Quantitative Ability

  • Quantitative Ability – POINTS TO REMEMBER

1. If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.
Eg: x3+3x2+2x+6=0 has no positive roots

2. For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.

3. For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)

4. Complex roots occur in pairs, hence if one of the roots of an equation is 2+3i, another has to be 2-3i and if there are three possible roots of the equation, we can conclude that the last root is real. This real root could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum.

For a cubic equation ax3+bx2+cx+d=o
Sum of the roots = - b/a
Sum of the product of the roots taken two at a time = c/a
Product of the roots = -d/a

b.For a bi-quadratic equation ax4+bx3+cx2+dx+e = 0
Sum of the roots = - b/a
Sum of the product of the roots taken three at a time = c/a
Sum of the product of the roots taken two at a time = -d/a
Product of the roots = e/a

6. If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)

7. Consider the two equations


a. If a1/a2 = b1/b2 = c1/c2, then we have infinite solutions for these equations.
b. If a1/a2 = b1/b2 <> c1/c2, then we have no solution.
c. If a1/a2 <> b1/b2, then we have a unique solution.

8. Roots of x2 + x + 1=0 are 1, w, w2 where 1 + w + w2=0 and w3=1

9. a + b = a + b if a*b>=0
else, a + b >= a + b

10. The equation ax2+bx+c=0 will have max. value when a<0>0. The max. or min. value is given by (4ac-b2)/4a and will occur at x = -b/2a

11. a. If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.

b. If for two numbers x*y=k (a constant), then their SUM is MINIMUM if x=y (=root(k)). The minimum sum is then 2*root (k).

12. Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.

13. For any 2 numbers a, b where a>b

a. a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)

b. (GM)^2 = AM * HM

14. For three positive numbers a, b, c

(a + b + c) * (1/a + 1/b + 1/c)>=9

15. For any positive integer n

2<= (1 + 1/n)^n <=3

16. a2 + b2 + c2 >= ab + bc + ca
If a=b=c, then the case of equality holds good.

17. a4 + b4 + c4 + d4 >= 4abcd (Equality arises when a=b=c=d=1)

18. (n!)2 > nn

19. If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s

20. If n is even, n(n+1)(n+2) is divisible by 24

General Awareness Test 2017

Total Time allotted for Test = 40 Minutes, Timer : 00:00

General Awareness Test 2017 for MBA Exams like XAT

General Awareness 2017 - Questions 1 - 60

3 Marks for each right answer and -1 Mark for each wrong answer.
Total Marks = 180

Q1. 'The Great Indian Novel' is a book written by:

Q2. In which year was the 'All India Radio' set up?

Q3. Who wrote the line: ' A thing of beauty is a joy forever'?

Q4. Entomology is the science that studies ?

Q5. Who is the current CEO & MD of Infosys?

Q6. Periyar Tiger Reserve is located in which state?

Q7. Capital of Australia is:

Q8. How many Gold Medals did India win in 2014 Commonwealth game?

Q9. Which country hosted 2016 Olympics?

Q10. Who among the following has become the first Indian to be honoured with Harvard Medal?

Q11. The total cost of the India's Mars Orbitor Mission is:

Q12. Who is the going to be the new chief justice of India from 4th January 2017?

Q13. How much was India's Growth Rate in 2015-16?

Q14. If the cash reserve ratio is lowered by the RBI, its impact on credit creation will be to

Q15. Excise duty is a tax levied on the

Q16. Who among the following has been appointed the National Security Advisor (NSA) to the Prime Minister of India?

Q17. Which of the following technology firms unveiled a prototype driverless car, recently?

Q18. Finance Commission is constituted every:

Q19. Census of India is conducted every ____ Years and lastly it was done in ____

Q20. Which film won the best picture Oscar award in 2016:

Q21. Who is current President of world bank:

Q22. Who is the present CEO of Apple?

Q23. The state which has the highest sugarcane production in India is

Q24. The mineral in which India depends largely on imports is

Q25. Indian general election of 2014 was held to constitute the 16th Lok Sabha, electing members of parliament for parliament. How many total constituencies / seats are there in current Lok Sabha?

Q26. Telangana is ___ state of India and its Capital is ____

Q27. Who is current Director-General of WTO

Q28. Which company acquired online fashion portal Myntra.Com in 2014

Q29. Who won 2016 nobel prize for Peace?

Q30. Who among the following has been named as the TIME magazine Person of the Year 2016?

Q31. Which Indian village has recently earned the tag of becoming India’s first digital village in India?

Q32. Who was recently elected as the President of FICCI for the year 2017?

Q33. Name the Indian states that have jointly topped the Ease of Doing Business Reforms Ranking 2015-16??

Q34. Who was recently selected by the UN Security Council as the next UN Secretary-General?

Q35. Which country has topped the Global Competitiveness Index, GCI 2016-17 released in September 2016.?

Q36. Who is appointed as the Chairman of Life Insurance Corporation (LIC) of India?

Q37. Which stock exchange became the first Indian stock exchange to file Initial Public Offering with SEBI?

Q38. Which of the following Indian Actress has been ranked 10th in the world in the list of “Forbes magazine”?

Q39. Who is recently appointed as the Managing Director of the State Bank of India?

Q40. Which company has acquired Yahoo for $4.8 billion in July 2016?

Q41. Who has been elected as the Chairman of the International Chamber of Commerce (ICC)?

Q42. Who has been elected and appointed as the new President of Taiwan?

Q43. Who has been declared as the new Chief Minister of Assam?

Q44. Which is the 1st country of the world to put a ban on Deforestation?

Q45. Who among the following headed the 7th Pay Commission?

Q46. Who of the following was not selected for 2016 Rajiv Gandhi Khel Ratna?

Q47. Who was sworn in as President of Brazil in August 2016?

Q48. Majuli recently became the first island district of India. Majuli is located in which of the following states?

Q49. Who among the following has topped the Forbes 2016 list for “World's Most Powerful People”?

Q50. When is Constitution Day celebrated in India to spread awareness about Indian Constitution?

Q51. Who is the author of the book titled “An Era of Darkness: The British Empire in India” that was recently released by released by the Vice President of India M. Hamid Ansari

Q52. Who among the following is appointed as CEO of the World Bank?

Q53. Who among the following won the 2016 Nobel Prize in Literature?

Q54. Who of the following will be the Chief Guest at the Republic Day celebrations on 26 January 2017?

Q55. Who was recently sworn in as the Governor of Punjab?

Q56. Which Indian state has recently abolished Agricultural Income Tax?

Q57. Which state celebrated the bicentenary (200 years) of the 1817 Paika revolt against the British Empire in 2016?

Q58. Which Indian para-athlete recently became the first Indian to win two gold medals at the Paralympics?

Q59. Name the film that has been selected as India's entry to the 89th Academy Awards (Oscars) to be held in 2017 in the Foreign Language Film category.

Q60. Which movie won the Best Film Award at the first BRICS Film Festival that recently concluded in New Delhi?