The Territorial Army exam has been the target of several aspirants. The pre-mentioned sectional and overall cut-off of the exam is the best way to measure and implement your strategy in the exam. But as the prior knowledge is always helpful in getting the maximum in minimum time, the candidates need to get introduced to the type of question which are asked in the exam. The mathematics section of the exam has diverse types of question and is also termed as the scoring part of the exam. The most prominently asked questions in mathematics are as follows.

**SI and CI combination**– Questions related to the combination of the SI and CI are asked in the exam.

Ex. Find the difference between SI and CI on a certain sum of money for rate 4% for 2 years is 2 rupees. The sum is

Sol – using the formula difference = PR^{2}/100^{2}

2 = P X 4^{2}/ 100^{2}

2 = P X 16/10000

P = 1250

**Profit Loss**– Some simple but tricky questions are asked in the profit loss.

Example – The selling price of an article is 80% of the cost price. The profit of loss is?

Sol – let the CP = 100 then SP =?

(100X100) / 80 = 125

The profit = 125 – 100 = 25

**Consecutive Discount**– Two or more discounts given consecutively on any item are also asked in the T.A. exam.

Example – A consecutive discount of 10% and 20% is given on a book. The total percentage of the discount given on it is?

Sol – x + y – (xy)/100

10 + 20 – (10X20)/100

30 – 2 = 28%

**HCF and LCM**– The questions related to the HCF and LCM are asked in the T.A. Exam. Example – The HCF and LCM of two numbers is 864 and 114. If one number is 288, then the other number is?

Sol. LCM X HCF = product of the 2 numbers

864 X 114 = 288 X x

(864 X 144)/ 288 = x

X = 432

**Trigonometry**– Some basic trigonometric function that need a good estimate and problem solving ability becomes a part of T.A. exam.

Example = if 3 tanØ = 4, then sinØ =?

Sol = 5 tanØ = 4

Or tanØ = 4/3

4/3 = P/B

So P = 4, B = 3 and H = 5

So, then sinØ = P/H

Sin Ø = 4/5

**Number system**– The question related to the number system which checks the correct use of BODMAS are also asked in the exam.

Example – A number doubles when 9 is added to it. If the resultant triples, it becomes 75. The number is?

Sol – let the number be x.

Than 3 (x+9) = 75

X+9 = 25

X = 25-9

X = 16

**Simplification**– Simplification questions are also asked where the BODMAS and other basic mathematical identities like roots squares are included in one problem.

Example = 1120/ √x = 80

Sol. = 1120/ √x = 80

1120 / 80 = √x

14 = √x

X = 14^{2}

X = 196

**Partnership**– The questions about partnership are the easiest question of the math section of the T.A. Exam.

Example – A starts a business with 2100 and B joins the business later with 3600 capital. If they got equal profit at the end of the year, for what period does B put his capital in business?

Sol A = 2100 X 12 months

B = 3600 X x months

2100 X 12 = 3600 X x

X = 7 months

**Algebra**– The basic algebraic identities and questions are asked in the T.A. exam which need a bit prior practice.

Example = If (x + (1/x)) = ½, then what will be the value of 2x/ (2x^{2}+ 5x + 2)

Sol – Dividing all the terms of 2x/ (2x^{2}+ 5x + 2) by x

2 / (2x + 5 + 2/x)

2 / (5 + 2(1 + 1/x))

Putting the value of (x + (1/x)) = ½

2 / (5 + 2 X 1/2)

2/(5+1)

=1/3

**Logarithm**– Like CDS and NDA, the questions of logarithm are asked in the T.A. exam. The questions are simple and need just the basics of the log concept.

Example = If log x (9/16) = ½, then x =?

Sol – log x (9/16) = ½

X ^{½} = 9/16

X = (9/16)^{2}

X = 81/256

**Conclusion** – The above-mentioned questions will provide hints to the T.A. aspirants to prepare for the mathematics section of the exam and will help the aspirants in making their strategy for the exam. The questions on these topics are mostly asked and practicing these will raise the score of the candidates to reach up to the level of the cuttoff. So, start practicing for the section and bring your best performance next time.

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