TM
Path to success KOTA (RAJASTHAN )
NATIONAL TALENT SEARCH EXAMINATION
(NTSE-2016) STAGE -1
BIHAR STATE : MAT
Date: 08/11/2015
SOLUTIONS
Max. Marks: 50
Time allowed: 45 mins
1.
The missing number in the series 40,120,60,180,90, ? , 135 is
(1) 110
(2) 270
(3) 105
Ans. (2)
Sol.
40,120,60,18 0,90,
×3 ¸ 2 ×3 ¸2
(4) 210
, 135
×3
¸2
2.
The odd numbers from 1 to 45 which are exactly divisible by 3 are arranged in an ascending order. The number at
6th position is
(1) 18
(2) 24
(3) 33
(4) 36
Ans. (3)
Sol. 3, 9, 15, 21, 27, 33
3.
The mean of four numbers a, b, c, d is 100. If c = 70, then the mean of the remaining number is
(1) 30
(2)
85
2
(3)
170
3
(4) 110
Ans. (4)
Sol. ATQ
Þ
a+b+c+d
= 100
4
a + b + c + d = 400
Mean of a, b and d =
Þ
a + b + 70 + d = 400 Þ
a + b + d = 400 – 70 = 330
330
= 110
3
4.
If the radius of a circle is increased by 50%, the perimeter of the circle will increase by
(1) 20%
(2) 30%
(3) 40%
(4) 50%
Ans. (4)
Sol. Percentage increase of perimeter
3 pr – 2 pr
pr
× 100 =
× 100 = 50%
2pr
2 pr
5.
If the statement ‘some men are honest’ is false, which among the following statements will be true. Choose the
correct alternative given below
(i) All men are honest
(ii) No men are honest
(iii) some men are not honest
(iv) All men are dishonest
(1) (i), (ii) and (iii)
(2) (ii), (iii) and (iv)
(3) (i), (iii) and (iv)
(4) (ii), (i) and (iv)
Ans. (2)
Sol. Statement’ some men are honest’ is false from the statement valid conclusion from alternative is
No men are honest
Some men are not honest
All men are dishonest
=
1
6.
In a certain code GALIB is represented by HBMJC. TIGER will be represented by
(1) UJHFS
(2) UHJSF
(3) JHUSF
(4) HUJSF
Ans. (1)
Sol. Each letter is coded by its next letter.
7.
Choose the proper alternative given in the codes to replace the question mark.
Bee- Honey, Cow- milk, Teacher - ?
(1) Intelligence
(2) Marks
(3) Lessons
(4) Wisdom
Ans. (4)
Sol. Honey is produced by bee, Milk is produced by Cow in the same way Lession is produced by Teacher
8.
P is the father of R and S is the son of Q and T is the brother of P. If R is the sister of S, how is Q related to T ?
(1) Wife
(2) Sister- inlaw
(3) Brother-inlaw
(4) Daughter-inlaw
Ans. (2)
Sol.
T
®
male,
P
Q
R
S
®
female, = ® couple
Question 9-14 Read the table below and based on this table answer questions from 9 to 14.
Area under Major Horticulture Crops (in lakh hectares)
9.
Year
Fruits
Vegetables
Floweres
2005-06
53
72
1
Total HortiCulture
Area
187
2006-07
56
75
1
194
2007-08
58
78
2
202
2008-09
61
79
2
207
2009-10
63
79
2
209
Which of the following two years have recorded the highest rate of increase in area under the total horticulture ?
(1) 2005-06 and 2006 - 07
(2) 2006-07 and 2008 - 09
(3) 2007-08 and 2008 - 09
(4) 2006-07 and 2007 - 08
Ans. (4)
Sol. Total Horticulature
2006 - 07
—
3.74%
2007 - 08
—
4.12%
2008 - 09
—
2.47%
2009 - 10
—
0.96%
Clearly, 2006-07 and 2007-08 have recorded the highest rate of increase in area under the total horticulture.
2
10.
In the year 2009-10 shares in the area under flowers, vegetables and fruits in the area under total horticulture are
respectively
(1) 1,38 and 30 percent
(2) 30,38 and 1 percent
(3) 38,30 and 1 percent
(4) 35,36 and 2 percent
Ans. (1)
Sol. Area of flowers =
2
× 100 = 0.95%
209
Area of vegetables =
Area of fruits =
11.
79
× 100 = 37.79%
209
63
× 100 = 30.14%
209
Which of the following has recorded the highest rate of increase in area during 2005-06 to 2009-10 ?
(1) Fruits
(2) Vegetables
(3) Flowers
(4) Total horticulture
Ans. (3)
Sol. Increase % of fruits =
63 - 53
× 100 = 18.86%
53
Increase % of vegetable =
Increase % of flowers =
79 - 72
× 100 = 8.86%
72
2 -1
× 100 =100%
1
Increase % of horticulture =
209 - 187
× 100 =11.76%
187
Clearly, flowers has recorded the highest rate of increases in area during 2005-06 to 2009-10.
12.
Find out the horticulture crop that has recorded an increase of area by around 10 percent from 2005-06 to
2009-10.
(1) Fruits
(2) Vegetables
(3) Flowers
(4) Total horticulture
Ans. (2)
Sol. From solution of Q.11
Clearly vegetable ahs recorded an increase of area by around 10% from 2005-06 to 2009-10.
13.
What has been the share of area under fruits, vegetables and flowers in the area under total horticulture in 2007-08 ?
(1) 53 percent
(2) 68 percent
(3) 79 percent
Ans. (2)
Sol. Area % =
138
× 100 = 68.31%
202
3
(4) 100 percent
14.
In which year, area under fruits has recorded the highest rate of increase ?
(1) 2006-07
(2) 2007-08
(3) 2008-2009
Ans. (1)
Sol. 2006-07 –
56 - 53
× 100 = 5.66%
53
2007-08 –
58 - 56
× 100 = 3.57%
56
2008 - 09 –
2009 -10 –
15.
Ans.
Sol.
16.
Ans.
Sol.
17.
Ans.
Sol.
18.
Ans.
Sol.
19.
Ans.
Sol.
(4) 2009-10
61 - 58
× 100 = 5.17 %
58
63 - 61
× 100 = 3.27%
61
Clearly, year 2006-07 area under fruits has recorded the highest rate of increase.
A deductive argument is invalid if :
(1) Its premises are true but its conclusion is false
(2) Its premises are false but its conclusion is true
(3) Its premises and conclusions are all true
(4) Its premises and conclusion are all false
(4)
A deductive agrument is one in which if the premises are true then it is guranteed that the conclusion will be true. So
a deductive argument will be invalid if premises are false and if premises are false then conclusion will definitely be
false.
In certain code Mathura is coded as JXQEROX. The code of HOTELS will be
(1) ELQBIP
(2) LEBIQP
(3) ELIPQB
(4) LEQIBP
(1)
Each letter coded 3 letters backward.
If we want to seek new knowledge of facts about the world, we must rely on reason of the type
(1) Deductive
(2) Demonstrative
(3) Physiological
(4) Inductive
(4)
Inductive reasoning is the process of making generalized decisions after observing or witnessing repeated specific
instances of something inductive arguments are always open to question as by definition the conclusion is a bigger
bag than the evidence on which it is based.
When the purpose of a definition is to explain the use or to eliminate ambiguity the definition is called.
(1) Theoritical
(2) Lexical
(3) Persuasive
(4) Stipulative
(1)
Theoretical definition a coherent group of tested general propositions commonly regarded as correct that can be
used as principles explnation and prediction for class of phenomena.
Assertion (A) : Formal Communication tends to be fast and flexible.
Reason (R) : Formal Communication is a systematic and orderly flow of information
(1) Both (A) and (R) are correct, but (R) is not correct explanation of (A)
(2) (A) is correct, but (R) is false
(3) (A) is false, but (R) is correct
(4) Both (A) and (R) are correct and (R) is correct explanation of (A)
(3)
Formal communication is not past and flexible but it is systematic and orderly.
4
20.
At present a person is 4 times older than his son and is 3 years older than his wife. After 3 years the age of the son
will be 15 years. The age of the person’s wife after 5 years will be :
(1) 48
(2) 45
(3) 50
(4) 42
Ans. (3)
Sol.
Father
Son
Mother
Present
4x
x
4x – 3
After 3 years
4x + 3
x+ 3
4x
given
x + 3 = 15
x = 12
After 5 yrs mother age
= [12 × 4 – 3] + 5 = 50 years.
21. Among the following statements two are contradictory to each other. Select the correct code the represent them
Statement
(a) All poets are philosophers
(b) Some poets are philosophers
(c) Some poets are not philosophers
(d) No philosopher is a poet
Codes
(1) (a) and (d)
(2) (a) and (c)
(3) (b) and (c)
(4) (a) and (b)
Ans. (1)
Sol. (a)
22.
ilosophers
Ph
Poets
(d)
Poets
Philosophers
Poet
Ans.
The next term in the series is
2,5,9,19,37, ?
(1) 75
(2) 78
(3) 80
(4) 73
(1)
Pattern is x 2 + 1, x 2 – 1, x2 + 1, x2 –1 ......
In communication, the language is
(1) Intra personal
(2) The symbolic code
(3) The non- verbal code (4) The verbal code
(4)
The verbal code communication is composed of sound, words and language whcih depends upon particulars region
and culture. So language is the code for verbal communication.
One day Prakash left home and walked 10 km. towards south, turned right and walked 5 km, turned right and
walked 10 km turned left and walked 10 km. How many km, will he have to walk to reach his home straight ?
(1) 20
(2) 15
(3) 30
(4) 10
(2)
Sol.
A
Ans.
Sol.
23.
Ans.
Sol.
24.
10 KM
Home
B
10 km
10 km
5 km
Distance – 10 + 5 = 15 km
5
Question 25-30 : The following questions are based on the tabulated data given below :
A company has 20 employees with their age (in years) and salary (in 1000/- Rs. per month) mentioned against each of
them.
S.No.
Age in
Salary
years
(in 1000/- Rs.
per month)
25.
1
44
35
2
32
20
3
54
45
4
42
35
5
31
20
6
53
60
7
42
50
8
51
55
9
34
25
10
41
30
11
33
30
12
31
35
13
30
35
14
37
40
15
44
45
16
36
35
17
34
35
18
49
50
19
43
45
20
45
50
Classify the data of each employee in class interval of 5 years. Which class interval of 5 years has the maximum
average salary.
(1) 41- 45 years
(2) 46 - 50 years
(3) 51 - 55 years
(4) 36 - 40 years
Ans. (3)
Sol. 41 – 45 yrs average = 35
46 – 50 yrs average = 50
51 – 55 yrs average = 53.33
36 – 40 yrs average = 37.5
26. What is the average salary (in thousand Rs. per month) in the age group of 40 – 50 years ?
(1) 42.5
(2) 40.5
(3) 36.5
(4) 35
Ans. (1)
340
= 42.5
8
27. What percentage (%) of employees are getting salary ³ Rs. 40,000 per month ?
(1) 50%
(2) 35
(3) 32%
Ans. (4)
Sol. Average Salary =
Sol. Salary % ³ 40,000 per months =
9
× 100 = 45%
20
6
(4) 45%
28.
What percentage of employees are getting salary less than the average salary of all the employees ?
(1) 50 %
(2) 55%
(3) 47 %
(4) 45%
Ans. (2)
11
´ 100 = 55%
20
29. What is the average age of employees ?
(1) 38.6 years
(2) 47.2 years
Ans. (4)
Sol. employees % =
(3) 45.3 years
(4) 40.3 years
806
= 40.3
20
Sol. average age of employee =
30.
What is the percentage (%) of employees in the class interval of 30–35 years ?
(1) 25%
(2) 30%
(3) 35%
Ans. (3)
Sol. 30 – 35 yrs employees % =
(4) 20%
7
× 100 = 35%
20
31.
If the series 4,5,8,13,14,17,22, ............ is continued in the same pattern which of the following is not a term of this
series
(1) 31
(2) 32
(3) 33
(4) 35
Ans. (3)
Sol.
4
5
8 13 14 17 22 23 26 31 32 35
+1 +3 +5 +1 +3 +5 +1 +3 +5 +1 +3
32.
Complete the series BB, FE, II ML, PP ............. by choosing one of the following options
(1) TS
(2) ST
(3) RS
(4) SR
Ans. (1)
Sol.
BB
FE
+4
+3
II
+3
ML
+4
+4
PP
+3
+3
TS
+4
+4 +3
33.
A man started walking from his house towards south. After walking 6 km., he turned to his left and walked 5 km.
then he turned left and walked further 3 km. He again turned to his left and continued his walk for 9 km. How far is
he away from his house.
(1) 3 km
(2) 4 km
(3) 5 km
(4) 6 km
Ans. (3)
Home
Sol.
9 km
A
B
6 km
3 km
5 km
Req. distance
AB 2 + BC 2
= (9 - 5)2 + (6 - 3)2 =
4 2 + 32 =
16 + 9 =
25 = 5 km.
7
34.
In a Post-Office, stamps of three different denominations Rs. 7,Rs. 8, Rs. 10 are available. The exact amount for
which one cannot buy stamps is
(1) 19
(2) 20
(3) 23
(4) 29
Ans. (1)
Sol. Rs. 20 = 2 × 10
Rs. 23 = 2 × 8 + 7
Rs. 29 = 3 × 7 + 1 × 8
Clearly, we cannot buy stamps of Rs. 19.
35.
In certain coding method the word QUESTION is encoded a DOMESTIC. In this coding, what is the code for the
word RESPONSE ?
(1) OMESUCEM
(2) OMESICSM
(3) OMESICEM
(4) OMESISCM
Ans. (3)
Sol. QUESTION — DOMESTIC
from corresponding letter
E ® M, S ® E, O ® I, N
®
C
So, RESPONSE — OMESICEM
36.
If two propositions having the same subject and predicate terms can both be true but both cannot be false, the
relation between those two propositions is called?
(1) Contradictory
(2) Contrary
(3) Sub-contrary
(4) Subaltern .
Ans. (3)
Sol. Sub-contrary Proposition : A proposition related to another in such a way that both can be true but both cannot
be false.
37.
One writes all number from 50 to 99 without the digits 2 and 7. How many numbers have been written.
(1) 32
(2) 36
(3) 40
(4) 38
Ans. (1)
Sol. [(99– 50) + 1] – 18 = 32
38.
If a large diamond is cut up into little bits, it will lose its value just as an army when divided into small units of
soldiers, it loses its strength”. The argument put above may be called as
(1) Analogical
(2) Deductive
(3) Statistical
(4) Casual
Ans. (1)
Sol. Analogical argument - is an explect representation of a form of analogical reasoning that cities accepted similarities between two system to support the conclusion that some further similarties exist.
8
39.
Given below are two premises and four conclusions drawn from those premises. Select the code that expresses
conclusion drawn validly from the premises (separately or jointly).
Premises
(a) All gods are mammals
(b) No cats are dogs
Conclusions
(i) No cats are mammals.
(ii) Some cats are mammals.
(iii) No dogs are cats.
(iv) No dogs are non- mammals.
Codes:
(1) (i) only
(2) (i) and (ii)
(3) (iii) and (iv)
(4) (ii) and (iii)
Ans. (3)
Poets
Cat
Sol.
40.
Clearly, No dogs are cat
and No dogs are non-mammals
Given below is a diagram of three circles A, B and C inter-related with each other. The circle A represents the class of Indians,
the circle B represents the class of scientist and circle C represents the class of politicians, p, q, r, s......... represent different
regions. Select the code containing the region that indicates the class of Indian schismatics who are not politicians.
C
p
A
q
s
r
B
Codes :
(1) q and s only
(2) s only
(3) s and r only
(4) p, q and s only
Ans. (2)
Sol. Clearly from venn diagram S only indicate Indian scientists who are not politicians.
41. The next term in the series :
AB, ED, IH, NM,...........is
(1) TS
(2) ST
(3) TU
(4) SU
Ans. (1)
Sol. B A E D
IH
NM
TS
+3
+3
+4
+4
+5
+6
+5
+6
*Correction in the question AB replaced to BA.
If STREAMERS is coded as UVTGALDOR, then KNOWLEDGE will be coded as
(1) MPQYLCDFD
(2) MPQYLDCFD
(3) PMYQLDFCD
(4) YMQPLDDFC
Ans. (2)
42.
S
Sol.
T R E A M E R S
+2
K N O W L
–1
+2
U V T G A L D Q R
E D G E
–1
M P Q Y L D C F D
9
43.
A is brother of B. B is the brother of C. C is the husband of D. E is the father of A. D is related to E as :
(1) Daughter
(2) Daughter-inlaw
(3) Sister-inlaw
(4) Sister
Ans. (2)
Sol.
E
A
C
B
D
- Male,
– Femals Þ Couple
Two numbers are in the ratio 3 : 5. If 9 is subtracted from the numbers, the ratio becomes 12 : 23. The numbers are
(1) 30, 50
(2) 36, 60
(3) 33, 55
(4) 42, 70
Ans. (3)
44.
Sol. ATQ
3x - 9
12
=
5x - 9
23
by solving x = 1
No. are – 33, 55
45. The mean of the ages of father and his son is 27 years. After 18 years, father will be twice as old as his son. Their
present ages are
(1) 42, 12
(2) 40, 14
(3) 30, 24
(4) 36, 18
Ans. (1)
Sol.
Son
Father
x
y
ATQ
x+y
= 27
2
Þ
x + y = 54
....(1)
Q
y + 18 = 2 (x + 18)
y – 2x = 18
...(2)
by solving (1) and (2)
x = 12, y = 42
46. The next term in the series : 2,7,28,63,126, ......
(1) 215
(2) 245
(3) 276
(4) 296
Ans. (1)
Sol. Pattern : n3 + 1 , n3 – 1 in alternate.
47. A man pointing to a lady said” The son of her only brother is the brother of my wife”. The lady is related to the man
as
(1) Mother’s sister
(2) Grand mother
(3) Mother inlaw
(4) Sister of father inlaw
Ans. (4)
Lady
Sol.
Man
- Male,
– Femals Þ Couple
10
48.
In the series
6,4,1,2,2,8,7,4,2,1,5,3,8,6,2,2,7,1,4,1,3,5,8,6 how many pairs of successive numbers have a difference of 2 each ?
(1) 4
(2) 5
(3) 6
(4) 8
Ans. (NA)
6,4 ,1,2,2,8,7, 4,2 ,1, 5,3 , 8,6 ,2,2,7,1,4, 1,3,5,8,6
Sol.
Answer is 7 not given in option
49.
The mean marks obtained by a class of 40 students is 65. The mean marks of half of the students is found to be 45.
The mean marks of the remaining students is :
(1) 85
(2) 60
(3) 70
(4) 65
Ans. (1)
Sol. Total marks of 20 students
= 65 × 40 – 45 × 20 = 1700
mean =
50.
1700
= 85
20
Anil is twice as old as Sunita. Three years ago, he was three times as old as Sunita. The present age of Anil is :
(1) 6 years
(2) 8 years
(3) 12 years
Ans. (3)
Sol.
Sunita
Anil
x
2x
Before 3yrs
x–3
2x – 3
ATQ
2x – 3 = 3(x – 3)
by solving x = 6
\
Present age of Anil = 12
11
(4) 16 years