and 𝑎′ 𝑥 + 𝑏 ′ 𝑦 +
𝑐 ′ 𝑧 + 𝑑′ = 0 be mutually perpendicular, then :
a) 𝑎𝑎′ + 𝑏𝑏 ′ + 𝑐𝑐 ′ + 𝑑𝑑′ = 0
b) 𝑎𝑎′ + 𝑏𝑏 ′ + 𝑐𝑐 ′ = 0
𝑎
𝑏
𝑐
c) 𝑎′ = 𝑏′ = 𝑐 ′
d)
𝑎
𝑎′
+
𝑏
𝑏′
+
𝑐
𝑐′
=0
=
87. The co-ordinates of the point which divides the
join of the points (2,-1,3)and (4,3,1) in the ratio
3:4 internally are given by :
a) 2/7, 20/7, 10/7
b) 10/7, 15/7, 2/7
c) 20/7, 5/7, 15/7
d) 15/7, 20/7, 3/7
88. The equation of the plane through the
intersecting of the planes 𝑥 + 2𝑦 + 3𝑧 − 4 =
0, 4𝑥 + 3𝑦 + 2𝑧 + 1 = 0 and passing through
the origin will be :
a) 𝑥 + 𝑦 + 𝑧 = 0
b) 7𝑥 + 4𝑦 + 𝑧 = 0
c) 17𝑥 + 14𝑦 + 11𝑧 = 0
d) 17𝑥 + 14𝑦 + 𝑧 = 0
89. The acute angle between the planes 2𝑥 − 𝑦 +
𝑧 = 6 and 𝑥 + 𝑦 + 2𝑧 = 3 is :
a) 60o
b) 75o
c) 45o
d) 30o
90. If A(1,2,3), B(-1,-1,-1) the points , then the
distance AB is :
a) √29
b) √5
c) √21
d) none of these
91. The equation to the perpendicular from the
point(𝛼, 𝛽, 𝛾) to the plane 𝑎𝑥 + 𝑏𝑦 + 𝑐𝑧 + 𝑑 = 0
is :
𝑥−𝑎
𝑦−𝑏
𝑧−𝑐
= 𝑐𝛾
𝑏𝛽
𝑥−𝛼
𝑦−𝛽
𝑧−𝛾
= 𝑏 = 𝑐
𝑎
𝑥
𝑦
𝑧
𝑥
𝑦
𝑧
a) 𝑎𝛼 =
b) 𝑎 = 𝑏 = 𝑐
c)
d) 𝛼 = 𝛽 = 𝛾
92. Performing 3 iteration of bisection method of
smallest positive approximate root of equation
𝑥 3 − 5𝑥 + 1 = 0, is :
a) 0.25
b) 0.125
c)
0.3769
d) 0.1875
93. Let f(0) = 1, f(1) = 2.72, then the trapezoidal rule
1
gives approximate value of ∫0 𝑓(𝑥) 𝑑𝑥 is :
a) 8.72
c) 1.72
b) 1.86
d) 0.86
94. Shaded region is represented by :
a) (2𝑥 + 5𝑦 ≥ 80, 𝑥 + 𝑦 ≤ 20, 𝑥 ≥ 0, 𝑦 ≤ 0)
b) (2𝑥 + 5𝑦 ≥ 80, 𝑥 + 𝑦 ≥ 20, 𝑥 ≥ 0, 𝑦 ≥ 0)
c) (2𝑥 + 5𝑦 ≤ 80, 𝑥 + 𝑦 ≤ 20, 𝑥 ≥ 0, 𝑦 ≥ 0)
d) (2𝑥 + 5𝑦 ≤ 80, 𝑥 + 𝑦 ≤ 20, 𝑥 ≤ 0, 𝑦 ≤ 0)
95. For the following LLP. Minimize 𝑧 = 4𝑥 + 6𝑦
subject to the constraints 2𝑥 + 3𝑦 ≥ 6, 𝑥 + 𝑦 ≤
8, 𝑦 ≥ 1, 𝑥 ≥ 0 the solution is:
3
a) (0,2) and (1,1)
b) (0,2) and (2 , 1)
c) (0,2) and (1,6)
d) (0,2) and (1,5)
96. If the line of regression of Y on X and X on Y
make angle is 30o and 60o respectively with the
positive direction of x-axis, then the correlation
between X and Y is :
a)1/√2
b) 1/2
c) 1/√3
d) 1/3
97. If 𝜃 is the angle between two regression lines
with correlation coefficient 𝛾, then :
a) sin 𝜃 ≥ 1 − 𝛾 2
b) sin 𝜃 ≤ 1 − 𝛾 2
c) sin 𝜃 ≤ 𝛾 2 + 1
d) sin 𝜃 ≤ 𝛾 2 − 1
98. (0.5) −
(0.5)2
2
+
(0.5)3
3
−
(0.5)4
4
+ ............is equal
to :
3
1
2
1
log 𝑒 2
a) log 𝑒 2
b) log
c) log 𝑒 𝑛!
d)
99. The coefficient of 𝑥 𝑛 in the expansion of
is :
a)
c)
4𝑛−1 + (−2)𝑛
𝑛!
4𝑛−1 + (−2)𝑛−1
𝑛!
b)
d)
4𝑛−1 + (2)𝑛
𝑛!
4𝑛 + (−2)𝑛
𝑛!
𝑒 7𝑥 +𝑒 𝑥
𝑒 3𝑥
100. The area formed by triangular shaped region
bounded the curves 𝑦 = sin 𝑥 , 𝑦 =
cos 𝑥 , 𝑎𝑛𝑑 𝑥 = 0, is :
a) (1 + √2)𝑠𝑞 unit
b) √2 𝑠𝑞 unit
c) (√2 − 1)𝑠𝑞 unit
d) 1 𝑠𝑞 unit