Model Questions on MATH SET 2

1. The selling price of 10 oranges is the cost price of 13 oranges. then the profit percentage is :
(1) 30%
(2) 10%          
(3) 13%                               
(4) 3%


2.  A shop man bought pens at the rate of 7 for Rs10 and sold them at the profit of 40%.how many pens would a customer get for Rs 10.
(1) 6                                   
(2) 4
(3) 5                                   
(4) 3

3.  A train running at 36 km/hr passes another train completely in 12 s, which is half of its length, running in the opposite direction at 54 km/hr. If it also passes a railway platform in 1.5 min, what is the length of the platform (in meters)?
(1) 700                               
(2) 860                        
(3) 900                               
(4) 1, 000   

       
4.  Two rice varieties costing Rs 20 per kg and Rs 30 per kg were mixed as 2 : 3 and sold so as to gain 10%. What was the SP of the mixture (Rs/kg)?
(1) 31.2                              
(2) 28.6                       
(3) 30                                 
(4) 26      
        
5.  A circle of radius 8 cm has its radius decreased by 2 cm. What is the approximate percentage decrease in area?
(1) 25%                             
(2) 50%                      
(3) 38%                             
(4) 43.75%   
  
6.  In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?
(1) 1520                             
(2) 1250                      
(3) 2008                             
(4) None of these

7. The ratio of the present ages of Sonu and Monu is 7: 6 respectively. Eight years ago the respective ratio of their ages was 5 : 4. What will be Monu’s age four years from now?
(1) 28 years                       
(2) 32 years    
(3) 24 years                       
(4) 30 years    

8. The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?
(1) 7                                   
(2) 9                
(3) 11                                 
(4) 5   
             
9. A invests Rs. 24000 to start a business. Four months later B joins him by investing Rs. 31000 and after another two months C joins them by investing Rs. 40000. At the end of one year the business earns a profit of Rs. 12028. What is C's share in the profit?
(1) Rs. 4464                      
(2) Rs. 3844   
(3) Rs. 3720                      
(4) Rs. 3270   

10. 2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
(1) 4                                   
(2) 8                
(3) 6                                   
(4) 2

Answers with solutions:


1.(1) 
Profit percentage = (13-10)*100/10 = 30%

2. (3) 
The S.P. of 7 pens = 10*140/100 = Rs 14
∴The S.P. of I pens = 14/7 = Rs 2
∴The pens for Rs 10 = 10/2 = 5

3. (1)
Crossing time = l1+ l2 / relative speed
l1 = x
l2 = x/2
Relative speed = 36 + 54 = 90 km/hr = 90 x 5/8 = 25 m/s
Time = 12 sec
12 = x + x/2 / 25
x = 200 m
Now train crossing the platform
l1 = 200 m,    l2 = length of platform = y
Time = 1.5 min = 90 sec
Speed = 36 km/hr = 10 m/s
90 = 200 + y / 10
Y = 700 m

4.  (2) 
CP of the mixture = 20 x 2 + 30 x 3  / 5   = 26
SP = 1.1 x 6 = 28.6

5.  (4) 
Original area of the circle = π (8)2 = 64 π
New area of the circle = π (6)2 = 36 π
% decrease in area = 64 π  - 36 π / 64 π x 100 = 43.75%

6.  (4) 
Total Students in school = 3600
Number of boys = 4/9 x 3600 = 1600
Number of boys who like hockey = 20% of 1600 = 320
Number of girls = 2000
Number of girls who like hockey = 60% of 2000 = 1200
Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080 

7.  (1)
Let the present ages of Sonu and Monu be 7x and 6x. Now
7x – 8 /6x – 8 = 5/4
x = 4
Present age of Monu = 24 years
Monu’s age four years from now = 24 + 4 = 28 years

8.  (2)
 Let the numbers be x, x + 2 and x + 4. Then
x + (x + 2) + (x + 4) = x + 20
x = 7
So the middle number is 9.

9.  (3)
 The ratio of their investments = 24000 x 12: 31000 x 8 : 40000 x 6 = 36 : 31:30
Since the ratio of investment is also the ratio of profit,
C’s share = 30/97 x 12028 = 3720

10. (2) 
2 M x 6 = 2 W x 9 = 3 C x 8
2 M = 3 W = 4 C
The ratio of efficiency of man, woman and children = 1/2: 1/3: 1/4 = 6: 4: 3
Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.
So the total work to be done = 2x6x6 = 72 units
Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units
Remaining work = 72 – 24 = 48 units
Number of men required to complete the remaining work in one day = 48/6 = 8

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Model Questions on Math SET 1 with solution for TA written Exam

Model Paper of Math SET 1

1. The average age of 40 boys in a class is 15. The average age of a group of 18 boys in the class is 16 and the average age of another 12 boys in the class is 14. What is the average age of the remaining boys in the class?
(1) 15•25 years
(2) 14.4 years
(3) 14•75 years
(4) None of these

2. Ruby invested an amount of Rs. 5,800 for 2 years. At what rate of compound interest will she get an amount of Rs. 6394•5 at the end of two years ?
(1) 5 p.c.p.a.
(2) 4 p.c.p.a.
(3) 6 p.c.p.a.
(4) 8 p.c.p.a.

3. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
(1) 6 hrs
(2) 9 hrs
(3) 15 hrs
(4) None of these

4. A lent Rs 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest is
(1) 5%
(2) 7%
(3) 8%
(4) None of these

5. Train A and B travel to a place at a speed of 35 and 55 km/h respectively. If car B takes 7/2  hours  less time than A for the journey, the distance of the place is_
(1) 300.25 km
(2) 400 km
(3) 350.565 km
(4) 336.875 km

6.  In an exam, 60% of the total student passed. If the number of failed students is 320 then the total number of students is
(a) 600
(b) 700
(c) 800
(d) 900

7.  A cycle is bought for Rs 840 and sold at Rs 920. What is the percentage gain
(a) 10.50%
(b) 8.52%
(c) 7.35%
(d) 9.52%

8.  If Raj’s salary is 30% more than Amar’s salary, the how many percent is Amar’s salary less than that of Raj’s?
(a) 56%
(b) 23.07%
(c) 50/3%
(d) 50.6%

9. Find the number of ways in which 5 different beads can be arranged to form a necklace.
(a) 120
(b) 60
(c) 30
(d) 12

10. A card is drawn from a pack of playing cards, what is the probability of getting either a red or a red queen?
(a) 4/13
(b) 7/13
(c) 1/13
(d) 1/26

ANSWERS

1. (2)
Total students are 40 × 15 = 600
So, 18 x 16 + (12 + 14) = 456
Left student is 10 and their average is =600-456= 144÷ 10=14.4

2. (1)
The interest in 2 years is 594.5 which is 10.25% of 5800. Hence the rate of interest is 5% p.a.

3. (2)
Upstream speed = 5 km/hr
Downstream speed = 15 km/hr
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs

4. (4)
Let the rate of interest is=x
(X * 5000 * 2)/100 + (3000 * 4 * x)/100 = 2200
x = 10%

5. (4)
Let Car A takes t hrs to reach  the place
Distance is same,
35 t = 55(t – 7/2)
T = 77/8
Distance = 35 * 77/8 = 336.87 km

6. (c)
Let the number of student is x out of that 40% have failed.
40/100 * x = 320
x = 320 * 100/40 = 800

7. (d)
CP = Rs 840 and SP = Rs 920
Gain = 920 – 840 = Rs 80
gain percentage = 80/840 * 100 = 9.52%

8. (b);
Amar’s salary is less than of Raj 2y
(R/100 + R * 100)% = (30/(100 + 30) * 100)%
(30/130 *100 )% = 300/13% = 23% APPROX

9. (d)
According to formula:
Number of arrangements = (5-1)!/2 = 12

10. (b)
26/52 + 2/52 = 28/52 = 7/13

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Model Papers of Reasoning for TA written exam

Practice Papers.

Practice Mock test Papers with solution for TA written exam.

Mock test for Reasoning

Paper 1: Reasoning 1

Paper 2: Reasoning 2

Paper 3: Reasoning 3

Paper 4: Reasoning 4

Paper 5: Reasoning 5

Paper 6: Reasoning 6

Paper 7: Reasoning 7

Paper 8: Reasoning 8

Paper 9: Reasoning 9

Paper 10: Reasoning 10

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Best Books for Territorial Army Exam Preparation

ITA written exam is one of the toughest exam as compare to others, but some candidates find it easier and don't find need of any preparation or coaching necessary it. 
Apparently there are only few candidates who makes it without any preparation or professional coaching. 
Practice makes a man perfect, indeed it got some meaning in it.

If you are a serious TA aspirant and ready to do some smart and hard work to join Indian Territorial Army , then start your preparation from scratch. Here are two good and recommended books which are going to be helpful for your TA written exam preparation. You can buy these books online with huge discounts from the links mentioned below.

• A Modern Approach To Verbal & Non-Verbal Reasoning by RS Aggarwal

Its a decent book for preparing for competitive exams & building logical & reasoning skills. Its like an All-in-One with everything in it

• Objective General English

Quite good for competitive exams and even for learning English Grammar and vocabulary.

 

• Lucent General Knowledge (Subjective)

Use it for best result and batter guidance. The contents are good enough to choose for any competitive examinations.

• Quantitative Aptitude by R. S. Aggarwal

In most of the competitive exams the syllabus will be too huge and Quantitative aptitude will be a part of it, the book covers almost all concepts related to quantitative aptitude in detail.

All the Best for Territorial Army Exam.....

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Previous year Question Papers of Territorial Army Written Exam

See the pattern of occurrence of the questions. That will give you an idea as to which topics to concentrate on. Read More

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Permission/NOC to Civil Government Servants to join Territorial Army

If you face any trouble to get a NOC or stamp & signature on application form from your Office,
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Medical Procedure of the Recommended Candidates at SSB

★ Recommended candidates appear before the medical board for carrying out their medical board after the SSB results.
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Complete Syllabus for Territorial Army Written exam, July 2106

The Syllabus for TA (PIB) Written exam has been modified as under.

Changes will be implemented with effect from July PIB onwords.

Syllabus of the Examination.

STANDARD :
The standard of the papers in Elementary Mathematics will be a
Matriculation level. The standard of papers in other subjects will
approximately be such as may be expected of a graduate of an Indian
university.

SYLLABUS :
Paper – I. 
Reasoning and Elementary Mathematics.
(a) Part – 1. Reasoning. The question paper will be designed to test
the candidates ability to complete sequences making logical conclusion based on simple patter of numbers, statements, figures,letters etc as may be expected of a rational thinking person without any special study of the subject.
(b) Part – 2. Elementary Mathematics.
(i) Arithmetic. Number System – natural numbers, integers,
rational and real numbers. Fundamental operations – addition,
subtraction, multiplication, division, square roots, decimal fraction.
(ii) Unitary Method. Time and distance, time and work, percentages, application to simple and compound interest, profit and loss, ratio and proportion, variation.
(iii) Elementary Number Theory. Division algorithm, prime and
composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 & 11.
Multiples and factors, factorization theorem, HCF and LCM. Euclidean algorithm, logarithms to base 10, laws of logarithms, use of logarithmic tables.
(iv) Algebra. Basic operations, simple factors, remainder theorem,
HCF, LCM, theory of polynomials, solutions of quadratic equations,relation between its roots and coefficients (only real roots to be considered). Simultaneous linear equations in two unknowns-analytical and graphical solutions. Simultaneous linear equations in two variables and their solutions. Practical problems leading to two simultaneous liner equations or in equations in two variables or quadratic equations in one variable and their solutions. Set language and set notation, rational expressions and conditional identities, laws of indices.
(v) Trigonometry. Sine x, cosine x, tangent x when O° < x < 90°.
Values of sine x, cos x and ten x, for x = 0°, 30°, 45°, 60° & 90°.
Simple trigonometric identities. Use of trigonometric tables. Simple
cases of heights and distances.
(vi) Geometry. Lines and angles, plane and plane figures theorems on

• Properties of angles at a point.
• Parallel lines.
• Sides and angles of a triangle.
• Congruency of triangles.
• Similar triangles.
• Concurrence of medians and altitudes.
• Properties of angles, sides and diagonals of a parallelogram, rectangle and square.
• Circle and its properties, including tangents and normal.
• Loci.

(vii) Mensutration. Areas of squares, rectangles, parallelograms,
triangle and circle. Areas of figures which can bisect into the figures (field book). Surface area and volume of cuboids, lateral surface and volume of right circular area of cylinders. Surface area and volume of spheres.
(viii) Statistics. Collection and tabulation of statistical data, graphical representation-frequency polygons, bar charts, pie charts, etc.Measures of central tendency.

Paper – II. 
General Knowledge and English.
(a) Part – 1. General Knowledge. General knowledge including
knowledge of current events and such matters of everyday observation and experience in scientific aspects as may be expected of an educated person who has not made a special study of any scientific subject. The paper will also include questions on history of India and geography of nature which candidates should be able to answer without special study.
(b) Part – 2. English. The question paper will be designed to test the
candidates’ understanding of English and workman - like use of words.
Questions in English are from synonyms, antonyms, reading
comprehension, Para jumbles, error spotting, jumbled sentences,
sentence correction and fill in the blanks.

P:S: Use Black ball point pen only while circling in OMR sheet.

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Join Indian Territorial Army as an Officer, Recruitment JULY 2016

Applications are invited from gainfully employed young men for an opportunity of donning the uniform and serving the nation. Territorial Army Officers,based on the concept of enabling 
motivated young men to serve in a military environment without having to sacrifice their primary professions.

Date of written Exam:  31 JULY 2016

Last Date of Receipt of Application : 30 JUNE 2016 at respective Territorial Army Group Headquarters.

Type of Exam : Objective (OMR Answer Sheet will be used)

Qualifying Marks : Minimum 40% marks in each part of the paper

separately and overall average of 50%. 

CONDITIONS OF ELIGIBILITY :

• (a) Nationality : Only male citizens of India.
• (b) Age Limits : 18 to 42 years on the date of application.
• (c) Educational Qualifications : Graduate from any recognized university.
• (d) Physical Standards : A candidate must be physically and medically fit in all respects.
• (e) Employment : Gainfully Employed.
• Note : Serving member of the Regular Army/ Navy/ Air Force/ Police/GREF/ Para Military and like forces are not eligible

PENALTY FOR WRONG ANSWERS : Candidates should note that there will be penalty (Negative Marking) for wrong answers marked by a candidate in the Objective Type Question Papers.

HOW TO APPLY: 

All desirous civilian candidates can obtain Application Form from Employment News or download from www.indianarmy.nic.in (FREE OF COST) and send it alongwith self addressed envelope (28 x12 cms) with postal stamps affixed worth Rs. 27/- and two passport size photographs (No other cost for submission) to the respective Territorial Army Group Headquarters as per the choice of following examination centres. NO OTHER DOCUMENTS TO BE ATTACHED WITH APPLICATION FORM.

Click here to download Complete Advertisement

Click here to download Application form

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Training Process of Indian Territorial Army

Training in Infantry TA is carried out on Urban and provincial systems.

Urban systems of training : Training is carried out on weekends and holidays. Four hours training is counted as one day.

Recruit Training : 32 days in the first year only including a camp of not less than 4 days if the trainee volunteers with the written consent of his employer, if any.

Annual Training : A minimum of 30 days extendible up to a maximum of 60 days including a camp for 14 days.

Post Commission Training: All Officers are required to undergo 10 weeks of Post commission Training within two years of their commissioning.

Voluntary Training to gain additional military training, provided the trainee Volunteers with the written consent of the employer, if any.

Provincial systems of training

Recruit Training : For a continuous period of 30 days in the first year only.

Annual Training : For a continuous period of two calendar months in the first and subsequent years.

Post commission Training: 10 weeks post commission training is compulsory within two years of commissioning.

Voluntary Training to gain additional military training, provided the trainee volunteers with the written consent of his employer, if any.

Departmental TA



Recruit Training: This is carried out for a continuous period of 30 days in the first year in a camp. No recruit training is there for Medical and Nursing Officers of General Hospital (TA).

Annual Training: In the first and subsequent years annual training is carried out for a continuous period of 30 days in a camp. For Officers of General Hospital (TA), this is carried out on weekends, without a camp, four hours training being counted as one day.

Post Commission Training: 30 days post commission training within two years of commissioning is compulsory for all Departmental TA Officers, except Medical Officers of Railway (TA) units and Officers of General Hospitals (TA).

Voluntary Training : Departmental TA personnel who volunteer with the specific consent of their departments can be attached for voluntary training.

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