NDA 2027 Sample Paper (Paper 1 - Mathematics)

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S A M P L E Q U E S T I O N P A P E R

NDA 2027 (Paper 1 - Mathematics)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

120 300 150 Min +2.5 / −0.83

GENERAL INSTRUCTIONS

1. This paper contains 120 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 2.5 marks; 0.83 mark (one-third of the marks) is deducted for each wrong answer.

4. Total time allowed is 150 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

NDA 2027 (Paper 1 - Mathematics)
SAMPLE QUESTION PAPER

Questions 120 Max Marks 300 Time 150 Min Marking +2.5 / −0.83

Attempt all questions. Choose the one correct option for each.

MATHEMATICS

1. What angle does the line segment joining (5, 2) and (6, 2. What are the degree and order respectively of the
- 15) subtend at (0, 0)? differential equation y=x((d y)/(d x))2+((d x)/(d y))2

(A) (π/6) (A) 1,2

(B) (π/4) (B) 2, 1

(C) (π/2) (C) 1, 4

(D) (3π/4) (D) 4, 1

3. Read the following information and answer the three 4. If A= [arraycc 0 & 1 \\ 1 & 0 array] , then the value of A
items that follow : Let f(x)= x²+2x-5 and g(x) = 5x+30 4 is

Consider the following statements : (1). f [g(x)] is a
(A) [arraycc 1 & 0 \\ 0 & 1 array]
polynomial of degree 3. (2). g[g(x)] is a polynomial of
(B) [arraycc 1 & 1 \\ 0 & 0 array]
degree2. Which of the above statements is/are correct ?
(C) [arraycc 0 & 0 \\ 1 & 1 array]
(A) 1 Only
(D) [arraycc 0 & 1 \\ 1 & 0 array]
(B) 2 only

(C) Both 1 and 2

(D) Neither 1 nor 2

5. If the range of a set of observations on a variable X is
known to be 25 and if Y = 40 + 3X, then what is the range
of the set of corresponding observations on Y?

(A) 25

(B) 40

(C) 75

(D) 115

6. Let f(x) be an indefinite integral of sin2x. Consider the following statements : Statement 1: The function f(x)
satisfies f(x+π) =f(x) for all real x. Statement 2: sin2(x+π) = sin2x for all real x Which one of the following is correct in
respect of the above statements ?

(A) Both the statements are true and Statement 2 is the correct explanation of Statement 1

(B) Both the statements are true but Statement 2 is not the correct explanation of Statement 1

(C) Statement 1 is true but Statement 2 is false

(D) Statement 1 is false but Statement 2 is true

7. What is the angle between the lines x + y = 1and x - y 8. Let f(x) = x + 1/x-, where x ∈ (0, 1). Then which one of
= 1? the following is correct?

(A) π / 6 (A) f(x) fluctuates in the interval

(B) π / 4 (B) f(x) increases in the interval

(C) π / 3 (C) f(x) decreases in the interval

(D) π / 2 (D) None of the above

9. Which one of the following is the second degree 10. Consider the following expressions : (1). x+x2-(1)/(x)
polynomial function f(x) where f(0)=5,f(-1)=10 and f(1) = (2). √a x2+b x+x-c+(d)/(x)-ex2 (3). 3 x2-5 x+a b (4).
6? (1)/(x)-(2)/(x+5) (5). (1)/(x)-(2)/(x+5) Which of the above
are rational expressions ?
(A) 5x²-2x+5

(B) 3x²-2x-5 (A) 1.4 and 5 only

(C) 3x²-2x+5 (B) 1, 3, 4 and 5 only

(D) 3x²-10x+5 (C) 2, 4 and 5 only

(D) 1 and 2 only

11. A flower-bed in the form of a sector has been fenced 12. If a vertex of a triangle is (1,1) and the midpoints of
by a wire of 40 m length. If the flower-bod has the two sides of the triangle through Midpoints of two sides
greatest possible area, then what is the radius of the of the triangle through this vertex are (-1,2) and (3,2)
sector? then the centroid of the triangle is

(A) 25m (A) (-(1)/(3), (7)/(3))

(B) 20 m (B) (-1, (7)/(3))

(C) 10 m (C) ((1)/(3), (7)/(3))

(D) 5m (D) (1, (7)/(3))

13. If 5 of a Company's 10 delivery trucks do not meet 14. Consider the following functions: 1. f (x) = ex, where
emission standards and 3 Of them are chosen for x > 0 2. g(x) = |x - 3| Which of the above functions is/are
inspection, then what is the probability that none of the continuous?
trucks chosen will meet emission standards ?
(A) 1 only
(A) (1/8) (B) 2 only
(B) (3/8) (C) Both 1 and 2
(C) 1/12 (D) Neither 1 nor 2
(D) 1/4

15. The centroid of the triangle with vertices (2, 3), (-2, - 16. If sin θ = 3 sin(θ+2α), then the value of (tan θ +α) +
5) and (3, 5) is at 2 tan α is equal to

(A) (1, 1) (A) - 1

(B) (2, - 1) (B) 0

(C) (1, - 1) (C) 1

(D) (1, 2) (D) 2

17. In which one of the following intervals is the function 18. If the centroid of a triangle formed by (7, x), (y, -6)
f(x) = x² + 5x + 6 decreasing? and (9, 10) is (6, 3), then the values of x and y are
respectively
(A) (-∞, 2)

(B) [3,∞) (A) 5,2

(C) (-∞,∞) (B) 2,5

(D) (2, 3) (C) 1,0

(D) 0,0

19. Let A and B are two mutually exclusive events with 20. What is the order of [arraylll x & y & z array][arraylll
P(A)= 1/3 and P(B)= 1/4 What is the value of P ( ˉA ∩ ˉB ) a & h & g \\ h & b & f \\ g & f & c array][arrayl x \\ y \\ z
? array]

(A) 1/6 (A) 3 x 1

(B) ¼ (B) 1 x 1

(C) 1/3 (C) 1 x 3

(D) 5/12 (D) 3 x 3

21. The average age of a combined group of men and 22. If r=x i+y j+z k ,then what is r ·(i+j+k) equal to ?
women is 25 years. If the average age of the group of
(A) x
men is 26 year and that of the group of women is 21
(B) x+y
years, then the percentage of men and women in the
group is respectively (C) -(x+y+z)

(D) (x+y+z)
(A) 20.80

(B) 40.60

(C) 60,40

(D) 80,20

23. What is the coefficient of the middle term in the 24. What is the variance of the first 11 natural numbers?
binomial expansion of (2 + 3x)4?
(A) 10
(A) 6 (B) 11
(B) 12 (C) 12
(C) 108 (D) 13
(D) 216

25. The median of the observations 22, 24, 33, 37, x+ 1, 26. If ,then the expression A³-2A² is
x+3, 46, 47, 57, 58 in ascending order is 42. What are the
(A) a null matrix
values of 5th and 6th observations respectively ?
(B) an identity matrix
(A) 42,45
(C) equal to A
(B) 41, 43
(D) equal to -A
(C) 43, 46

(D) 40, 40

27. The equation of the locus of a point which is 28. Read the following information and answer the two
equidistant from the axes is items that follow : Let f(x) = x² , g(x) = tan x and h(x)= In
x. What is [fo(fof)](2) equal to?
(A) y = 2x

(B) x = 2y (A) 2

(C) y = ±x (B) 8

(D) 2y + x = 0 (C) 16

(D) 256

29. An equilateral triangle has one vertex at (-1,-1) and 30. If n! has 17 zeros ,then what is the value of n?
another vertex at (-√3,√3). The third vertex may lie on
(A) 95
(A) (-√2,√2) (B) 85
(B) (√2,-√2) (C) 80
(C) (1,1) (D) No such value of n exists
(D) (1,-1)

31. If the regression coefficient of Y on X is – 6, and the 32. Read the following information and answer the two
correlation coefficient between X and Y is -(1/2) . then items that follow : Consider the function f(x)= 3x4 -20x3-
the regression coefficient of X on Y would be 12x²+288x+ I In which one of the following intervals is
the function decreasing ?
(A) 1/24

(B) -(1/24) (A) (-2,3)

(C) -(1/6) (B) (3,4)

(D) 1/6 (C) (4,6)

(D) (6,9)

33. If sec (θ-α), sec θ and sec (θ+α) are in AP. Where cosα 34. If x 7 x>7 Where x>0,then which one of the following
≠ 1,then what is the value of sin²θ+cosα? is correct?

(A) 0 (A) x∈(0,∞)

(B) 1 (B) x ((1)/(7), 7)

(C) -1 (C) x(0, (1)/(7)) (7, ∞)

(D) ½ (D) x ((1)/(7), ∞)

35. Let AUB= {x|(x-a)(x-b) > 0,where a < b} What are A 36. How many terms are there in the expansion of (1 +
and B equal to? 2x + x²)5+ (1+ 4y + 4y²)5 ?

(A) A={x|x > a} and B= {x|x > b} (A) 12

(B) A={x|x a} and B= {x|x > b} (B) 20

(C) A={x|x < a} and B ={x|x< b} (C) 21

(D) A={x|x > a} and B= {x|x b} (D) 22

37. If α andβ(≠0) are the roots of the quadratic equation 38. A unit vector perpendicular to each of the vectors 2 i-
x2+a x-β=0 , then the quadratic expression -x2+a x+β j+k and 3 i-4 j-k is
where x∈R has
(A) 1√(3) i+1√(3) j-1√(3) k
(A) Least value -(1/4) (B) 1√(2) i+(1)/(2) j+(1)/(2) k
(B) Least value -(9/4) (C) 1√(3) i-1√(3) j-1√(3) k
(C) Greatest value (1/4) (D) 1√(3) i+1√(3) j+1√(3) k
(D) Greatest value (9/4)

39. Which one of the following is correct in respect of the 40. The correlation coefficient computed from a set of 30
cube roots of unity ? observations is 0.8. Then the percentage of variation not
explained by linear regression is
(A) They are collinear

(B) They lie on a circle of radius √3 (A) 80%

(C) They form an equilateral triangle (B) 20%

(D) None of the above (C) 64%

(D) 36%

41. If V is the variance and M is the mean of first 15 42. The mean weight of 150 students in a certain class is
natural numbers, then what is V + M² equal to ? 60 kg. The mean weight of boys in the class is 70 kg and
that of girls is 55 kg. What is the number of boys in the
(A) (124/3)
class?
(B) (148/3)
(A) 50
(C) 248/3
(B) 55
(D) 124/9
(C) 60

(D) 100

43. A geometric progression (GP) consists of 200 terms. 44. The variance of 25 observations is 4. If 2 is added to
If the sum of odd terms of the GP is m, and the sum of each observation, then the new variance of the resulting
even terms of the GP is n, then what is its common ratio ? observations is

(A) m/n (A) 2

(B) n/m (B) 4

(C) m+ (n/m) (C) 6

(D) n+(m/n) (D) 8

45. A spacecraft located at i+2 j+3 k is subjected to a
force by λκ̂ by firing a rocket. The spacecraft is subjected
to a moment Of magnitude 46.

(A) λ
(A) 0
(B) √3 λ
(B) 1 / 2
(C) √5 λ
(C) 1
(D) none of the above
(D) 2

47. The fifth term of an AP of n terms, whose sum is n2 - 48. If (0.2)x=2 and log 2 = 0.3010, then what is the
10
2n, is value of x to the nearest tenth?

(A) 5 (A) -10.0

(B) 7 (B) -0.5

(C) 8 (C) -0.4

(D) 15 (D) -0.2

49. Let matrix B be the adjoint of a square matrix A, l be 50. If a fair die is rolled 4 times, then what is the
the identity matrix of same order as A. If k(≠0) is the probability that there are exactly 2 sixes ?
determinant of the matrix A, then what is AB equal to ?
(A) (5/216)
(A) l (B) (19/144)
(B) kl (C) 125/216
(C) k²l (D) 175/216
(D) (1/k)l

51. Let s={2,4,6,..........,20}.What is the maximum 52. If a=-+k b=-2+3k and b=-m+jk are three coplanar
number of subsets does s have? vectors and |c|=√(6) , then which one of the following is
correct?
(A) 10

(B) 20 (A) m = 2 and n ± 1

(C) 512 (B) m = ± 2 and n = - 1

(D) 1024 (C) m = 2 and n = -1

(D) m = ± 2 and n = 1

53. The axis of the parabola y2 + 2x = 0 is 54. If A = {1, 2}, B = {4 3} and C = {3, 4}, then what is
the cardinality of (A x B) ∩ (A x C) ?
(A) x = 0

(B) y = 0 (A) 8

(C) x = 2 (B) 6

(D) y = 2 (C) 4

(D) 1

55. If a ≠ b ≠ c, then one value of x which satisfies the 56. A binary number is represented by (cdccddcccddd)
2
equation |arrayccc 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & where c>d. What is its decimal equivalent?
x+c & 0 array|=0 is given by
(A) 1848
(A) a (B) 2048
(B) b (C) 2842
(C) c (D) 2872
(D) 0

57. Read the following information and answer the three 58. The sum of the first five terms and the sum of the
items that follow: A curve y=memx where m>0 intersects first ten terms of an AP are same. Which one of the
y-axis at a point P. What is the equation of tangent to the following is the correct statement?
curve at P?
(A) The first term must be negative
(A) y=mx+m (B) The common difference must be negative
(B) y=-mx+2m (C) Either the first term or the common difference is
(C) y=m²x+2m negative but not both

(D) y=m²x+m (D) Both the first term and the common difference are
negative

59. What is the number of outcomes when a coin is 60. Consider the information given below and answer the
tossed and then a die is rolled only in case a head is items that follow. A survey was conducted among 300
shown on the coin? students. It was found that 125 students like to play
cricket 145 students like to play football and 90 students
(A) 6
like to play tennis 32 students like to play exactly two
(B) 7
games out of the three games. How many students like to
(C) 8 play exactly only one game?
(D) None of the above
(A) 196

(B) 228

(C) 254

(D) 268

61. The equation ax + by + c = O represents a straight 62. A straight line with direction cosines (0, 1, 0) is
line
(A) parallel to x-axis
(A) for all real numbers a, b and c (B) parallel to y-axis
(B) only when a ≠0 (C) parallel to z-axis
(C) only when b ≠0 (D) equally inclined to all the axes
(D) only when at least one of a and b is non-zero

63. If two dice are thrown and at least one of the dice 64. If |z+4| ≤ 3, then the maximum value of | z + 1 | is
shows 5, then the probability that the sum ia 10 or more
(A) 2
is
(B) 3
(A) 1/6
(C) 6
(B) 4/11
(D) zero
(C) 3/11

(D) 2/11

65. The sum of the binary numbers (11011) ,(10110110) 66. In any discrete series (when all values are not the
2
and (10011xOy) is the binary number (101101101) . same), if x represents mean deviation about mean and y
2 2 2
What are the values of X and y? represents standard deviation, then which one of the
following is correct?
(A) X= 1, y = 1

(B) x= 1, y = 0 (A) y≥x

(C) x = 0, y = 1 (B) y≤x

(D) x = 0, y = 0 (C) x=y

(D) x

67. The ratio of roots of the equations ax² bx + c = 0 and 68. What is 2 θ1+ 2 θ equal to ?
px² + qx + r =0 are equal. If D and D are respective
1 2 (A) cos2θ
discriminants, then what is D D equal to ?
1 2
(B) tan2θ
(A) a2p2
(C) sin2θ
(B) b2q2
(D) cosec2θ
(C) c2r2

(D) None of the above

69. What is one of the square roots of 3+ 4i, where i = √1 70. What is the solution of the differential equation ((d
? y)/(d x))-a=0

(A) 2 + i (A) y = xea + c

(B) 2 - i (B) x = yea + c

(C) -2 + i (C) y = ln x + c

(D) -3- i (D) x = ln y + c

71. If the second term of a GP is 2 and the sum of its 72. Read the following information and answer the three
infinite terms is 8, then the GP is items that follow : Consider the function f(x) = g(x) + h(x)
where g(x) = sin(x/4) and h(x)=cos (4x/5) What is the
(A) 8,2,½,⅛,.....
period of the function f(x)?
(B) 10,2,⅖,2/25,...
(A) 10π
(C) 4,2,1,½,¼,...
(B) 20π
(D) 6,3,3/2,¾
(C) 40π

(D) 80π

73. What is the solution of the differential equation (d 74. 8 coins are tossed simultaneously. The probability of
x)/(d y)=(x+y+1)/(x+y-1) ? getting at least 6 heads is

(A) y-x + 4In(x + y) = c (A) 7/64

(B) y + x + 2 In(x + y)=c (B) 57/64

(C) y-x + In(x + y) = c (C) 37/256

(D) Y+x+2 In(x + y) = c (D) 229/256

75. Let a⃗, b⃗ and c⃗ be three mutually perpendicular
vectors each of unit magnitude A=a+b+c, B=a-b+ c
76.
c=a-b-c ,then which one of the following is correct?

(A) |A|>|B|>|c| (A) 1

(B) |A|=|B| ≠|c| (B) 2

(C) |A|=|B|=|c| (C) 4

(D) |A| ≠|B| ≠|c| (D) None of the above

77. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Then the number 78. Three groups of children contain 3 girls and ,1 boy; 2
of subsets of A containing two or three elements is girls and 2 boys; 1 girl and 3 boys. One child is selected
at random from each group. The probability that the
(A) 45
three selected consists of 1 girl and 2 boys is
(B) 120
(A) 13/32
(C) 165
(B) 9/32
(D) 330
(C) 3/32

(D) 1/32

80. The points P(3, 2, 4), Q(4, 5, 2), R(5, 8, 0) and S(2, -1,
6) are

(A) vertices of a rhombus which is not a square

79. (B) non-coplanar

(C) collinear
(A) -1 (D) coplanar but not collinear
(B) 0

(C) 1

(D) 2

81. What is 82. The mean and standard deviation of a binomial
equal to? distribution are 12 and 2 respectively. What is the
number of trials?
(A) 0

(B) -(π/4) (A) 2

(C) -(π/2) (B) 12

(D) π/2 (C) 18

(D) 24

83. If |arraylll x & y & 0 \\ 0 & x & y \\ y & 0 & x array|=0
then which one of the following is correct ?

(A) x/y is one of the cube roots of unity
84. then
(B) x is one of the cube roots of unity

(C) y is one of the cube roots of unity what is λ equal to?

(D) x/y is one of the cube roots of -1 (A) 7

(B) -7

(C) 9

(D) -9

85. Coefficient of correlation is the measure of 86. Consider the following discrete frequency
distribution : What is the value of the median of the
(A) central tendency
distribution ?
(B) dispersion
(A) 4
(C) both central tendency and dispersion
(B) 5
(D) neither central tendency nor dispersion
(C) 6

(D) 7

87. The maximum value of the function f(x) = x3 + 2x2 - 88. If A = sin²θ + cos4θ, then for all real θ, Which one of
4x + 6 exists at the following is correct?

(A) x = -2 (A) 1≤A≤2

(B) x = 1 (B) 3/4≤A≤1

(C) x = 2 (C) 13/16 ≤A≤1

(D) x = -1 (D) 3/4≤A≤13/16

89. If the constant term in the expansion of (√(x)-kx2)10 90. Consider the following in respect of matrices A, B
is 405, then what can be the values of k ? and C of same order(Where A′ is the transpose of the
matrix A.): (1). (A+B+C)′ = A' + B'+C′ (2). (AB)' = A'B' (3).
(A) ±2
(ABC)′ = C'B'A' Which of the above are correct?
(B) ±3
(A) 1 and 2 only
(C) ±5
(B) 2 and 3 only
(D) ±9
(C) 1 and 3 only

(D) 1,2 and 3

91. What is the number of diagonals of an octagon ? 92. The total number of 5-digit numbers that can be
composed of distinct digits frorn 0 to 9 is
(A) 48

(B) 40 (A) 46360

(C) 28 (B) 30240

(D) 20 (C) 27216

(D) 15120

93. If tan(α + β) = 2 and tan(α - β) = 1, then tan (2α) is 94. If a=2+3+4k and b=3+2+λk are perpendicular, then
equal to what is the value of λ ?

(A) -3 (A) 2

(B) -2 (B) -3

(C) -1/3 (C) 4

(D) 1 (D) 5

95. In a bolt factory, machines X, Y, Z manufacture bolts 96. What is (1 - sin2 θ)(1 + tan2θ) equal to?
that are respectively 25%, 35% and 40% of the factory's
(A) sin2 θ
total output. The machines X, Y, Z respectively produce
(B) cos2 θ
2%, 4% and 5% defective bolts. A bolt is drawn at random
from the product and is found to be defective. What is (C) tan2 θ

the probability that it was manufactured by machine X? (D) 1

(A) 5/39

(B) 14/39

(C) 20/39

(D) 34/39

97. Consider the following statements : 1. Pie diagrams
are suitable for categorical data. 2. The arc length of a
sector of a pie diagram is proportional to the value of the 98.
component represented by the sector. Which of the
statements given above is / are correct? (A) 2n - 1

(A) 1 only (B) n

(B) 2 only (C) n!

(C) Both 1 and 2 (D) 2n

(D) Neither 1 nor 2

99. If A, B and Care subsets of a given set,then which
one of the following relations is not correct?

(A) AU(A⋂B) = AUB

(B) A⋂(AUB) = A

(C) (A⋂B)UC = (AUC)⋂(BUC)

(D) (AUB)⋂C = (A⋂C)U(B⋂C)

100. Consider the following statements : Statement 1 : Range is not a good measure of dispersion. Statement 2 :
Range is highly affected by the existence of extreme values. Which one of the following is correct in respect of the
above statements?

(A) Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1

(B) Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation of statement 1

(C) Statement 1 is correct butStatement 2 is not correct

(D) Statement 2 is correct but Statement 1 is not correct

101. Let ABCD be a parallelogram whose diagonals 102. Consider the following in respect of matrices A and
intersect at P and let O be the origin. What is O A+O B+O B of same order(where I is the identity matrix and O is
C+O D equal to? the full matrix ): (1). A²-B² = (A + B) (A-B) (2). (A-I) (I +
A)=0 = A²=I Which of the above is/are correct?
(A) 2 O P

(B) 4 O P (A) 1 only

(C) 6 O P (B) 2 only

(D) 8 O P (C) Both 1 and 2

(D) Neither 1 nor 2

103. There are 3 coins in a box. One is a two-headed 104. If A=[arraycc α & α \\ - α & α array] then what is AAT
coin; another is a fair coin; and third is biased coin that equal to (where AT is the transpose of A) ?
comes up heads 75% of the time. When One Of the three
(A) Null matrix
coins is selected at random and flipped, it shows heads.
(B) Identity matrix
What is the probability that it was the two-headed coin ?
(C) A
(A) (2/9)
(D) - A
(B) (1/3)

(C) 4/9

(D) 5/9

105. If A, B and C are subsets of a Universal set; then 106. Consider the following statements : 1. The matrix
which one of the following is not correct(where A′ is the
complement of A ) ?

(A) AU (B⋂C) = (AUB)⋂(AUC)
is singular. 2. The matrix
(B) AU(AUB) = (B'⋂A′)UA

(C) A' U(BUC)=(C′⋂B′)⋂A′

(D) (AUB)UC= (AUC)U(BUC)

is non-singular. Which of the above

statements is / are correct?

(A) 1 only

(B) 2 only

(C) Both 1 and 2

(D) Neither 1 nor 2

107. If f(x)=x33-5 x22+6 x+7 increases in 3 2 the interval 108. The cofactor of the element 4 in the determinant
T and decreases in the interval S, then which one of the
following is correct ?

(A) T=(-∞, 2) (3, ∞) and S=(2,3)
is
(B) T=φ and S=(-∞, ∞)

(C) T=(-∞, ∞) and S=φ (A) 2
(D) T=(2,3) and S=(-∞, 2) (3, ∞) (B) 4

(C) 6

(D) -6

109. If K= ((π)/(18)) ((5 π)/(18)) ((7 π)/(18)) , then what 110. What is the value of
is the value of K ?
(A) √2-1
(A) 1/2 (B) √2+1
(B) 1/4 (C) 3
(C) 1/8 (D) 4
(D) 1/16

111. For what value of k are the two straight lines 3x + 112. What is ∫ sin2 x dx + ∫ cos2 x dx equal to? where c is
4y = 1 and 4x + 3y + 2k = 0 equidistant from the point an arbitrary constant.
(1, 1)?
(A) x + c
(A) (1/2) (B) x2 / 2 + c
(B) 2 (C) x2 + c
(C) -2 (D) None of the above
(D) -(1/2)

113. What is the equation of the straight line parallel to 114. What is the value of log 27 + log 32 ?
9 8
2x + 3y + 1 = 0 and passes through the point (-1, 2)?
(A) 7/2
(A) 2x + 3y -4 = 0 (B) 19/6
(B) 2x + 3y - 5 = 0 (C) 4
(C) x + y -1 = 0 (D) 7
(D) 3x - 2y + 7 = 0

115. What is ∫ 3 x x d x equal to (where c is the constant 116. Let f(x) be defined as follows : f(x)=\arrayll 2 x+1, &
of integration. )? -3 x -2 \\ x-1, & -2 ≤ x 0 \\ x+2, & 0 ≤ x 1 array. Which one
of the following statements is correct in respect of the
(A) 4 x+c
above function?
(B) 4 x+c
(A) It is discontinuous at x = -2 but continuous at every
(C) (1- 2 x)24+c
other point.
(D) (1- 2 x)24+c
(B) It is continuous only in the interval (-3, -2).

(C) It is discontinuous at x = 0 but continuous at every other
point.

(D) It is discontinuous at every point.

117. The sum of the roots of the equation ax2 + x +c= 0 118. The line passing through the points (1, 2, -1) and (3,
(where a and c are non-zero) is equal to the sum of the -1, 2) meets the yz-plane at which one of the following
reciprocals of their squares. Then a, ca2, c2 are in points?

(A) AP (A) ( 0, -7/2, 5/2 )

(B) GP (B) (0, 7/2, ½)

(C) HP (C) (0, -7/2, -5/2 )

(D) None of the above (D) (0, 7/2, -5/2 )

119. If A is a subset of B, then which one of the following 120. If θ = π/8,then what is the value of (2 cosθ + 1)10
is correct? (2cos2θ - 1)10(2cos4θ-1)10?

(A) Ac ⊆ Bc (A) 0

(B) Bc ⊆ Ac (B) 1

(C) Ac = Bc (C) 2

(D) A ⊆ A ∩ B (D) 4

ANSWER KEY

1. (C) 2. (D) 3. (D) 4. (A) 5. (D) 6. (D) 7. (D)

8. (C) 9. (C) 10. (B) 11. (C) 12. (D) 13. (B) 14. (C)

15. (A) 16. (B) 17. (A) 18. (A) 19. (D) 20. (B) 21. (D)

22. (D) 23. (D) 24. (A) 25. (A) 26. (B) 27. (C) 28. (D)

29. (D) 30. (A) 31. (B) 32. (C) 33. (A) 34. (A) 35. (C)

36. (C) 37. (D) 38. (A) 39. (C) 40. (D) 41. (C) 42. (A)

43. (D) 44. (B) 45. (C) 46. (A) 47. (B) 48. (C) 49. (B)

50. (B) 51. (D) 52. (D) 53. (B) 54. (C) 55. (D) 56. (D)

57. (A) 58. (C) 59. (B) 60. (C) 61. (D) 62. (A) 63. (C)

64. (C) 65. (B) 66. (D) 67. (B) 68. (C) 69. (A) 70. (A)

71. (C) 72. (B) 73. (C) 74. (C) 75. (C) 76. (B) 77. (C)

78. (A) 79. (B) 80. (C) 81. (C) 82. (C) 83. (D) 84. (B)

85. (B) 86. (C) 87. (A) 88. (B) 89. (C) 90. (C) 91. (A)

92. (C) 93. (A) 94. (B) 95. (A) 96. (D) 97. (C) 98. (D)

99. (D) 100. (A) 101. (B) 102. (B) 103. (A) 104. (B) 105. (C)

106. (A) 107. (A) 108. (C) 109. (C) 110. (B) 111. (D) 112. (A)

113. (A) 114. (A) 115. (D) 116. (C) 117. (A) 118. (D) 119. (B)

120. (B)