NIMCET - 2013 (Actual Paper) : (QW) ( W) ( W) Hij K LMNH K
NIMCET - 2013 (Actual Paper) : (QW) ( W) ( W) Hij K LMNH K
NIMCET - 2013 (Actual Paper) : (QW) ( W) ( W) Hij K LMNH K
4. If the straight line 7N 9O 0 always passes 16. If N̅ and N̅ are the means of two distributions such that
through (1, –2) then 7, 9 and c are in N̅ { N̅ and N̅ is the mean of the combined
(a) AP (b) HP (c) GP (d) None distribution, then
(a) N̅ { N̅ (b) N̅ { N̅
5. A six faced die is a biased one. It is thrice more likely to (c) N̅
k̅ | lk̅ }
(d) N̅ { N̅ { N̅
show an odd number than to show an even number. It is
thrown twice. The probability that the sum of the
17. The area enclosed within the curve |N| |O | 1 (in
numbers in the two throws is even, is
U W X Y square units) is
(a) V (b) V (c) V (d) V
(a) √2 (b) 1 (c) √3 (d) 2
8. Person A can hit a target 4 times in 5 attempts. Person B 20. Atal speaks truth in 70% and George speaks the truth in
can hit a target 3 times in 4 attempts. Person C can hit a 60% cases. In what percentage of cases they are likely in
target 2 times in 3 attempts. They fire a volley. The contradict each other in stating the same fact?
g g gg
probability that the target is hit atleast two times, is (a) (b) (c) (d)
W_ W_ W_ W_
g W
(a) (b) (c) (d) 1
U X 21. A man observes the angle of elevation of the top of a
mountain to be 30°. He walks 1000 feet nearer and finds
]/ √hij k
9. The value of the integral[_ N is the angle of elevation to be 45°. What is the distance of
√hij kl√mnh k
] ] ] the first point of observation from the foot of the
(a) 0 (b) (c) (d)
U U mountain?
(a) 500√3•√3 1‚ ft (b) 500•√3 1‚ ft
10. If o is a cube root of unity, then find the value of
1 o o o (c) 500•√3 1‚ ft (d) 500√3•√3 1‚ ft
p1 o o o p
22. The sum of y terms of an arithmetic series is 216. The
o o o o
(a) 3o (b) 3o (c) 3o (d) 3o value of the first term is n and the value of the nth term is
2n. The common difference, is
g
11. If the vector 21̂ 32̂, 1̂ 2̂ ./ and 31̂ ./ form three (a) 1 (b) g (c) (d)
coterminous edges of a parallelopiped, then the volume
of parallelopiped is 23. Force 31̂ 22̂ 5. / and 21̂ 2̂ 3. / are acting on a
(a) 8 (b) 10 (c) 4 (d) 14 / to the
particle and displace it from the point 21̂ 2̂ 3.
/
point 41̂ 22̂ 7. then the work done by the force is
(a) 18 units (b) 30 units
(c) 24 units (d) 36 units
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NIMCET – 2013 (Actual Paper)
| | | ” }•
24. The value of 9ƒ ∙ 9„ ∙ 9}… … is 38. If N 7 cos “ , O 9 sin “ then ”k } is
(a) 3 (b) 6 (c) 9 (d) None –— –— – ˜—
(a) (b) (c) ˜•— (d)
˜ } •ƒ ˜}k ƒ –k ƒ
25. The minimum value of the function O 2N g 21N
36N 20 is 39. A random variable N has the distribution law as given
(a) –120 (b) –126 (c) –128 (d) None below :
N 1 2 3
26. In how many different ways can the letters of the word
“CORPORATION” be arranged so that all the vowels •(¤ N) 0.3 0.4 0.3
always come together The variance of the distribution is
(a) 810 (b) 1440 (c) 2880 (d) 50400 (a) 0.4 (b) 0.6 (c) 2 (d) None
27. If log k O 100 and log N 10, then the value of O is 40. The value of tan \ 2 tan 2\ 4 tan 4\ 8 cot 8\ is
(a) 2 _ (b) 2 __ (c) 2 ___ (d) 2 ____ (a) cot \ (b) tan \ (c) sin \ (d) cos \
28. The equations of the line parallel to the line 2N 3O 7 41. The sum of integers between 200 and 400, that are
and passing through the middle point of the line segment multiples of 7 is
joining the points (1, 3) and (1, –7) is (a) 8729 (b) 8700 (c) 8972 (d) 8279
(a) 2N 3O 4 0 (b) 2N 3O 4 0
(c) 2N 3O 8 0 (d) 2N 3O 8 0 ›œj k k
42. limk→_ k } ›œj k is equal to
29. In a ∆ABC, if ( 7 9)(7 9 ) 79. The measure (a) 0 (b) 1 (c) (d) g
of the angle ∠J is
] ] ]
(a) g (b) X (c)
g
(d) None 43. Two fair dice are tossed. What is the probability that the
total score is a prime number?
W Y
30. The number of non-negative integers less than 1000 that (a) X (b) (c) (d) •
contain the digit 1 are
(a) 9 (b) 9g (c) 10 9 (d) 10g 9g 44. Find the equation of the circle which passes through (–1,
1) and (2, 1) and having centre on the line N 2O 3 0
31. The lines 3N 4O 4 0 and 6N 8O 7 0 are (a) 2N 2O 2N 7O 13 0
tangent to the same circle. The radius of this circle is (b) N O 2N 7O 13 0
g g U Y
(a) (b) U (c) W (d) _ (c) 2N 2O 2N 7O 13 0
(d) N O 2N 7O 13 0
32. The area of the parallelogram whose diagonals are
+ 31̂ 2̂ 2. / and 4 1̂ 32̂ 4. / is 45. Let +, b and c are be the position vectors of three vertices
(a)10√3 (b) 5√3 (c) 10√2 (d) 5√2 A, B and C of a triangle respectively. Then the area of this
triangle is given by
33. If sin N 7 cos N 9 then what is the expression for (a) (+ 6 4) ∙ 0
|7 sin N cos N| in terms of 7 and ? (b) |+ 6 4 0 6 0 0 6 +|
(a) √7 9 1 (b) √7 9 1 (c) + 6 4 4 6 0 0 6 +
(c) √7 9 1 (d) √7 9 1 (d) None of these
34. If A and B are two events such that •( ∪ I) 46. The sum of the focal distances of any point on the ellipse
, •( ∩ I) g, and •(I• )
W
X
, then the events and I k} •}
1 with eccentricity e is given by
˜} –}
are (a) 27ž (b) 29 (c) 27 (d) 29ž
(a) dependent (b) independent
(c) mutually exclusive (d) None of these 47. If sin N sin N 1, then cos N cosU N is equal to
(a) 0 (b) 1 (c) –1 (d) 2
35. If three vectors 21̂ ,̂ /, 1̂
. 22̂ / and 31̂
3. •,̂ /
5.
are coplanar, then λ is 48. An experiment succeeds twice often as it fails. The
(a) –1 (b) –2 (c) –3 (d) –4 probability that in the next six trials there will be atleast
four successes is
36. The equation of the base of an equilateral triangle is U_
(a) Y •
U•X
(b) Y •
_
(c) Y •
gg
(d) Y •
N O 2 and the vertex is (2, –1). The length of the side
of the triangle is
g _
49. Sum of 20 terms of the series 1 2 3 4 ⋯ is
(a) ’ (b)√2 (c)’ (d) ’ (a) 180 (b) 200 (c) 210 (d) 220
g g
¢
37. The total number of numbers that can be formed using 50. If tan ¡ ¢l
and ß ¢l
then 7 9 is equal to
the digits 3, 5 and 7 only if no repetitions are allowed, is (a)
]
(b)
]
(c)
]
(d) w
(a) 39 (b) 105 (c) 15 (d) 27 g U X
55. What is the profession of Rakesh’s wife? 64. Which pair of numbers comes next in the following
(a) Teacher (b) Doctor series?
(c) Lawyer (d) Cannot be determined
(a) 25 22 (b) 26 23 (c) 26 24 (d) 25 23
56. What is Ajay’s grandfather’s occupation?
(a) Teacher (b) Lawyer Directions (Q.65 and 66):
(c) Doctor (d) Cannot be determined (i) All G’s are H’s
(ii) All G’s are J’s or K’s
57. Find the missing element in the series (iii) All J’s and K’s are G’s
A, CD, GHI, ........., UVWXY (iv) All L’s are K’s
(a) LMNO (b) MNOP (c) NOPQ (d) OPQR (v) All N’s are M’s
(vi) No M’s are G’s
58. In a code language, ‘FRIEND’ is coded as ‘GTLISJ’. Which
of the following is coded as ‘HWDVI’ in that language? 65. If no P’s are K’s, which of the following must be true ?
(a) HAPPY (b) GUARD (c) BEADS (d) SPEED (a) All P’s are J’s (b) If any P is a G, it is a J
(c) No P is an H (d) If any P is an H, it is a G
59. There are four brothers Alan, Bob, Carl and Dave. Dave is
two years older than Bob, Bob is one year younger than 66. Which of the following is inconsistent with one or more
Carl. Alan, who is 34, is two years younger than Carl. the conditions?
Who is the oldest? (a) All H’s are G’s
(a) Alan (b) Bob (c) Carl (d) Dave (b) All H’s that are not G’s are M’s
(c) Some H’s are both M’s and G’s
(d) No M’s are H’s
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NIMCET – 2013 (Actual Paper)
67. Shyam is taller than Pradeep and Pradeep is as tall as Questions 74 to 76 are based on the following:
There are three switches A, B and C which can be in ON/OFF
Anurag. But Anand is shorter than Suresh, who is as tall
position. Their settings change as per the following rules:
as Anurag. If Pradeep is taller than Praveen, who is the (i) If A is the only switch as ON, change B to ON
(ii) If A and B are only switches as ON, change C to ON
tallest of all?
(iii) If all three switches are ON, change C to OFF
(a) Pradeep (b) Praveen (c) Suresh (d) Shyam (iv) For all other situations, all switches in ON are changed
to OFF and all switches in OFF are changed to ON
68. When Rajeev was born his father was 32 years older
than his brother and his mother was 25 years older than 74. If switches A and B are ON and C is OFF, their changed
his sister. If Rajeev’s brother is 6 years older than Rajeev settings will be
and his mother is 3 years younger than his father, how (a) A ON, B OFF, C OFF (b) A ON, B ON, C ON
old was Rajeev’s sister when he was born? (c)A ON, B OFF, C ON (d) A OFF, B ON, C OFF
(a) 15 years (b) 14 years (c) 7 years (d) 10 years
75. If only B is ON, the changed setting will be
69. Dhoni starts from his office at 8 A.M. on a Sunday (a) A ON, B ON, C ON (b) A ON, B ON, C OFF
morning, travels 10 km towards West and then turns to (c) A ON, B OFF, C ON (d) A OFF, B OFF, C ON
his left and walks 8 km. Then he again turns to his left
and walks 4 km and then stops. What is the shortest 76. If only B is ON in the changed setting, which of the
distance to his office from the point where he stopped? following could have been the original setting?
(a) 18 km (b) 8 km (c) 10 km (d) None (a) A ON, B ON, C ON (b) A ON, B OFF, C ON
(c) A OFF, B ON, C OFF (d) A OFF, B OFF, C ON
70. A treasure chest has less than 100 gold coins. The
number of coins is 77. If the third day of a month falls on Friday, what day will
(i) One more than a multiple of 3 be on the fourth day after twenty first of the month?
(ii) Two more than a multiple of 4 (a) Monday (b) Tuesday (c) Saturday (d) Thursday
(iii) Three more than a multiple of 5 and
(iv) Four more than a multiple of 6 78. Ana is a girl and has the same number of brothers as
How many coins are there in the chest? sisters. Andrew is a boy and has twice as many sisters as
(a) 58 (b) 88 (c) 98 (d) 38 brothers. Ana and Andrew are the children of Emma.
How many children does Emma have?
71. Read the statements and then decide which of the (a) 2 (b) 3 (c) 5 (d) 7
conclusions logically follow.
Statements: 79. The best answer to “Who is the tallest ?” is
(1) All mangoes are golden in colour (a) Dany (b) Binu
(2) No golden coloured things are cheap (c) Dany or Binu (d) Both Dany and Binu
89. Jimmy saw the time while going to the tennis court. He 99. Fill in the blank with appropriate form of noun :
saw the hour hand is 20° away from 4. After he returned Don’t blame yourself, it’s not your ___________
from tennis court, he noticed that the hour hand is 20° (a) misunderstanding (b) error
away from 4. If the took ten minutes to go to tennis court (c) slip (d) fault
and he walked at the same speed while going to the
tennis court and while returning, how much time did he 100. Fill in the blank:
spent at the tennis court? The instructor, along with the class, ________ angry about
(a) 60 minutes (b) 80 minutes the room change
(c) 70 minutes (d) 50 minutes (a) are (b) have (c) has (d) is
90. There are 8 balls looking alike, seven of which have equal 101. Choose the suitable word for the blank to make it a
weight and one is slightly heavier. The weighing balance meaningful statement.
is of unlimited capacity. Using this balance, the minimum What you say is ______ any comprehension
number of weighings required to identify the heavier ball (a) before (b) beside (c) behind (d) beyond
is
(a) 1 (b) 2 (c) 3 (d) 4 102. Fill in the blank with a suitable preposition:
If you want to avoid traffic, you need to leave _______ 7:30
A.M.
(a) until (b) by (c) during (d) at
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NIMCET – 2013 (Actual Paper)
103. Choose the word that best expresses the meaning of the 114. Convert the Hexadecimal number 4DF to its octal
given idiom : “to smell a rat”. equivalent
(a) To suspect something bad(b) To misunderstand (a) 2333 (b) 2337 (c) 2773 (d) 2373
(c) To detect bad smell (d) To forsake
115. A tautology is a Boolean formula that is always true.
104. Out of the given alternatives, choose the word that best Which of the following is a tautology?
expresses the meaning of the word ABRIDGE. (a) N (b) (N N̅ )O (c) N O• N̅ (d) (NO) N̅
(a) Judge (b) Release (c) Shorten (d) Dissolve
116. Acronym of EEPROM is
105. ‘A dog’s breakfast’ means (a) Extended Erasable Programmable Memory
(a) Breakfast cooked for a dog (b) Electrically Erasable Read Only Memory
(b) Breakfast cooked by a dog (c) Electrically Erasable Programmable Read Only
(c) Something that has been done very badly Memory
(d) None of these (d) Extended Erasable Page-Oriented Memory
106. Change the speech: 117. For reproducing sound, a CD audio player uses a
She says, “I like going to the sea side”. (a) Quartz crystal (b) Titanium needle
(a) She says that she likes going to the seaside (c) Barium ceramic (d) Laser beam
(b) She says I like going to the seaside
(c) She says that she liked going to the seaside 118. When we open an internet site, we see www. What does
(d) She says she like going to the seaside www stand for?
(a) World Wide Word (b) World Wide Web
107. Arrange the following to form a correct sentence (c) World Wide Webinar (d) Word Widing Works
P: will normally be granted
Q: candidates should note 119. The answer of the operation (10111) 6 (1110) in hex
R: that no request for equivalent is
S: change of centre (a) 150 (b) 14 C (c) 142 (d) 13 E
(a) SRQP (b) PRQS (c) QSPR (d) QRSP
120. The minimum number of bits to represent a character
108. Rewrite the sentence after correcting the error: from ASCII code set is
She was one of the average student of the class. (a) 2 (b) 8 (c) 5 (d) 7
(a) She was one of the average students of the class
(b) She is one of the average student of the class
(c) She was one among the average student of the class
(d) She is an average students of the class