Indian Army Mathematics Question Paper – Hindi PDF

Practice Indian Army Soldier GD, Clerk, Havildar, Technical, Tradesman and Nursing Assistant mathematics section online. All the questions are collected from the previous year question papers and hence, can be marked as important ones.

You may also like to download Indian army sample papers, and also the written exam syllabus of the Indian army GD.

Indian Army Mathematics Questions – Online Test

Q1. किसी दो संख्या का योगफल 22 है तथा उनका गुणनफल 40 है । इन संख्याओं के व्युत्क्रम का योगफल कितना होगा?
if the sum of two numbers is 22 and their product is 40 then what will be the sum of their inverse?

  1. 11/20
  2. 4
  3. 2
  4. 1/2
  5. Answer is: 11/20
  1. Solution with Explanation
  2. According to the question
    x +y = 22
    x*y = 40
    from this, x = 22-y
    Further, y²-22y+40 = 0
    y²-(20+2)y+40= 0
    y²-20y-2y+40= 0
    y(y-20)-2(y-20)
    y=2 ; y = 20
    If y = 2 ; x = 20
    If y = 20 ; x = 2
    Sum of the inverse of x and y
    1/x + 1/y
    1/20 + 1/2
    11/20

Q2. किसी त्रिभुज का एक कोण बाकी दो कोणों के योगफल के बराबर है तो बताएं त्रिभुज कैसा होगा?
If one angle of a triangle is equal to the sum of other two angles then the type of the triangle will be?

  1. न्यूनकोण त्रिभुज/Acute triangle
  2. समकोण त्रिभुज/Right Triangle
  3. अधिकोण त्रिभुज/Obtuse Triangle
  4. विषमबाहु त्रिभुज/Scalene triangle
  5. Answer is: समकोण त्रिभुज/Right Triangle
  1. Solution with Explanation
  2. Let ABC be a triangle.
    ∠A+∠B+∠C=180
    Given that ∠A=∠B+∠C
    So ∠B+∠C +∠B+∠C =180
    2(∠B+∠C) =180
    ∠B+∠C =90
    Hence ∠A=90 it is a right angled triangle

Q3. किसी त्रिभुज ABC में tan A + tan B + tan C का मान क्या होगा?
In a triangle ABC, calculate tan A + tan B + tan C.

  1. 1
  2. 0
  3. tan A. tan B. tan C
  4. -1
  5. Answer is: tan A. tan B. tan C
  1. Solution with Explanation
  2. In triangle ABC, ∠A + ∠B + ∠C = 180°
    A + B + C = 180° or
    A + B = 180 – C
    tan (A + B) = tan (180 – C) = tan C
    (tan A + tan B)/(1 – tan A*tan B) = tan C
    tan A + tan B = tan C – tan A*tan B*tan C
    tan A + tan B + tan C = tan A*tan B*tan C

Q4. मान ज्ञात करें : ( sin 2 45 0 + cos 2 45 0 ) / tan 2 60 0
Calculate : ( sin 2 45 0 + cos 2 45 0 ) / tan 2 60 0

  1. 13/16
  2. 5
  3. 1/3
  4. -1/2
  5. Answer is: 1/3
  1. Solution with Explanation
  2. ( sin 2 45 0 + cos 2 45 0 ) / tan 2 60 0
    = 1 / tan 2 60 [ since sin 2 θ + cos 2 θ = 1 ]
    = 1/ (√3) 2
    = 1 / 3

Q5. दो समान्तर रेखा 3x + 4y + 10 = 0 एवं 3x + 4y – 10 = 0 के बीच की दूरी क्या होगी?
Find the distance between two parallel lines 3x + 4y + 5 = 0 and 3x + 4y – 10 = 0

  1. 0
  2. -4√5
  3. 2√5
  4. 3
  5. Answer is: 3
  1. Solution with Explanation
  2. 3x + 4y + 5 = 0 and
    3x + 4y – 10 = 0
    y-intercept = 10/4 = 2.5 at point P(0, 2.5)Distance d, from P(0, 2.5) to line [1] is :

    d = [3(0) +4(2.5) +5] / [(3)^2 + (4)^2]

    d = 15 / 5 = 3 units

Q6. किसी घन के दो विकर्ण के बीच का कोण क्या होता है?
What is the angle between two diagonals of a cube?

  1. 45°
  2. 60°
  3. 90°
  4. cos-1(1/3)
  5. Answer is: cos-1(1/3)
  1. Solution with Explanation
  2. sides of the cube are  a, b and c
    diagonal = d
    Vector
    Diagonal #1 = a + b +c =D
    Diagonal #2 = b+a +c= Dx.y= |x||y|cos d

    #1.#2-> (a+b+c).(-b+a+c)= |D||D|cos d —(1)

    (a+b+c).(-b+a+c)=a.a + -b.b + c.c ( a.c, a.b or a.c=0 since there are orthogonal) and a.a=b.b=c.c
    =a.a=|a|^2 —-(2)
    by Scalar, d^2= c^2 + b^2 + a^2 since a=b=c,
    D^2=|D||D|=3a^2 = —-(3)
    Substitute (2) and (3) in (1);

    |a|^2= 3|a|^2 Cos d
    Cos d= 1/3

Q7. ABC तीन कुलक है और A ∪ (B ∩ C) = x है, तो x का मान क्या होगा?
if ABC is a set of 3 and A ∪ (B ∩ C) = x, then find x.

  1. (A ∩ C) ∪ (B ∩ C)
  2. (A ∪ C) ∩ (B ∪ C)
  3. (A ∪ B) ∩ (B ∪ C)
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: (A ∪ B) ∩ (B ∪ C)
  1. Solution with Explanation
  2. A ∪ (B ∩ C)
    Individually, it will become
    (A ∪ B) and (B ∪ C)
    Further, they will intersect and form
    (A ∪ B) ∩ (B ∪ C)

Q8. A एक सार्वत्रिक कुलक है, तो E ∩ A किसके बराबर होगा?
If A is a universal set then E ∩ A will be equal to?

  1. E
  2. A
  3. ϕ
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: ϕ
  1. Solution with Explanation
  2. There will be no intersection between E and the universal set A
    ∴ E ∩ A = ϕ

Q9. दशमलव संख्या 43 को बाइनरी संख्या में बदलो
Convert 43 in the binary number system.

  1. (111111)2
  2. (101011)2
  3. (101101)2
  4. (110101)2
  5. Answer is: (101011)2
  1. Solution with Explanation
  2. Binary 43 = 1010112
    The binary for 43 is 101011

Q10. यदि 5x2 + 13x + k = 0 का एक मूल दूसरे मूल का व्युत्क्रम है तो k का मान क्या होगा?
if one root of 5x2 + 13x + k = 0 is equal to the inverse of another root then the value of k is?

  1. 13
  2. 5
  3. 0
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: 5
  1. Solution with Explanation
  2. In a quadratic equation ax² + bx + c = 0
    Product of roots = c/a
    Here we have the equation 5x^2 + 13x + k = 0
    Product of roots = k/5If one root is equal to the inverse of the other, then let one root is p, the other would be 1/p. So, thier product will always be 1.
    1 = k/5
    k = 5
    Hence, the value of k is 5

Q11. log 2 = .3010,  log 3 = .4771 . log 18 का मान क्या है?
calculate:log 2 = .3010,  log 3 = .4771 . log 18 = ?

  1. 13
  2. 1.2552
  3. 0
  4. 1/13
  5. Answer is: 1.2552
  1. Solution with Explanation
  2. 18 = 2· 32. Therefore,
    log 18 = log (2· 32)
    log 2 + log 32
    log 2 + 2 log 3
    .3010 + 2(.4771)
    .3010 + .9542
    1.2552

Q12. यदि log 3 = .4771  है, तो log 3000 का मान ज्ञात करें-
if  log 3 = .4771   Evaluate log 3000

  1. -6
  2. 3.4771
  3. -9
  4. -5
  5. Answer is: 3.4771
  1. Solution with Explanation
  2. If we write 3000 in scientific notation, then
    log 3000 = log (3 × 103)
    log 3 + log 103
    .4771 + 3
    3.4771

Q13. एक आयत की लंबाई व चौड़ाई का अनुपात 7:4 है और परिमाप 88 सेमी है तो लम्बाई और चौड़ाई का अंतर क्या होगा?
If the ratio of length and breadth of a rectangle is 7:4 and its perimeter is 88cm, then what will be the difference of its length and breadth.

  1. 16 सेमी/Cm.
  2. 12 सेमी/Cm.
  3. 28 सेमी/Cm.
  4. 14 सेमी/Cm.
  5. Answer is: 12 सेमी/Cm.
  1. Solution with Explanation
  2. Perimeter Of Rectangle = 2(length + breadth)
    2(7x + 4x) = 88 cm
    2(11x) = 88 cm
    22x = 88
    x = 4
    The difference of its length and breadth
    length = 7*4 = 28 cm
    breadth = 4*4 = 16 cm
    Length – Breadth = 28 – 16
    = 12

Q14. 2, 6, 8, 24 का गुणोत्तर माध्य क्या होगा?
the Geometric mean of 2, 6, 8, 24 is

  1. √48 = 4√3
  2. 16
  3. 24
  4. 4.8
  5. Answer is: √48 = 4√3
  1. Solution with Explanation
  2. Geometric Mean of 4 Numbers = multipication of these numbers/ 4th root
    2*6*8*24
    48*48
    4√48*48
    √48
    4√3

Q15. 10.4 की.ग्रा., 40 की.ग्रा का कितना प्रतिशत है?
What percent of 40 k.g is 10.4 kg?

  1. 26%
  2. 24.6%
  3. 28%
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: 26%
  1. Solution with Explanation
  2. 40/100*x = 10.4
    2x/5 = 10.4
    x = 26%

Q16. यदि 4a3 + 1 = 501 तो ‘a’ का क्या मान होगा ?
If 4a3 + 1 = 501 then value of a is?

  1. 4
  2. 5
  3. 6
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: 5
  1. Solution with Explanation
  2. 4a³ = 501-1
    4a³ = 500
    a³ = 500/4
    a³ = 125
    a = 5

Q17. x2 + 15x + 56 के क्या गुणनखण्ड होंगे?
Factorization of x2 + 15x + 56 is?

  1. (x – 7)(x – 8)
  2. (x – 7)(x + 8)
  3. (x + 7)(x + 8)
  4. (x + 7)(x – 8)
  5. Answer is: ( x + 7 )( x + 8 )
  1. Solution with Explanation
  2. x² + 15x + 56
    x² + (7 + 8)x + 56
    x² + 7x + 8x + 56
    x(x + 7) + 8(x + 7)
    (x + 8) (x + 7)

Q18. 5000 रु पर 8% दर से 2 साल का साधारण ब्याज क्या होगा?
What will be the simple interest of Rs 5000 at the rate of 8% for 2 years?

  1. Rs. 1200
  2. Rs. 1000
  3. Rs. 800
  4. Rs. 750
  5. Answer is: 800
  1. Solution with Explanation
  2. Simple Interest = (Principal*Rate*Time)/100
    Simple Interest = (5000*8*2)/100
    Simple Interest = 800

Q19. एक आदमी 2.5 कि.मी. 10 मिनट में पूरा करता है। उसकी चाल किलोमीटर प्रति घंटा बताओ.
Find speed in Km/hr. if a man completes 2.5 km. in 10 minutes.

  1. 10 कि.मी. प्रति घंटा/km/hr
  2. 15 कि.मी. प्रति घंटा/km/hr
  3. 12 कि.मी. प्रति घंटा/km/hr
  4. इनमे से कोई भी नहीं/none of the above
  5. Answer is: 15 km/hr
  1. Solution with Explanation
  2. Speed = Distance/Time
    Distance = 2.5 km
    Time = 10 minutes = 10/60 hours
    (2.5*60)/100
    15 km/hr

Q20. x का मान क्या होगा?
Find the Value of x.
indian_army_gd_maths

  1. 47°
  2. 37°
  3. 38°
  4. 42°
  5. Answer is: 37°
  1. Solution with Explanation
  2. Vertically opposite angles are always equal
    ∴ 72° = x + 35°
    x = 72° – 35°
    = 37°

If you think that any of the answers to the questions is wrong, or if you want to discuss and clear your doubts about any topic then please feel free to comment. We will respond in the best possible way.

Check Also: Indian Army GD Maths Questions

89 Comments

Add a Comment
  1. Hi sir I m just in 12 . I scored 53.80% in 10 .
    I have a skin problem name psoriasis.
    It is full on my body .
    Can I apply for army bharti.
    Because my father said that u should b in army.and at a good post.

    1. Hi Anil.
      Sorry to say but at this moment you cannot apply for army. Try some treatment, if you get cured than you can look forward to join Indian army.

  2. Sir mere 10th main 1 subject me less than 40% (math)hain but mere 10th main 62% hain and diploma main 76& main eligible hu for the post of technical?

    1. Hi Sagar.
      We regret to say, but you cannot apply for the post of technical in Indian Army, as according to the criteria you must have scored atleast 40% marks in every subject in both your 10th and 12th.

  3. Please help me for previous year question paper for army technical written test

    1. Hi Kang.
      We are providing you a link, from there you can get the papers for Indian Army technical.
      Indian Army Written Exam Important Questions Answers & Previous Year Papers

  4. hlooo sir……….i am now in cls 12 in science stream……what should I do aftr the 12..????i m confused????

    1. Hi Suyal.
      May we know in which field you are most interested at, so that we can help you in a more proficient way.

  5. Pradeep kumar malik

    Hi sir ,I have scored 99% in 10th class
    what should I do sir after +2 science

    1. Hi Pradeep.
      May we know in which filed you are most interested at, so that we could help you in a more proficient way.

  6. Sir I m in 10th now I’m taking maths in 11 so if I apply after 10th and can I continue 11 after applying .

    1. Hi Ajay.
      Please be more specific about your query, so that we can help in much more proficient way.

  7. Sir,
    NCC Certificate ke fayde bta de mera pass A hai, abhi mai nhi lga paya hu, written k time lga skta hu. Kitna benefit hoga mujhe clerk me NCC se. NCC B an C certificate k bhi benefit bta de

    1. Hi Jitendra.
      If you are NCC A certificate holder, then you will get relaxation in written
      Soldier GD = 5 marks
      Soldier Clerk/ Store Keeper/ Technical/ Soldier Technical/ Nursing = 5 marks
      Soldier Tradesmen = 5 marks

      NCC B Certificate
      Soldier GD = 10 marks
      Soldier Clerk/ Store Keeper/ Technical/ Soldier Technical/ Nursing = 10 marks
      Soldier Tradesmen = 10 marks

      NCC C Certificate
      Soldier GD = exempted from CEE
      Soldier Clerk/ Store Keeper/ Technical/ Soldier Technical/ Nursing = 15 marks
      Soldier Tradesmen = exempted from CEE

  8. prafulla kumar parida

    Sir.
    me indian army me name resignation kiya
    tha. mera email or password khogeyahe.
    kya me ab new registration kar saktahun.

    1. Hi Prafulla. However, you can register again, but still i would recommend you to ask your query in the feedback form in the official website of Indian Army.

  9. prafulla kumar parida

    Sir
    mera 12th class me one subject me 30 mark hai kya me indian army clerk join karasatka hain.

    1. Hi Prafulla. You have to mention your subject in which you have secured 30 marks, only then i would be able to analyze.

  10. prafulla kumar parida

    sir me indian army really re name registered
    kiya tha.ab me indian army really re from apply Karen per me jis nomber per name registered kiya tha us nomber per verification code massage nehni aarehihe
    plz sir help me

    1. Hi Prafulla. There is a feedback form in the official website of the Indian army. Ask your query there to get the suitable answer.

  11. Sir, can you suggest me a book for the post of survivor automated cartographer (Havildar) as I have looked over the market both online and offline but I did not find any particular book for this post.

    1. Hi Bimal. For the post of Havildar(Army Education Corps), i would suggest you some books which you can buy online by clicking on the link provided below.
      Indian Army HMT Havildar Major Technical Exam English Medium
      Indian Army H.M.T. Havildar Major Technical Hindi Medium

  12. Hi sir
    I have scored 75% in 10th class.
    And i have to join indian army gd.
    What should i do sir?

    1. Hi Arbaaz. You can easily become a part of the open rally of Indian army soldier GD which is conducted in different states time to time.

  13. Sir,I complete 10th standard.I have more than 50% marks in each subject.Can I join indian army

    1. Hi Gursharan. There is an open rally bharti for soldier Gd, you can apply for that. Apart from it, for other posts, the required percentage is 50% marks in aggregate and 40% marks in each subject in class 10th and class 12th.

  14. sir i have got 77.40 percent marks in 10 th bord and each subject I have more than 50 Mark’s can I join army

    1. Hi Yogesh. You have secured a good percentage in class 10th and you can easily appear in the army soldier General Duty. But, as per my suggestion, first you must focus on securing good marks in class 12th as well. Then, you would be able to apply for other posts too.

  15. Grt to reading your reply sir,
    I just completed my diploma sir., My doubt is that, I have a microvascular surgery on my left hand small finger, because of a glass cut.But now i van take 15 pushups and everything without any problem..,but i can’t bend and hold that finger completely. So , is this make me out of medical test in Indian army??

    1. Thanks a ton Amarnath. I would suggest you to ask your query in the Feedback form of the official website of Indian army to get a better solution.

  16. Sir main army m hona chaahta hu. +2 or computer course kiya h 1saal ka or ab b.tech krra hu CSE mai. sir how can i join it?

    1. Hi Rinkesh. Here, you have not mentioned your marks in class 10th and 12th which matters the most for your selection in Indian army. if you percentage in class 10th and 12th is more than 50% in total and more than 40% in each subject, then you can surely join Indian army by being a part of its written exam and open rally.

  17. sir i completed my 2 puc sir and i wanted to join in indian force but i am diabetic so there is any chance and i finised black belt in karate sir

    1. Hey Mouli, sadly diabetic people are unfit to join Indian army in any trade.

  18. Hello sir ji ….my question is that ….technical me kya running hotti hai ager ha tohh kitna km ki hotti hai….???

    1. Yes Sonu, if you are applying for soldier technical, then you will need to clear the physical fitness test first, and it involves running of 1.6 km or 1600 meters.

  19. Sir I have completed my +2 with arts .can I apply for army clerk?

    1. Yes Anil, you can now apply for soldier clerk. But make sure that you check the other eligibility criteria. Check your eligibility via this app “Indian Army Eligibility Checker“.

  20. Sir is there any measure of penis and testicle in Indian army?

    1. Prof. Rajeev Mehra

      No Anil, there is no standards for the size of penis and testicals. However, if there is any abnormality or signs of diseases in those areas, then one can be declared as unfit for army.

  21. Sir i have no math subject in 12th and my mathematics is so weak. Am i eligible for army?

    1. Hey Dhansi, Yes you are eligible to apply for army. You can apply for soldier GD or tradesman, as there is not much use of maths.

  22. Sir, please tell me graduate student are eligible for army technical soldier category?

    1. Hey Akash, if you fit in all the eligibility criteria, then you can apply for soldier technical.

  23. Sir clerk mai physical ke marks bhi add hote hai kya overall merit me. Relationship recruitment dekh ra hu.

    1. Yes Rohit, all the marks from every test are added to make the final merit list.

  24. Sir clerk ka sample paper konse site se download kare plz help!

    1. Hey Rohit, you can get all the sample papers you want from 4ono.com. Just write “army previous year papers” in the search box of 4ono. You well find plenty of sample papers for clerk.

  25. Is asthma patient eligible for army?

    1. Hey Akash, sorry to say, but people with the problem of asthma are not eligible to apply for army.

  26. Sir mai army me jana chahti hu mujhe kya krna hoga?

    1. Hey Harshita, you first need to have a graduation degree to apply for the army. After that you can apply for army via CDS, TGT etc.

  27. Sir, maine matrice first division pass kiya hai, Math me 37% hai. Kya gd me bharti ho sakta hun?

    1. Yes Dhiraj, you can apply for Indian army. One need to have minimum 33 marks in each subject in class 10th, to be eligible to apply for soldier GD.

  28. Sir i hav a doubt, question paper for technical(arms) and technical(aviation) will be same or different?

    1. Prof. Rajeev Mehra

      Hey Shankar, the exam for different posts are different. So, exams for Technical (arms) and technical (aviation) will be different.

  29. vinay kumar chapra bihar

    Sir mai hamesa run pass karta hu mera clerk me merrit list nhi banta hai mujhe tips dijiye exam pass Marne k liye mera English weak hai.

    1. Hey Vinay, please refer to the article “how to prepare for Indian army“. You will get lot’s of tips and trick on how to prepare for army.

  30. Sir What is Syllabus for Army Clerk according to new pattern?

    1. Prof. Rajeev Mehra

      Hello Sanjay, please see the article “army exam and syllabus” to see the syllabus of Indian army. You will find all the details needed there.

  31. Sir, do i need to have a hard preparation for the clerk post?

    1. Prof. Rajeev Mehra

      Hello Samuel, the written exam for clerk and technical post are considered quite tough. But, army written exams are easier than other government exams. In any case you should prepare the best you can.

    2. Prof. Rajeev Mehra

      Hello Samuel, the written exam for clerk and technical post are considered quite tough. But, army written exams are easier than other government exams. In any case, you should prepare the best you can.

  32. Sir kya aap mujhe kuch important questions bata sakte hain? please sir help me! mai army join karna chata hun. Sir mai ek chote se gaon se hun, yehan to koi coaching bhi nahi hai.

    1. Prof. Rajeev Mehra

      Hello Ravi, relax! there is no need of coaching, as you can crack the exam on your own. I think you need a good book to prepare from. Just click on the following link : best books for army.

  33. Sir mera name Ravi Tiwari hai. Mai ye pochna chata hun ki technical solider ki test ki teyeare kaise karun? book name please.

    1. Prof. Rajeev Mehra

      Hello Ravi, to know which books is best for you to prepare for technical soldier, please visit our article “best books for army”. You can even order a book from there if you like.

  34. mohammad akhtar ali

    sir nursing stand ke paper ke bare main bataye

    1. Prof. Rajeev Mehra

      Hello Akhtar, Nursing assistant exam paper consist of 200 marks. Mostly Question comes from the General Knowledge, Maths, Biology and Chemistry. Time duration for Nursing assistant exam is 1hr and To qualify the exam you should get more than 80 marks.

  35. Respected Sir,
    I want to join Indian Army as an software engineer, Can you please help me to know what are the basic requirements and qualifications?

    1. Prof. Rajeev Mehra

      Hello! Moris, you can join Indian army as technical soldier, or through TGC entry. If you apply for soldier technical then you will need the following qualifications:-

      age between 17½ to 23 years, 12th (PCM) pass with 50% aggregate marks and 40% in each subject.

      To be eligible for the post of Lieutenant (technical) you need to have the following qualification.

      Age – 16½-19½ Years
      Qualifications – 10+2 (70% marks with PCM)

      For TGC

      Age – 21-27 Years
      Qualifications – BE / B.Tech streams of Engineering / B.Arch MSc computer.

  36. please solve Q.20

    1. Prof. Rajeev Mehra

      Hello Horil lal, the question you are asking has already been solved in the comment. Please see the comments, you will find solution for all the questions there.

  37. Thank you for this answer. Please inform me if there are any exam like this.

    1. Prof. Rajeev Mehra

      Hello Pravin, glad to know that you liked this article. Though, I could not understand your question properly, but I guess you are asking for the Army upcoming recruitment, if it is so, then just click on the link given. You will get the list of upcoming recruitment for this year. Do comment again, if it was something else you wanted to ask.

  38. I am so grateful, because as I verified the answers, I felt that I was in exam hall. Thanks a lot for this questions which gave me a little experience.

  39. sir, please question no.1 ko solve kar dijiye.
    thank you!

    1. Prof. Rajeev Mehra

      The solution is given in the comment. Please check carefuly.

  40. What are the qualification for soldier technical open bharti?

    1. Prof. Rajeev Mehra

      Hi Aman,
      Visit the following link army eligibility criteria to know the qualification of Soldier technical.

  41. Please give solution of Q – 6, 11, and 13.

    1. Solution: 6
      solution
      solution: 11
      using the formula log(m*n) = log m + log n
      Therefore, we can say that log 13 + log 1/13 = log(13*1/13)
      hence, log(1) = 0.
      Answer: 13
      Let the length of rectangle be x.
      therefore the ration will become 7x and 4x.
      Now the perimeter of a rectangle is given by
      2l + 2b = p which is equal to 88cm
      putting the ratios in given formula
      2 * 7x + 2 * 4x = 88
      14x + 8x = 88
      22x = 88
      x = 4
      therefore length will be 7 * 4 = 28 and breadth will be 4 * 4 = 16
      The difference of length and breadth will be
      28 – 16 = 12cm

  42. Please help me with Previous year question paper.

    1. Hi lanka,
      You can follow this link to download previous year and sample papers regarding different trades of Indian army. Download Indian Army Sample Papers.

  43. First of all i would like to say thank you. This is very nice way.

  44. Please solve, Q.1, Q.2, Q.4, Q.5, Q.6, Q.7, Q.8, Q.9

    1. Solution 1:
      let the numbers be x and y
      according to the question
      x + y = 22
      xy = 40
      ————–
      Therefore from 1st eqn.
      y = 22 – x
      putting in 2nd eqn.
      x(22 – x) = 40
      by solving we will get quadratic eqn.
      x2 – 22x + 40 = 0
      x2 – x(20 + 2) + 40 = 0
      x2 – 20x -2x + 40 =0
      x(x – 20) – 2(x -20)
      therefore the roots are
      ————–
      x = 20 & x = 2
      Acc. to 1st eqn
      if x = 20 then y = 2 and x = 2 then y = 20
      ————–
      Now we have to find the sum of inverse of x and y i.e 1/x + 1/y
      therefore: 1/2 + 1/20 or 1/20 + 1/2
      both will be equal to: 11/20


      Solution 2:
      Correct answer is Right Triangle because this is the only possible case in which the sum of two angles(45°) is equal to the third angle which is 90°.


      Solution 3:
      Solution 3


      Solution 4:
      Note: sin 60 = √3/2, cos 30 = √3/2, tan 45 = 1, cos 60 = 1/2, sin 30 = 1/2
      putting these values in given eqn. we get
      3/4 x 3/4 + 1 x 1/2 x 1/2
      9/16 + 1/4
      13/16


      Solution 5:
      Formula to get distance between two lines is:
      |c1 – c2|/√a2 + b2
      putting values from given equations:
      |10 – (-10)|/√32 + 42
      20/√9 + 16 = 20/√25 = 20/5
      hence, 4.


      Solution 8:
      Intersection of any set with its universal set is always outputs the same set hence answer is E.


      Solution 9:
      Answer is 101011

  45. Respected sir,
    I have a doubt on solving the questions 14, 17 and the 20 th question is not complete. Can you please help me to learn how to solve the above problems.

    1. Hi Anuja,
      Thanks for asking your doubts,
      Question 14:
      Formula to calculate GM is n√an
      First multiply all the given numbers as follow
      2 X 8 X 6 X 24 = 2304
      now since there are 4 numbers now we have to calculate the 4th root of 2304, which can be achieved by factorizing 2304.
      the final equations will look like
      4√2304
      4√2x2x2x2 X 2x2x2x2 x 3×3
      so the 4th root will be 2 X 2√3
      therefore the GM is 4√3


      Question 17:
      This is simple factorisation question can be solved as follow.
      > x2 + 15x + 56
      > x2 + (7 + 8)x + 56
      > x2 + 7x + 8x + 56
      > x(x + 7) + 8(x + 7)
      therefore the roots are
      (x + 7)(x + 8)


      Question 20:
      This question is complete and an application of Vertically opposite angles:
      since vertically opposite angles are equal then,
      > x + 35 = 72
      > x = 72 -35
      > x = 37
      Solved!

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