SSC Combined Graduate Level (CGL) Tier-I ,2015
GENERAL AWARENESS
ENGLISH COMPREHENSION
Directions (1-10) : In the following questions, a sentence/ part of the sentence is printed in italic. Below are given alternatives to the italic sentence/part of the sentence which may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is No Improvement.
Directions (11-17) : In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentences.
Directions (18-19) : In the following questions, four words are given in each question, out of which only one word is correctly spelt. Find the correctly spelt word as your answer.
Directions (20-24) : In the following questions, read the passage carefully and
choose the best answer to each question out of the four alternatives.
PASSAGE
STEM :
Half a century ago, a person was far More likely to die from heart disease. Now,
cancer is the No. 1 cause of death. Troubling as this sounds, the comparison is
unfair. Cancer is, ,by far the harder problem a condition deeply ingrained in the
nature of multicellular life. Given these obstacles, cancer researchers are fighting
and even winning smaller battles : reducing the death toll from childhood cancers
and preventing and sometimes even curing cancers that strike people in their
prime. But when it comes to diseases of the elderly, there can be no decisive
victory.
The diseases that one killed earlier in life bubonic plague, smallpox, influenza,
tuberculosis were easier obstacles. Each had a precise cause that could be
confronted. The toll of heart diseases has been pushed into the future, with diet,
exercise and medicine that help control blood pressure and cholesterol. Because of
these interventions people between 55 and 84 are increasingly more likely to die
from cancer than from heart disease.
Directions (25-29) : In the following questions, read the passage carefully and
choose the best answer to each question out of the four alternatives.
PASSAGE
STEM:
It is strange that, according to his position in life, an extravagant man is admired or
despised. A successful businessman does nothing to increase his popularity by
being careful with his money. He is expected to display his success, to have a smart
car, an expensive life, and to be lavish with his hospitality. If he is not so, he is
considered mean and his reputation in business may even suffer in consequence.
The paradox remains that if he had not been careful with his money in the first
place, he would never have achieved his present wealth. Among the two income
groups, a different set of values exists. The young clerk who makes his wife a
present of a new dress when he hadn’t paid his house rent, is condemned as
extravagant. Carefulness’with money to the point of meanness is applauded as a
virtue. Nothing in his life is considered more worthy than paying his bills. The ideal
wife for such a man separates her housekeeping money into joyless little piles, and
she is able to face the milkman with equanimity and never knows the guilt of
buying something she can’t really afford.
Directions (30-34) : In the following questions, some parts of the sentences have errors and some are correct. Find out which part of a sentence has an error. The number of that part is the answer. If a sentence is free from error, your answer is (4) i.e. No error.
Directions (35-39) : In the following questions, sentences are given with blanks to be filled in with an appropriate word(s). Four alternatives are suggested for each question. Choose the correct alternative out of the four as your answer.
Directions (40-42) : In the following questions, out of the four alternatives, choose the one which best expresses the meaning of the given word.
Directions (43-45) : In the following questions, choose the word opposite in meaning to the given word.
Directions (46-50) : In each of the following questions, four alternatives are given for the Idiom/ Phrase printed in italic in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase as your answer.
GENERAL INTELLIGENCE & REASONING
Directions (1-2) : In each of the following quesuor.s. a series is given, with one tern-. missing. Choose the correct alternative from the given ones that will complete the series.
Ans .
1
- Explanation :
325-66=259
259-55=204
204-44=160
160-33=127
127-22=105
105-11=94
Ans .
3
- Explanation :
A -> +2 -> C -> +2 -> E -> +2 -> G
Z -> -2 -> X -> -2 -> V -> -2 -> T
B -> +2 -> D -> +2 -> F -> +2 -> H
Y -> -2 -> W -> -2 -> U -> -2 -> S
Ans .
3
- Explanation :
Spider climbs 5x units in 15 minutes
Therefore, Spider climb 7x units in
\( \frac{15}{5}*7 \) = 21 minutes
Ans .
3
- Explanation :
Ramesh and Suresh are sons of Gopal
Govind is father of Gopal
Therefore, Suresh is grandson of Govind
Ans .
4
- Explanation :
There is only 'R' in the given woord.
Therefore, the word REVERSE cnnot be formed
A D V E R T I S E M E N T
==> A D V I S E
A D V E R T I S E M E N T
==> D I V E R S E
A D V E R T I S E M E N T
==> T I M E
Ans .
4
- Explanation :
1 : C D
2 : E F A
3 : D E F
Therefore, sequence is D E F A C
Hence , E is to the left of F
Ans .
3
- Explanation :
(i) 5742613 = PISNHIC
(ii) 2375416 = NAPISCH
(iii) 4572316 = SPINACH
(iv) 7234516 = INASPCH
Therefore, third option is the right ans .
Ans .
3
- Explanation :
B -> 1
R -> 9
O -> 8
A -> 1
D -> 2
A,B=1 ; C,D=2 ; E,F=3 ; G,H=4 ; I,J=5 ;
K,L=6 ; M,N=7 ; O,P= 8 ; Q,R=9 ; S,T=10 ;
U,V=11 ; W,X=12 ; Y,Z=13 .
Therefore;
C -> 2
L -> 6
0 -> 8
C -> 2
K -> 6
Ans .
2
- Explanation :
T -> -1 -> S
. A -> -1 -> Z
. P -> -1 -> O
. Similarly ;
F -> -1 -> E
. R -> -1 -> Q
. E -> -1 -> D
. E -> -1 -> D
. Z -> -1 -> Y
. E -> -1 -> D
.
Ans .
4
- Explanation :
M I N K = I N K
L A M P = L A P
T E A M = T E A
W A R M = W A R
Ans .
4
- Explanation :
876 => 8 + 7 + 6 => 21 => 12
864 => 8 + 6 + 4 => 18 => 81
895 => 8 + 9 + 5 => 22 => 22
Similarly,
824 => 8 + 2 + 4 => 14 => 41
Ans .
1
- Explanation :
Option (1)
256 % 16 @ 5 # 28 = 52
=> 256 % 16 x 5 - 28 = 52
=> 16 x 5 - 28 = 52
=> 80 - 28 = 52
Option (2)
256 # 16 % 5 # 28 = 120
=> 256 - 16 % 5 - 28 = 120
=> 256 - \( \frac{16}{5} \) - 28 \( \neq \) 120
Option (3)
256 @ 16 % 5 * 28 = 408
=> 256 x 16 % 5 + 28 = 408
=> \( \frac{256 x 5}{16} + 28 \neq \) 408
Option (4)
256 # 16 @ 5 % 28 = 80
=> 256 - 16 x 5 % 28 = 52
=> 256 - 16 x \( \frac{5}{28} \neq \) 52
=> 80 - 28 = 52
Ans .
2
- Explanation :
(16+18)*(21-11)*32*8
=> 34-10 = 32-8
=> 24 = 24
Ans .
4
- Explanation :
M O O N
Two consonants M and N = -2
Three consonants S , T and R = -3
Directions (15-18) : In each of the following questions, select the missing number from the given responses.
Ans .
4
- Explanation :
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16
16 * 2 = 32
32 * 2 = 64
64 * 2 = 128
128 * 2 = 256
Ans .
2
- Explanation :
7 * 2 - 1 = 13
10 * 2 - 1 = 19
20 * 2 - 1 = 39
Ans .
2
- Explanation :
\( \sqrt625 + \sqrt676 + \sqrt729 \)
=> 25 + 26 + 27 = 78
Similarly,
\( \sqrt289 + \sqrt324 + \sqrt361 \)
=> 17 + 18 + 19 = 54
Ans .
3
- Explanation :
First Column (2+4)*6 => 6*6 = 36
Second Column (3+6)*9 => 9*9 = 81
Third Column (4+8)*12 => 12*12 = 144
Ans .
4
- Explanation :
< West ; ^ North ; > East
Required distance ,
AE = \( \sqrt ((AF)^2+(EF)^2) \)
= \( \sqrt ((4)^2 + (3)^2 ) \)
= \( \sqrt (16+9) \)
= \( \sqrt (25) \)
= 5 km
Ans .
1
- Explanation :
AD = 5 km.
Directions (21-22) :In each of the following questions, one or two statements is given followed by four/two conclusions, I, II, III and IV. You have to consider the statements to be true, even if it seems to be at variance from commonly known facts. You are to decide which of the given conclusions can definitely be drawn from the given statements. Indicate your answer.
Ans .
1,2
- Explanation :
First Premise is Particular Affermative (I-type)
Second Premise is Universal Negative (E-type)
I + E => O - type of Conclusion
"Some bous are not black"
This is Conclusion I .
Conclusion II is the Converse of the first Premise.
Thus, both the Conclusions follow .
Ans .
4
- Explanation :
All scientists working in America are talented.
Some scientists working in America are Indians.
Therefore, Some talented Indian scientists have migrated to America.
Thus, some Indian scientists are talented.
Directions (23-28) : In each of the following questions, select the related word/letters/number from the given alternatives.
Ans .
1
- Explanation :
The raw matrial of book is paper.
Similarly, the raw material of bread is flour.
Ans .
4
- Explanation :
Q -> +2 -> S
D -> +2 -> F
X -> +1 -> Y
M -> +1 -> N
Similarly,
U -> +2 -> W
I -> +2 -> K
O -> +1 -> P
Z -> +1 -> A
Ans .
4
- Explanation :
B -> +2 -> D
A -> +3 -> D
D -> +4 -> H
Similarly,
C -> +2 -> E
U -> +3 -> X
T -> +4 -> X
Ans .
2
- Explanation :
4*4*4=64
Similarly,
2*2*2=8
Ans .
3
- Explanation :
7 * 7 = 49
7 * 8 = 56
Similarly,
6 * 6 = 36
6 * 7 = 42
Ans .
3
- Explanation :
Hot is antonym of cold.
Similarly, light is an antonym of dark
Directions (29-34) : In each of the following questions, find the odd word/letters/number pair from the given alternatives.
Ans .
1
- Explanation :
Except the letter group QRP, all other letter groups have at least one vowel
Ans .
3
- Explanation :
A -> +2 -> C -> +2 -> E -> +2 -> G
H -> +2 -> J -> +2 -> L -> +2 -> N
M -> +1 -> N -> +1 -> O -> -3 -> L
T -> +2 -> V -> +2 -> X -> +2 -> Z
Ans .
2
- Explanation :
Affirm is different from the other three words.
Ans .
4
- Explanation :
35-66=>66-35=31
71-94=>94-71=23
24-57=>57-24=33
56-70=>70-56=14
Ans .
3
- Explanation :
125 = 5 * 5 * 5
343 = 7 * 7 * 7
729 = 9 * 9 * 9
Ans .
3
- Explanation :
Density is different from the other three words
Directions (35-36) : In each the following questions, which one of the given responses would be a meaningful order of the following?
Ans .
3
- Explanation :
Meaningful order of words :
4. Jungle
3. Tinder
2. Pulp
5. Paper
1. Book
Ans .
3
- Explanation :
Meaningful order of words :
2. Population
1. Pollution
4. Disease
3. Death
Ans .
3
- Explanation :
12439+11110=23549
23549+11110=34659
34659+11110=54769
45769+11110=56879
Ans .
2
- Explanation :
l u b t u b / l u b t u b / l u b t u b
Ans .
1
- Explanation :
In a standard dice, the su, of two oppposute is 7.
Therefore,
1 lies opposite 6.
2 lies opposite 5.
3 lies opposite 4.
Ans .
3
- Explanation :
Ans .
1
- Explanation :
Ans .
2
- Explanation :
The required region should be common to all the three diagrams .
Such region is marked 'C'.
Ans .
3
- Explanation :
The number of students who study History and Biology = 16 + 4 = 20
Ans .
4
- Explanation :
11 students got distinction in all three subjects.
required percentage = \( \frac{11+100}{500} \) = 2.2 %
Directions (45-46) : In the following questions, which answer figure will complete the pattern in the question figure?
Ans .
2
- Explanation :
Ans .
3
- Explanation :
Ans .
3
- Explanation :
Ans .
2
- Explanation :
Ans .
2
- Explanation :
Ans .
4
- Explanation :
P => 57,66,75,87,96
E => 03,11,20,34,40
R => 00,13,22,33,42
S => 02,12,24,31,44
O => 56,67,76,86,97
N => 04,10,23,32,43
QUANTITATIVE APTITUDE
Ans .
2
- Explanation :
Total distance covered by train in 5 minutes
= (500 + 625 + 750 + 875 + 1000) metre = 3750 metre
= 3.75 km.
Time = 5 minutes = \( \frac{5}{60} \) hour = \( \frac{1}{12} \) hour.
Speed of train = \( \frac{Distance}{Time} \) = \( (\frac{3.75}{\frac{1}{12}}) \)kmph
= (3.75 * 12) kmph
= 45 kmph
Ans .
1
- Explanation :
Principal : Interest = 25 : 1
=> Interest : principal = 1 : 25
Therefore, Rate = \( \frac{S.I. * 100 }{Principal * Time } \)
= \( \frac{1}{25} \)* 100 = 4% per annum
Ans .
4
- Explanation :
Time = 5 minutes = \( \frac{1}{12} \) hour
Therefore, Length of bridge = Speed * Time
= 15 * \(\frac{1}{12}\) = \( \frac{5}{4} \)km
= \( (\frac{5}{4}*1000) \)metre
= 1250 metre
Ans .
1
- Explanation :
\( \frac{p^2}{q^2} + \frac{q^2}{p^2} \)= 1
=> \( \frac{p^4+q^4}{p^2q^2} \)= 1 => \(p^4+q^4\) = \(p^2q^2\)
=>\(p^4 + q^4 - p^2q^2 \)= 0 ............(i)
Therefore, \(p^6 + q^6\) = \((p^2)^3+(q^2)^3\)
= \( (p^2+q^2)(p^4+q^4-p^2q^2) \)
[Since, \( a^3+b^3 \) = \( (a+b)(a^2-ab+b^2\))]
= \((p^2+q^2)*0\)=0
5
Ans .
1
- Explanation :
m + 1 = \( \sqrt n + 3 \)(Given)
=> m + 1 - 3 = \(\sqrt n\)
=> m - 2 = \(\sqrt n\)
On cubing both sides ,
\( (m - 2)^3 \) = \( (\sqrt n )^3 \)
=> \( m^3 - 3m^2 * 2 + 3m(2)^2 - 2^3 \) = \( n\sqrt n \)
[Since , \( (a - b)^3 \) = \( a^3-3a^2b + 3ab^2 - b^3 \) ]
=> \( m^3 - 6m^2 + 2m - 8 \) = \( n\sqrt n \)
=> \( \frac{m^3 - 6m^2 + 12m - 8 }{\sqrt n} - n \) = 0
=> \( \frac{1}{2} [\frac{m^3 - 6m^2 + 12m - 8 }{\sqrt n } - n] \) = 0
Ans .
1
- Explanation :
\( \frac{x}{1} \) = \( \frac{a-b}{a+b} \)
By componendo And dividendo ,
\( \frac{1-x}{1+x} \) = \( \frac{1 - \frac{a-b}{a+b} }{1 + \frac{a-b}{a+b} } \)
= \( \frac{a+b-a+b}{a+b+a+-b} \) = \( \frac{b}{a} \)
Similarly,
\( \frac{1-y}{1+y} \)= \( \frac{c}{d} \);
\( \frac{1-z}{1+z} \)= \( \frac{a}{c} \);
Expresssion
= \( \frac{(1-x)(1-y)(1-z)}{(1+x)(1+y)(1+z)} \)
= \( \frac{b}{c} * \frac{c}{b} * \frac{a}{c} \)= 1
Ans .
3
- Explanation :
\( \frac{\sqrt 7 - 1}{\sqrt 7 + 1} - \frac{\sqrt 7 + 1 }{\sqrt 7 - 1} \) = a + \( \sqrt 7 b \)
=>\( \frac{( \sqrt 7 - 1 )^2 - ( \sqrt 7 + 1)^2}{( \sqrt 7 + 1)( \sqrt 7 - 1 )} = a + \sqrt 7 b \)
=> \( \frac{-4 * \sqrt 7 * 1}{7 - 1} \)= a + \( \sqrt 7 \) b
[Since, \((a-b)^2-(a+b)^2\)=-4ab]
=>\( \frac{-4 \sqrt 7 }{6} \)= a + \( \sqrt 7 \)b
=> 0 - \( \frac{2}{3} \sqrt 7 \)= a + \( \sqrt 7 \)b
=> a = 0 , b = -\( \frac{2}{3} \)
Ans .
3
- Explanation :
\( \frac{1}{\sqrt 2 + 1 } \) = \( \frac{(\sqrt 2 - 1)}{(\sqrt 2 + 1)(\sqrt 2 - 1)} \)
( Rationalising the denominator )
\( \frac{\sqrt 2 - 1}{2 - 1} \) = \( \sqrt 2 - 1 \) \( \frac{1}{\sqrt 2 + \sqrt 3 } \) = \( \sqrt 3 - \sqrt 2 \)
\( \frac{1}{\sqrt 4 + \sqrt 3 } \) = \( \sqrt 4 - \sqrt 3 \)
\( \frac{1}{\sqrt 8 + \sqrt 9 } \) = \( \sqrt 9 - \sqrt 8 \)
Therefore, Expresssion = \( \sqrt 2 - 1 + \sqrt 3 - \sqrt 2 + \sqrt 4 - \sqrt 3 + \sqrt 5 - \sqrt 4 + \sqrt 6 - \sqrt 5 + \sqrt 7 - \sqrt 6 + \sqrt 8 - \sqrt 7 + \sqrt 9 - \sqrt 8 \) = \( \sqrt 9 - 1 \) = 3 - 1 = 2
Ans .
4
- Explanation :
\( \frac{\sqrt (a+2b)+ \sqrt (a-2b)}{\sqrt (a+2b)- \sqrt (a-2b)} \) = \( \frac{\sqrt 3}{1} \)
By componendo and dividendo,
\( \frac{\sqrt (a+2b)+ \sqrt (a-2b) +\sqrt (a+2b)- \sqrt (a-2b) }{\sqrt (a+2b)+ \sqrt (a-2b) - \sqrt (a+2b)+ \sqrt (a-2b)} \) = \( \frac{\sqrt 3 + 1}{\sqrt 3 - 1} \)
=> \( \frac{\sqrt (a+2b)}{\sqrt (a-2b)} \)= \( \frac{\sqrt 3 + 1}{\sqrt 3 - 1} \)
On squaring,
\( \frac{a+2b}{a-2b} \) = \( \frac{3+1+2\sqrt 3 }{3+1-2 \sqrt 3} \) =\( \frac{4+2\sqrt3}{4-2\sqrt3} \)
=> \( \frac{a+2b}{a-2b} \)= \( \frac{2 + \sqrt 3}{2 - \sqrt 3} \)
By componendo and dividendo,
\( \frac{a+2b+a-2b}{a+2b-a+2b} \)= \( \frac{2 + \sqrt 3 + 2 - \sqrt 3}{2 + \sqrt 3 + 2 + \sqrt 3} \)
=> \( \frac{2a}{4b} \) = \( \frac{4}{2\sqrt 3} \) => \( \frac{a}{2b} \) = \( \frac{2}{\sqrt 3} \)
=> \( \frac{a}{b} \) = \( \frac{4}{\sqrt 3} \)
Ans .
1
- Explanation :
Ans .
2
- Explanation :
Sum og interior angles of a pentagon
= (2n - 4 )* 90
= (2 * 5 - 4 )* 90 = 540 If PQ = QR = RS = ST
\( \angle POQ \) = \( \angle QOR = \angle ROS = \angle SOT = \frac{180}{4} = 45 \)
OP = OQ = OR = OS = OT = radii
\( \angle OPQ = \frac{180-45}{2} = \frac{135}{2} \)
\( \angle PQR - \angle RST = 4 * \frac{135}{2} = 270 \)
Ans .
4
- Explanation :
x = \( \frac{\sqrt 3 + \sqrt 2 }{\sqrt 3 - \sqrt 2 } \)
= \( \frac{(\sqrt 3 + \sqrt 2 )(\sqrt 3 + \sqrt 2 )}{(\sqrt 3 - \sqrt 2 )(\sqrt 3 +\sqrt 2)} \)
(Rationalising the denominator )
= \( \frac{(\sqrt 3 + \sqrt 2 )^2}{(\sqrt3)^2 - (\sqrt 2)^2} \)
= \( \frac{3+2+2\sqrt 6}{3-2} = 5 + 2 \sqrt 6 \)
= \( \frac{1}{x} = \frac{1}{5+2\sqrt 6} \)
= \( \frac{(5 - 2\sqrt 6)}{(5 + 2 \sqrt 6 )(5 - 2 \sqrt 6)} \)
= \( \frac{5 - 2 \sqrt 6}{25-24} \)
= 5 - 2 \sqrt 6
Therefore, \( x+\frac{1}{x}=5+2 \sqrt 6 + 2 - 2 \sqrt 6 = 10 \)
Therefore, \( x^3+\frac{1}{x^3} = (x+\frac{1}{x})^3-3x*\frac{1}{x}(x+\frac{1}{x}) \)
= \( (10)^3-3*10 \)
= 00 - 30 = 970
Ans .
3
- Explanation :
Ans .
2
- Explanation :
D, is the mid-point of BC.
AB = AC = 10 cm
AD is perpendicular to BC
BD = \( \sqrt (AB^2-AD^2) \)
\( = \sqrt (10^2-8^2) = \sqrt (100-64) = \sqrt 36 = 6 cm.\)
Therefore BC = 2 BD = 2 * 6 = 12 cm
Ans .
2
- Explanation :
QB = Tangent = 12 cm.
OQ = 13 cm .
\( \angle QBO = 90 \)
From ΔOQB,
OB = \( \sqrt (OQ^2-QB^2) \)
= \( \sqrt (13^2-12^2) \)
= \( \sqrt (169-144) \)
= \( \sqrt 25 = 5 \)cm.
Therefore, AQ = Shortest distance = OQ -OA = 13-5 = 8 cm.
Ans .
2
- Explanation :
\( \angle BAC = 90 \), from ΔABC, BC \( \sqrt (AB^2+AC^2) \)
= \( \sqrt (6^2+8^2) \)
= \( \sqrt (36+64) \)
= \( \sqrt 100 = 10 \)cm.
Seim-Perimeter of ΔABC = s = \( \frac{6+8+10}{2} = \frac{24}{2} = 12 \)cm.
Area of ΔABC = \( \frac{1}{2} * AC * AB \)
= \( \frac{1}{2}*8*6 \)= 24 sq.cm
In-radius = \( \frac{Δ}{s} = \frac{24}{12} = 2 cm \)
Ans .
4
- Explanation :
OA = OB = OC = \( \frac{AB}{2} \)
Therefore AC = \( \sqrt (OQ+A^2+OC^2) \)
=\( \sqrt ((\frac{AB}{2})^2+(\frac{AB}{2})^2) \)
= \( \sqrt (\frac{AB^2+AB^2}{4}) = \sqrt \frac{AB}{2}^2 = \frac{AB}{\sqrt 2} \)
Ans .
2
- Explanation :
ΔABC is similar to ΔDEF
Therefore, \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \)
= \( \frac{AB+BC+AC}{DE+EF+DF} = \frac{4}{1}\)
= \( \frac{Area of ΔABC}{Area of ΔDEF} = \frac{AB^2}{DE^2} = \frac{16}{1} \)
Ans .
3
- Explanation :
At 7:20,
Number of hours = \( 7\frac{20}{60} = 7\frac{1}{3} = \frac{22}{3}\)hours
The hour-hand traces 360° in 12 hours
Therefore, required angle = 220°-120°=100°
therefore, Angle traced by hour hand in \( \frac{22}{3} \) hours
= \( \frac{360°}{12}*\frac{22}{3} = 220 °\)
Since, Minute Hand traces 360° in 60 minutes .
Therefore, Angle traced by minute hand in 20 minutes = \( \frac{360°}{12}*20 \)= 120°
Ans .
4
- Explanation :
cos 230° + sin2 60° + tan2 45°+ sec260° + cos0°
= \( (\frac{\sqrt 3}{2})^2 + (\frac{\sqrt 3 }{2})^2 + 1^2 + 2^2 + 1 \)
= \( \frac{3}{4}+\frac{3}{4}+1+4+1 \)
= \( 6 + \frac{3+3}{4} \)
= \( 6+\frac{6}{4} = 6 +\frac{3}{2} = \frac{12+3}{2} = \frac{15}{2} = 7\frac{1}{2}\)
Ans .
4
- Explanation :
AB = Building = 48 metre
BC = Shadow = 48 \( \sqrt 3 \) metre
\( \angle ACB = \)?
Therefore tan \( \theta = \frac{AB}{BC} = \frac{48}{48\sqrt 3 } \)
=> tan \( \theta = \frac{1}{\sqrt 3} \)= tan 60°
=> \( \theta \) = 30°
Ans .
4
- Explanation :
cos x + cos2 x = 1
=> cos x = 1 - cos2x
=> cos x = sin 2 x ..........(i)
Therefore, sin8 x + 2 sin6 x + sin4 x
= \( (sin^4 x + sin^2 x) \)^2
= \( ((cos x)^2 + sin^2 x)^2 \)
= 1
Ans .
4
- Explanation :
\( \angle BAC = 85°\)
\( \angle BCA = 75°\)
\( \angle ABC = 180°-85°-75°=20°\)
Angle subtended by an arc at the centre is twice to that subtended at any point in the sircumfrance .
Therefore, \( 2 \angle ABC = \angle AOC \)
Therefore, \( \angle OAC = 40° \)
In ΔOAC,
OA =OC = radii
Therefore, \( \angle OAC = \angle OCA \)
Therefore, \( 2 \angle OAC = 180°-40°=140° \)
=> \( \angle OAC = \frac{140°}{2} = 70° \)
Ans .
3
- Explanation :
x = p cosec \( \theta \)
=> cosec \( \theta = \frac{x}{p} \)
Again , y = q cot \( \theta \)
=> cot \( \theta = \frac{y}{q} \)
Therefore, \( cosec^2 \theta - cot^2 \theta \)= 1
=> \( \frac{x^2}{p^2} -\frac{y^2}{q^2} \) = 1
Ans .
4
- Explanation :
OC = Height of plane = h km (let)
\( \angle DOA = \angle OAC = \)60°;
\( \angle BOE = \angle OBC= \)30°
AB = 2 km.
AC = x km(let)
Therefore, BC = (2-x) km.
From, ΔOAc
tan 60° = \( \frac{OC}{AC} \)
=> \( \sqrt 3 = \frac{h}{x} \)
=> x = \( \frac{h}{\sqrt 3 } \)km......(i)
From ΔOBC,
tan 30° = \( \frac{OC}{CB} \)
=> \( \frac{1}{\sqrt 3} = \frac{h}{2-x} \)
=> \( \sqrt 3 h = 2 - \frac{h}{\sqrt 3 }\)
[From equation (i)]
=> \( \sqrt 3 h + \frac{f}{\sqrt 3 }= 2 \)
=> \( \frac{3h+h}{\sqrt 3} = 2 \)
=> \( 4h=2\sqrt 3 \)
=> h = \( \frac{2\sqrt 3}{4} = \frac{\sqrt 3}{2} \)km. = \( \frac{1.732}{2} = 0.866\)km.
Ans .
3
- Explanation :
In ΔABC,
\( AB^2 = AC^2+BC^2 \)
=> \( c^2 = a^2+b^2 \)..........(i)
From ΔABC,
cosec B = \( \frac{AB}{AC} = \frac{c}{b} \).........(ii)
cos A = \( \frac{AC}{AB} = \frac{b}{c} \)
Therefore, cosec B - cos A = \( \frac{c}{b}-\frac{b}{c} \)
= \( \frac{c^2-b^2}{bc} = \frac{a^2}{bc} \)
Ans .
4
- Explanation :
\( \sqrt(\sqrt(\sqrt 0.00000256)) \)
=\( \sqrt(\sqrt(0.0016) \)
=\( \sqrt 0.04 \)
= 0.2
Ans .
2
- Explanation :
1 man \( \equiv 2 women \equiv 3 boys \)
Therefore, 1 man + 1 woman + 1 boy \( \equiv \) 3 boys + \(\frac{3}{2} \)boys + 1 boy
\( \equiv \)(3+\frac{3}{2}+1)boys \( \equiv \frac{11}{2}\)boys
Therefore, By \( M_1D_1 = M_2D_2 \),
3*44=\( \frac{11}{2}*D_2 \)
=> \( D_2 = \frac{2*3*44}{11} = 24 \)days
Ans .
2
- Explanation :
.
Ans .
3
- Explanation :
=> 18 * 2 * 12 * 6 * 8x = 32 * 3 * 9 * 9 * 10 * 8
=> x = \( \frac{32 * 3 * 9 * 9 * 10 * 8}{18 * 2 * 12 * 6 * 8} \)
= 30 days
Ans .
1
- Explanation :
Part of tank filled by inlet pipe in 1 hour = \( \frac{1}{6} - \frac{1}{6} = \frac{4-3}{24} = \frac{1}{24} \)
Hence, if there is no leak , the inlet pipe will fill the tank in 24 hours.
Capacity of the tank = 24 * 60 * 4 = 5760 litres
Ans .
4
- Explanation :
Required percentage increase in area = \( (x+y+\frac{xy}{100}) \)%
= \( 20+20+\frac{20*20}{100} \)%
= 44%
Ans .
4
- Explanation :
Whole surface area of a brick = 2 (l*b+b*h+h*l)
= 2 (22.5*10+10*7.5+7.5*22.5)
= 2 (225+75+0.75*225)
= 150 * 6.25
= 937.5
Number of Bricks = \( \frac{9.375*100*100}{937} \)= 100
Ans .
- Explanation :
Length of park = 3x metre (let)
Breadth = 2x metre
Perimeter of park = Distance covered by cyclist = \( \frac{12*8}{60} = \frac{8}{5} \)km.
= \( (\frac{8}{5}*1000) \)metre
= 1600 metre
According to the Question,
2(3x+2x)=1600
10x = 1600 => x = \( \frac{1600}{10} = 160 \)
Therefore, Area of the park = 3x*2x
= \(6x^2 = 6 * (160)^2\) = 153600 sq.metre
Ans .
1
- Explanation :
Required single discount = \( x+y-\frac{xy}{100} \)%
= \( 20+15+\frac{20*15}{100} \)%
= (35-3)% = 32%
Ans .
2
- Explanation :
Let the marked price of article be Rs.x and its C.P. Rs.100,
According to the question,
\( x * \frac{80}{100} = \frac{100*120}{100}\)
=> x = \( \frac{120*100}{80} \)= Rs.150
S.P. after a discount of 30% = \( \frac{150*70}{100} \)
= Rs.105 i.e. gain = 5%
Ans .
3
- Explanation :
Single equivalent discount for 20% and 10%
= \( (20 + 10 - \frac{20*10}{100} ) \)%
= 28%
Therefore, C.P. = (100-28)% of 1500
= \( \frac{1500*72}{100} \) = Rs.1080
Actual C.P.=Rs.(1080+20)
= Rs. 1100
Therefore, S.P. on 20% profit = \( \frac{1100*120}{100} \)= Rs.1320
Ans .
2
- Explanation :
Let each vessel contain 1 litre of mixture.
Therefore, Total quantity of milk = \( \frac{6}{7}+\frac{5}{7}+\frac{3}{4} \)
= \( \frac{24+20+21}{28} = \frac{65}{28} \)litre
Total quantity of water = \( \frac{1}{7}+\frac{2}{7}+\frac{1}{4} \)
= \( \frac{4+8+7}{28} =\frac{19}{28} \)litre
Therefore, Required Ratio = \( \frac{65}{28} : \frac{19}{28} \)
= 65:19
Ans .
2
- Explanation :
x+x+1+x+2+x+3+x+4+x+5=6K
6x+15=6K
\( x + \frac{15}{6} = K \)
\( x + \frac{5}{2} = K \).......(i)
Again,
\( \frac{x+(x+1)+......(x+6)+(x+7)}{8} \)
= \( \frac{8x}{8}+\frac{28}{8}=x+\frac{7}{2}\)......(ii)
Now, \(x+ \frac{7}{2}-x+\frac{5}{2} = 1 \)
Ans .
1
- Explanation :
Let incomes of A and B be Rs.3x and Rs.2x respectively.
Let the expenditure of A and B be Rs.5y and Rs.3y respectively.
According to the question,
3x-5y=1000......(i)
2x-3y=1000......(ii)
By equation (i)*2 - (ii)*3
-y = -1000
Therefore y = 1000
From equation (i),
3x = 6000
Ans .
4
- Explanation :
Let C.P. of each article be Re.1.
Therefore, C.P. of 9 particles = Rs.9
Therefore, S.P. of 9 particles = rs.10
Therefore, Profit percent = \( \frac{10-9}{0.9}*100 = 11\frac{1}{9} \)%
Ans .
4
- Explanation :
Required percentage change = \( 10-20+\frac{10*-20}{100} \)%
= -12% Negative sign shows decreas
Ans .
2
- Explanation :
Sum of the cubes of first n natural numbers = \( \frac{n^2(n+1)^2}{2^2} \)
Their average = \( \frac{n(n+1)^2}{4} \)
here n=7,
Therefore ,
mean = \( \frac{7(7+1)^2}{4} = \frac{7*8*8}{4} = 112 \)
Directions (44-47): Study the following bar diagram carefully and answer the
four questions.
Production of buses of company A and company B over the given years.
Ans .
2
- Explanation :
Percentage increase
Year 2010 => \( \frac{70-64}{64}*100 \)= 9.4
Year 2011 => \( \frac{77-70}{70}*100 \)= 10
Year 2012 => \( \frac{85-77}{77}*100 \)= 10.4
Ans .
1
- Explanation :
Required average production = \( \frac{72+90+100}{3} \) thousands
= \( \frac{262}{3} = 87.33 \)thousands
Ans .
2
- Explanation :
Required average production = \( \frac{70+77+85+93}{4} \) thousands
= \( \frac{325}{4} = 81.25 \)thousands
Ans .
3
- Explanation :
Required Ratio = \( (\frac{64+70}{2}):(\frac{72+80}{2}) \)
= 67:76
Directions (48-50) : The pie-chart shows the proposed outlay for different
sectors during a Five-Year plan of Government of India. Total outlay is Rs. 40,000
crores. By reading the pie-chart answer the following three questions.
Ans .
2
- Explanation :
Since, 360° = Rs.40000 crores
Therefore, 1° = \( \frac{40000}{360} \)
Therefore, 72° = \( \frac{72*40000}{360} \)
= Rs.8000 crores
Ans .
1
- Explanation :
According to the Question ,
Outlay on argiculture x \( \frac{x}{100} \)
= Outlay of irrigation
=> 108° x \( \frac{x}{100} \) = 54%
=> x = \( \frac{54*100}{108} \)= 50%
Ans .
4
- Explanation :
Required Ratio = 54:45
= 6:5