# IBPSGraminBankRRBs Placement-Paper : 29080

I**BPS RRBs graming bank current affairs questions with answers**

1. India was recently elected into United Nations Joint Inspection Unit (JIU) after defeating?

China-Ans

USA

Russia

Brazil

2. NATGRID Stands For:

National Incumbent Grid

National Intelligence Grid-Ans

Narcotics Incumbent Grid

Narcotics Intelligence Grid

3. The Governments of Four Indian States (Jharkhand, MIzoram, Sikkim and Lakshwadeep) recently signed an MOU with Statistical Ministry for ISSP, it stands for –

Indian Statistical Strengthening Project-Ans

Indian Statistical Stability Project

Indian Substantial Stability Project

Indian Substantial Strengthening Project

4. Union Cabinet recently cleared Whistleblowers’ Bill 2011, which is meant to.

Provide protection to persons reporting misconduct by a government servant.-Ans

Initiate Action Against a Judge

Make Authorities more accountable to public

None of These

5. At what price the wheat will be provided to BPL (Below Poverty Line) Category by government under recently passed National food security bill prepared by Harsh Munder –

3 Rs./kg

2 Rs./kg-Ans

1 Rs./kg

4 Rs./kg

6. NCHER Bill for Higher (University) education was recently tabled into Rajya Sabha. This regulatory body will scrap currently existing UGC and AICTE bodies and Stands for –

National Committee for Higher Education and Research

National Commission for Higher Education and Research-Ans

National Commission of Higher Education and Research

National Committee of Higher Education and Research

7. Union Government recently approved operation of Social security fund which is meant for the benefit of ?

Unorganized Sector Workers-Ans

Civil Servants

Private Companies Workforce

Middle Income Families

8. Which Political Party won the recent MCD Elections after its Trifurcation?

Congress

BJP-Ans

Bahujan Samaj Party

Akali Dal

9. HRD Ministry recently launched a web portal for NSIGSE, a scheme meant to aid girls for their studies. In this scheme, I Stands for –

Information

Incentive-Ans

Inhibition

Intelligence

10. Who is current Union Urban Development Minister ?

Kamal Nath-Ans

Jairam Ramesh

Ajeet Seth

P Chidambaram

11. Urban Development Ministry recently Launched NCMC Card to provide better Travel experience to the people. The card is also known as –

Aadhaar Card

MORE-Ans

PAN Card

Voter ID Card

12 Integrated Skill Development scheme is meant for training rural youth for –

Textile and Apparel sector-Ans

Basic Computer Trainings

Telecom Sector

Agriculture Sector

13. Mamoni Scheme meant for reducing Maternal Mortality ratio is implemented in the state of –

Madhya Pradesh

Assam-Ans

Uttar Pradesh

Himachal Pradesh

14. CAG of India is recently appointed as External auditor of IAEA and WIPO. ‘C’ in the Name Stands for –

Controller

Comptroller-Ans

Commissioner

Cashier

15. Who is currently the CAG of India ?

Hari Narayan

Vinod Rai-Ans

S Y Quraishi

Montek Singh Ahluwalia

16. Kundankulam Nuclear Power Plant is being built in collaboration with which Country?

Australia-Ans

Russia

USA

france

17. Australia recently lifted ban on export of which of following Nuclear raw materials to India?

Uranium-Ans

Plutonium

Thorium

Aluminium

18. Dam 999 is a Banned film based on a Controversial Dam causing long lasting conflict between states of Kerala and Tamilnadu. That Dam is –

Idamalayar Dam

Mangalam Dam

Aathupalayam Dam

Mullaperiyar Dam-Ans

19. India was granted a Clean Waiver by NSG Members for implementation of Indo-US Nuclear Deal. ‘S’ in the name stands for –

Supporters

Suppliers-Ans

Sanctioning

Seizing

20. Which is the first Indian State to implement the Public service guarantee Act-

Rajasthan-Ans

Uttarakhand

Uttar Pradesh

Punjab

21 Government recently signed a tripartite peace agreement with UPDS, a prominent insurgent group in Assam. ‘S’ in the name stands for –

Development

Democratic-Ans

Demolishing

Dictators

22. Who is currently the Chairman of Planning Commission of India?

S Y Quarishi

M S Ahluwalia-Ans

Hari Narayan

C Rangrajan

23 Which is the first State/UT in the Country to issue E-Stamp Papers in all Denominations?

Rajasthan

Uttar Pradesh

Delhi-Ans

Uttarakhand

24 What is new time period of Advance booking of reservation tickets as proposed by railway ministry recently ? –

60 Days

90 Days

120 Days-Ans

150 Days

25. Aadhaar is an ambitious project under supervision of Nandan Nilekani and implemented by UIDAI, It stands for –

User Identification Agency of India

Unique Identification Authority of India-Ans

User Identification Authority of India

Unique Identification Agency of India

26. NDSAP is a recently approved policy to facilitate access to central government owned shareable information. It Stands For –

National Data Sharing and Accessibility Policy-Ans

National Data Secrecy and Applicability Policy

National Data Sharing and Applicability Policy

National Data Secrecy and Accessibility Policy

27 World Bank recently approved a Billion dollar loan to clean which of the following Indian Rivers-

Ganga-Ans

Yamuna

Narmada

Godavari

28. Which Indian state recently passed set up an ‘Agriculture Cabinet’ and passed a policy to make itself an organic state-

Madhya Pradesh-Ans

Assam

Uttar Pradesh

Himachal Pradesh

29. Rashtriya Swasthya Bima Yojana is meant to provide health insurance cover to which of the following –

Pregnant Women

BPL Families in unorganized sector-Ans

Civil Servants

Farmers

30. Recently Formed SIT (Special Investigation Team) on Black Money is headed by –

B P Jeevan Reddy-Ans

Vinod Rai

S Y Quraishi

U K Sinha

31. Which Indian State has the lowest CSR (Child Sex Ratio) in both Urban and Rural scenario according to a recently issued report?

Himachal Pradesh

Uttar Pradesh

Bihar

Haryana -Ans

32. Which Indian State recently offered Government jobs to Farmers whose lands were occupied for Rajiv gandhi Thermal Power Plant?

Uttar Pradesh

Haryana-Ans

Himachal Pradesh

Arunachal Pradesh

33. To what percent India recently increased its quota in IMF (International Monetary Fund) ?

3.00 %

2.75 %-Ans

4.00 %

2.50 %

34. Which Indian State recently became first to provide a guarantee of urban property titles to its residents ?

Tamilnadu

Kerala

Karnataka-Ans

Madhya Pradesh

35. How was India ranked for its Innovativeness according to recent Annual Global Innovation Barometer ?

Third

Fourth

Sixth-Ans

Second

36. Which two government schemes were recently converged to create for durability and effectiveness for the purpose –

NRHM and MPLADS

MPLADS and MGNREGA-Ans

MGNREGA and NRHM

RSBY and MGNREGA

37. Which Indian State recently received a Loan of $109 Million for its Agricultural Competitiveness Project ?

Haryana

Uttar Pradesh

Rajasthan-Ans

Himachal Pradesh

38. Which Train follows the longest Indian Railways route joining Dibrugarh Town (Assam) with Kanyakumari ?

Bhagirathi Express

Duranto Express

Vivek Express-Ans

Sampark Kranti

39. Who is The newly appointed USA Ambassador to India?

Nancy Powell-Ans

Albert Peter Burleigh

condoleezza rice

Jerome Bonnafont

40. The world Bank recently approved a $200 Million Loan to which Indian State in order to help it become India’s first Carbon Neutral State-

Haryana

Arunachal Pradesh

Assam

Himachal Pradesh-Ans

41. Who is the Current Union Rural Development Minister?

Kapil Sibal

Jairam Ramesh-Ans

Kamal Nath

Anand Sharma

42 Which State recently Engaged DMRC for a 560 – KM Bullet Train project in its territory?

Arunachal Pradesh

Karnataka

Kerala-Ans

Tamilnadu

43. Which Indian state is said to have best literacy rate (About 94 % Literacy) ?

Tamilnadu

Kerala-Ans

Karnataka

Goa

44. Which Rashtriya Lok Dal (RLD) leader recently Joined Union Ministers’ Cabinet as Civil Aviation Minister –

Ajit Singh-Ans

Jayant Chaudhary

Sanjay Singh Chauhan

Sarika Singh

45. Who is the Current Indian Foreign Secretary ?

A K Seth

Ranjan Mathai-Ans

U K Sinha

M S Ahluwalia

46. Whois the newly appointed Chief election commissioner of India ?

S Y Quereshi

V S Sampath-Ans

Montek Singh Ahluwalia

Hamid Ansari

47 Who is the newly appointed chief of Indian Navy ?

D K Joshi-Ans

Bikram Singh

V K Singh

P V Naik

48 Which country has recently appointed Mr. Michael Steiner as its ambassdor to India ?

Germany-Ans

USA

France

Spain

49. Who is the newly elected Home Minister of India ?

Mukul Roy

Sushil Kumar Shinde-Ans

P Chidambaram

Sharad Pawar

50. Mohammed Waheed, who recently visited India is the newly elected president of which country ?

Maldives-Ans

Iran

Syria

Libya

51. Which Indian State wil host world economic summit on India in November 2012 ?

Haryana-Ans

Himachal Pradesh

Maharashtra

Uttar Pradesh

52. India recently conducted its first naval exercise with Japan callled –

Sahyog Kaijin-Ans

Jimex 12

Slinex 12

Operation Shoorveer

53. The Indian Born person that is recently appointed as president of European Bank for Reconstruction and Development (EBRD)?

Suma Chakrabarti-Ans

Pranab Mukherjee

Sudarshan Patnaik

P Chidambaram

54. The Indian person appointed as executive director in world bank is –

Suma Chakrabarti

Arvind Virmani-Ans

Ashok Kumar Lahiri

Pranab Mukherjee

55. After a recent cabinet reshuffle followed by President Pranab Mukherjee’s resignation, Finance minsitry is given to P Chidambaram and Veerappa Molly has been given the ministry of –

Railways

Corporate Affairs and Power-Ans

Home Ministry

Defence

56 Which Indian State has the lowest CSR (Child Sex Ratio) in both Urban and Rural scenario according to a recently issued report?

Himachal Pradesh

Uttar Pradesh

Bihar

Haryana-Ans

57. Which Indian State recently offered Government jobs to Farmers whose lands were occupied for Rajiv gandhi Thermal Power Plant?

Uttar Pradesh

Haryana-Ans

Himachal Pradesh

Arunachal Pradesh

58. To what percent India recently increased its quota in IMF (International Monetary Fund) ?

3.00 %

2.75 %-Ans

4.00 %

2.50 %

59. Which Indian State recently became first to provide a guarantee of urban property titles to its residents ?

Tamilnadu

Kerala

Karnataka-Ans

Madhya Pradesh

60. How was India ranked for its Innovativeness according to recent Annual Global Innovation Barometer ?

Third

Fourth

Sixth-Ans

Second

61. Which two government schemes were recently converged to create for durability and effectiveness for the purpose –

NRHM and MPLADS

MPLADS and MGNREGA-Ans

MGNREGA and NRHM

RSBY and MGNREGA

62. Which Indian State recently received a Loan of $109 Million for its Agricultural Competitiveness Project ?

Haryana

Uttar Pradesh

Rajasthan-Ans

Himachal Pradesh

63. Which Train follows the longest Indian Railways route joining Dibrugarh Town (Assam) with Kanyakumari ?

Bhagirathi Express

Duranto Express

Vivek Express-Ans

Sampark Kranti

64. Who is The newly appointed USA Ambassador to India?

Nancy Powell-Ans

Albert Peter Burleigh

condoleezza rice

Jerome Bonnafont

65. The world Bank recently approved a $200 Million Loan to which Indian State in order to help it become India’s first Carbon Neutral State-

Haryana

Arunachal Pradesh

Assam

Himachal Pradesh-Ans

66. Who is the Current Union Rural Development Minister?

Kapil Sibal

Jairam Ramesh-Ans

Kamal Nath

Anand Sharma

67 Which State recently Engaged DMRC for a 560 – KM Bullet Train project in its territory?

Arunachal Pradesh

Karnataka

Kerala-Ans

Tamilnadu

68. Which Indian state is said to have best literacy rate (About 94 % Literacy) ?

Tamilnadu

Kerala-Ans

Karnataka

Goa

69. Which Rashtriya Lok Dal (RLD) leader recently Joined Union Ministers’ Cabinet as Civil Aviation Minister –

Ajit Singh-Ans

Jayant Chaudhary

Sanjay Singh Chauhan

Sarika Singh

70. Who is the Current Indian Foreign Secretary ?

A K Seth

Ranjan Mathai-Ans

U K Sinha

M S Ahluwalia

**Arithmetical Ability**

1. The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is –

a. 74

b. 78

c. 80

d. 90

Ans : Let the numbers be x and y .

∴ xy = 1575

And x/y = 9/7

∴ xy/x/y = 1575/9/7

∴ y2 = 1225

∴ y = 35 and x = 45

∴ The sum of the numbers = 45+35

= 80

2. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __

a. 3

b. 6

c. 9

d. 8.2

Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)

= 314.4+5.4-16.8-1

= 32

= 9

3. √6+√6+√6+… is equal to –

a. 2

b. 5

c. 4

d. 3

Ans : Let √6+√6+√6+…. be x.

∴ x =√6+x

∴ x2 = 6+x

∴ x2 + x – 6 = 0

∴ (x-3) (x+2) = 0

∴ x = 3

4. The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is –

a. 24

b. 32

c. 40

d. 28

Ans : Let the consecutive odd numbers be x and (x+2)

∵ x2 + (x + 2)2 = 394

∴ x2 + x2 + 4x + 4 = 394

∴ 2 x2 +4x – 390 = 0

∴ x2 + 2x – 195 = 0

∴ (x +15) (x-13) = 0

∴ x = 13

∴ Required sum = 13 +15 =28

5. When (6767 +67) is divided by 68, the remainder is-

a. 1

b. 63

c. 66

d. 67

Ans: (6767+ 67) = 67(6766 + 166)

As 66 is an even number

∴ 6766 is an even number

∴ (6766 + 1) is perfectly divisible by (67 + 1)

i.e. 68

∴ The remainder = 67

6. In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend then-

a. 4b-a2 /a =3

b. 4b-2a /a2 =2

c. (a+1)2 = 4b

d. A(a+2)/b = 4

Ans : As divisor is a, and dividend is b.

∴ Quotient = a/4

And Remainder = a/2

∴ b = a * a/4 + a/2

∴ 4b = a2 + 2a

∴ a(a+2)/b = 4

7. If 738 A6A is divisible by 11, then the value of A is-

a. 6

b. 3

c. 9

d. 1

Ans : As 738A6 A is divisible by 11.

∴ A + A + 3 = 6 + 8 + 7

∴ A = 9

8. The east positive integer that should be subtracted from 3011 * 3012 so that the difference is perfect square is-

a. 3009

b. 3010

c. 3011

d. 3012

Ans : ∵ 3011 * 3012 = 3011 (3011 + 1)

= (3011)2 + 3011

∴ Required least number = 3011

9. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-

a. 2850

b. 3750

c. 2750

d. 1000

Ans : Work done by Q = 19/23 + 8/23 – 1

4/23

∴ Wage of Q = 4/23 * 5750

= Rs. 1000

10. A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?

a. 15

b. 20

c. 18

d. 30

Ans : Work done by A = 6/24 = ¼

Work done by B = (x-6)/32

(where x is no. of days in which work is competed)

∵ ¼ + x – 6/32 + x/64 = 1

∴ 16 + 24 – 12 + x /64 = 1

∴ 3x + 4 = 64

∴ x = 60/3 = 20 days

11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-

a. 1

b. 2

c. 3

d. 4

Ans : The square root of

[(0.75)3/1 – 0.75 + {0.75 + (0.75)2 + 1}]

= √1.6875 + 2.3125

=√4

= 2

12. Given that √4096 = 64, the value of √4096 + √40.96 +√0.004096 is-

a. 70.4

b. 70.464

c. 71.104

d. 71.4

Ans : Given Exp. = √4096 + √40.96 +√0.004096

= 64 + 6.4 + 0.064

= 70.464

13. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is-

a. 5 : 3

b. 3 : 5

c. 3 : 4

d. 4 : 3

Ans : Let of M.P. be Rs. x.

∴ S.P. = Rs.3x/4

and C.P. = 3x/4 * 100/125

= Rs.3x/5

∴ required ratio = x: 3x/5

= 5:3

14. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, the monthly income of B is-

a. Rs.7,000

b. Rs.14,000

c. Rs.5,000

d. Rs.10,000

Ans : Let the monthly income of B be Rs. x.

∴ Monthly income of A = Rs. 2x and

Saving of A =5000 * 4/(4 + 1)

= Rs. 4000

Saving of B = Rs.1000

∵ 2x – 4000/x-1000 = 5/3

⇒ 6x – 12000 = 5x – 5000

∴ x = Rs.7000

15. The ratio of the sum of two numbers and their difference is 5:1. The ratio of the greater number to the smaller number is-

a. 2 : 3

b. 3 : 2

c. 5 : 1

d. 1 : 5

Ans : Let the numbers be x and y.

∵ x + y/ x – y = 5/1

⇒ 5x – 5y = x + y

⇒ 4x = 6y

⇒ x/y = 6/4

x : y = 3 : 2

16. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at-

a. 7.12 p.m.

b. 7.15 p.m.

c. 7.10 p.m.

d. 7.18 p.m.

Ans : Let the cistern be emptied at x p.m.

∵ x -3/3 + x – 4/4 = x – 5/1

⇒ 4x – 12 + 3x – 12/12 = x – 5/1

⇒ 7x – 24 = 12x – 60

⇒ 5x = 36

∴ x = 36/5

= 7 hr. + 12 min.

= 7.12 p.m.

17. If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?

a. 10 days

b. 12 days

c. 6 days

d. 8 days

Let x days are taken when they work together.

∴ Time taken by A to complete the work = (x + 4) days

And Time taken by B to complete the work = (x + 16) days

∵ 1/x = 1/x + 4 + 1/x + 16

∴ 1/x = x + 16 + x + 4/(x + 4) (x +16)

∴ 2×2 + 20x = x2 + 20x +64

∴ x2 = 64 (8)2

∴ x = 8 days

18. 250 men can finish a work in 20 days working 5 hours a day. To finish the work within 10 days working 8 hours a day, the minimum number of men required is-

a. 310

b. 300

c. 313

d. 312

Ans : Required no. of men = 250 * 5 * 20/8 * 10

=312.5

313

19. 2 men and 5 women can do a work in 12 days. 5 men 2 women can do that work in 9 days. Only 3 women can finish the same work in-

a. 36 days

b. 21 days

c. 30 days

d. 42 days

∵ (2m + 5w) * 12 = (5m + 2w) * 9

⇒ 24m + 60w = 45m + 18w

⇒ 21m = 42w

⇒ 1m = 2w

∴ 2m + 5w = 9w

∴ required no. of days = 9 * 12/3

= 36

20. While selling, a businessman allows 40% discount on the marked price and there is a loss of 30%. If it is sold at the marked price, profit per cent will be –

a. 10%

b. 20%

c. 16 2/3%

d. 16 1/3%

Ans : Let the M.P. be Rs.100.

∴ S.P = (100-40) = Rs.60

and C. P. = 60 * 100/(100-30) = Rs.600/7

∴ Reqd. % profit = 100-600/7 /600/7 * 100%

= (700 – 600)/7 * 600 * 100 * 7%

= 16 2/3%

21. Successive discount of 10% , 20% and 50% will be equivalent to a single discount of-

a. 36%

b. 64%

c. 80%

d. 56%

Ans : Equivalent to a single discount

= [100 – (100 – 10) (100 – 20) (100 – 50)/100*100]%

= [100 – 90*80*50/10000]%

= [100-36]%

= 64%

22. A retailer offers the following discount schemes for buyers on an article-

I. Two successive discounts of 10%

II. A discount of 12% followed by a discount of 8%.

III. Successive discounts of 15% and 5%

IV. A discount of 20%

The selling price will be minimum under the scheme-

a. I

b. II

c. III

d. IV

Ans : From (i) single discount = [10 + 10 – 10*10/100] % = 19%

From (ii) single discount = [12 + 8 -12*8/100] % = 19.04%

From (iii) single discount = [15 + 5 – 15*5/100] % = 19.25%

From (iv) single discount = 20%

∴ The S.P. will be minimum under the scheme IV.

23. Of three numbers, the second is thrice the first and the third number is three-fourth of the first. If the average of the three numbers is 114, the largest number is –

a. 72

b. 216

c. 354

d. 726

Ans : Let the first number be x.

∴ Second number = 3x and Third number = 3x/4

∵ x + 3x + 3x/4 = 3*114

⇒ 19x/4 = 342

∴ x = 342*4/19 = 72

∴ The largest number = 3*72

= 216

24. A car covers 1/5 of the distance from A to B at the speed of 8 km/hour, 1/10 of the distance at 25 km per hour and the remaining at the speed of 20 km per hour. Find the average speed of the whole journey-

a. 12.625 km/hr

b. 13.625 km/hr

c. 14.625 km/hr

d. 15.625 km/hr

Ans : If the whole journey be x km. The total time taken

= (x/5/8 + x/10/25 + 7x/10/20) hrs

= (x/40 + x/250 + 7x/200) hrs

= 25x + 4x + 35x/1000

= 64x/1000 hrs

∴ Average speed = x/64x/1000

= 15.625 km/hr

25. The average of 3 numbers is 154. The first number is twice the second and the second number is twice the third. The first number is-

a. 264

b. 132

c. 88

d. 66

Ans : Let the first number be x.

∴ Second number = x/2 and Third number = x/4

∵ x + x/2 + x/4 = 3 x 154

⇒ 7x/4 = 462

∴ x = 462*4/7

=264

26. The average salary of all the staff in an office of a corporate house is Rs. 5,000. The average salary of the officers is Rs. 14,000 and that of the rest is Rs. 4,000. If the total number of staff is 500, the number of officers is –

a. 10

b. 15

c. 25

d. 50

Ans : Let the number of officers be x.

∵ 5000*500 = 14000x + 4000(500-x)

∴ 2500000 =14000x + 2000000 – 4000x

∴ x = 500000/10000

= 50

27. The average marks of 40 students in an English exam are 72. Later it is found that three marks 64, 62 and 84 were wrongly entered as 60, 65 and 73. The average after mistakes were rectified is-

a. 70

b. 72

c. 71.9

d. 72.1

Ans : Correct average

= 40*72 + (64 + 62 +84) – 68 – 65 – 73/40

= 2880 + 210 – 206/40 = 2884/40

= 72.1

28. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be-

a. 5 : 7

b. 5 : 9

c. 7 : 5

d. 9 : 5

Ans : Quantity of gold in A = 7/9* wt. of A

Quantity of gold in B = 7/18* wt. of B

If 1 kg of each A and B are mixed to form third alloys C.

Then quantity of gold in 2 kg C = 7/9 + 7/18

= 7/6 kg

And Quantity of copper in 2 kg C = 2 – 7/6

= 5/6 kg

∴ Required ratio = 7/6 : 5/6 = 7 : 5

29. In a laboratory, two bottles contain mixture of acid and water in the ratio 2 : 5 in the first bottle and 7 : 3 in the second. The ratio in which the contents of these two bottles be mixed such that the new mixture has acid and water in the ratio 2 : 3 is-

a. 4 : 15

b. 9 : 8

c. 21 : 8

d. 1 : 2

Ans : Quantity of acid in first bottle = 2/7 x mix.

and Quantity of acid in second bottle = 7/10 x mix.

If x and 1 volumes are taken from I and II bottle respectively to form new mixture.

Then, (2/7 x + 7/10 * 1)/(5x/7 +3/10 * 1) = 2/3

⇒ 6x/7 21/10 = 10x/7 +6/10

⇒ 4x/7 = 15/10

∴ x = 15/10*7/4 = 21/8

∴ Required ratio = x : 1

= 21 : 8

30. A mixture contains 80% acid and rest water. Part of the mixture that should be removed and replaced by same amount of water to make the ratio of acid and water 4 : 3 is-

a. 1/3 rd

b. 3/7 th

c. 2/3 rd

d. 2/7 th

Ans : Let the initial wt. of mixture be 1 kg and x kg of mixture is taken out and replaced by same amount of water.

∵ Amt. of acid/Amt. of water = 0.8 – 0.8x/ (0.2 – 0.2x + x) = 4/3

⇒ 2.4 – 2.4x = 0.8 + 3.2x

⇒ 5.6x = 1.6

∴ x = 1.6/5.6 = 2/7th part

31. An employer reduces the number of his employees in the ratio 9 : 8 and increases their wages in the ratio 14 : 15. If the original wage bill was Rs. 189,900, find the ratio in which the wage bill is decreased-

a. 20 : 21

b. 21 : 20

c. 20 : 19

d. 19 : 21

Ans : Let the initial number of employees be 9x and the employer gives Rs. 14y as wage to each.

∵ 9x * 14y =18900

∴ xy = 150 and The later bill = 8x*15y = 120xy

= 120*150 = 18000

∴ Required ratio = 18000 : 18900

= 20 : 21

32. The batting average for 40 innings of a cricketer is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is-

a. 165

b. 170

c. 172

d. 174

Ans : Let the max. number of runs be x.

∴ The lowest score = (x-172)

∵ 40*50 = 38*48 + x + (x-172)

⇒ 2000 = 1824 + 2x – 172

∴ x= 174

33. Walking at 3 km per hour, Pintu reaches his school 5 minutes late. If he walks at 4 km per hour he will be 5 minutes early. The distance of Pintu’s school from his house is-

a. 1 ½ Km

b. 2 Km

c. 2 ½ Km

d. 5 Km

Ans : Distance of the school from the house

= 4*3/(4 – 3) * 5 +5/60 km

= 12*1/6

=2 km

34. Nitin bought some oranges at Rs. 40 a dozen and an equal number at Rs.30 a dozen. He sold them at Rs. 45 a dozen and made a profit of Rs.480. The number of oranges, he bought, was-

a. 48 dozen

b. 60 dozen

c. 72 dozen

d. 84 dozen

Ans : Let the number of oranges bought be x.

∴ 45x/12 – 70x/24 = 480

⇒ (45-35)/12 = 480

⇒ x = 480*12/10 = 576

= 48*12 = 48 dozen

35. A man buys two chairs for a total cost of Rs.900. By selling one for 4/5 of its cost and the other for 5/4 of its cost, he makes a profit of Rs.90 on the whole transaction. The cost of the lower priced chair is-

a. Rs.360

b. Rs.400

c. Rs.420

d. Rs.300

Ans : Let the cost price of 1 chair be Rs. x.

∴ C.P. of other chair = Rs. (900-x)

∵ 4/5 x + 5/4 (900-x) = 900 + 90

⇒ 4/5 x +1125 -5x/4 = 990

∴ 9x/20 = 135

∴ x = 135*20/9

= Rs. 300

∴ C.P. of the lower priced chair is Rs. 300.

36. By selling 100 oranges, a vendor gains the selling price of 20 oranges. His gain per cent is-

a. 20

b. 25

c. 30

d. 32

Ans : Let the S.P. of 100 Oranges be Rs. x.

∴ S.P. of 20 oranges = x/100 *20 = Rs. x/5

∴C.P. of 100 oranges = x – x/5

= Rs. 4x/5

∴ Reqd. Profit % = x/5 * 100*5/4x %

= 25%

37. 60% of the cost price of an article is equal to 50% of its selling price. Then the percentage of profit or loss on the cost price is-

a. 20% loss

b. 16 2/3% profit

c. 20% profit

d. 10% loss

Ans : Let the cost price be Rs. 100.

∵ S.P * 50/100 = 100*16/100

∴ S.P = 60*100/50

= Rs. 120

∴ Reqd. % profit = (120 – 100)% = 20%

38. Maninder bought two horses at Rs.40,000 each. He sold one horse at 15% gain, but had to sell the second horse at a loss. If he hand suffered a loss of Rs.3,600 on the whole transaction, then the selling price of the second horse is-

a. Rs.30,000

b. Rs.30,200

c. Rs.30,300

d. Rs.30,400

Ans: C.P. of two horses = 2*40000 = Rs. 80000

and S.P. of two horse = 80000 – 3600 = Rs. 76400

∴ S.P. of the other horse = 76400 – 46000 = 30400

39. A fruit-seller buys x guavas for Rs.y and sells y guavas for Rs. x. If x>y, then he made-

a. x2 – y2 / xy % loss

b. x2 – y2 / xy % gain

c. x2 – y2 / y2 % loss

d. x2 – y2 / y2 * 100% gain

Ans : C.P. of 1 guava = Rs. y/x [x>y]

and S.P. of 1 guava = Rs. x/y

∴ Reqd. Gain% = x/y – y/x/ y/x * 100%

= x2 – y2 /y2 *100%

40. A jar contain 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?

a. 25

b. 30

c. 35

d. 40

Ans : Let after adding x red marbles, the red marbles with be 60% of the total.

∵ (10+x)/ (10 + x) + 30 = 60/100

⇒ 10 + x/40 + x = 3/5

⇒ 50 + 5x = 120 + 3x

x = 70/2 = 35

41. If a number multiplied by 25% of itself gives a number which is 200% more than the number, then the number is –

a. 12

b. 16

c. 35

d. 24

Ans : Let the number be x.

∵ x*25x/100 = x + 200x/100

⇒ x2/4 = 3x

⇒ x2 – 12x = 0

⇒ x – 12 = 0

∴ x = 12

42. The value of an article depreciates every year at the rate of 10% of its value. If the present value of the article is Rs.729, then its worth 3 years ago was-

a. Rs.1250

b. Rs.1000

c. Rs.1125

d. Rs.1200

Ans : Let the worth 3 years ago be Rs. x.

∵ 729 = x (1 – 10/100)3

⇒ 729 = x*9*9*9/10*10*10

∴ x = Rs. 1000

43. The price of onions has been increased by 50%. In order to keep the expenditure on onions the same the percentage of reduction in consumption has to be-

a. 50%

b. 33 1/3%

c. 33%

d. 30%

Ans : Reqd. Percentage of reduction

= 50*100/(100 + 50) %

= 5000/150 %

= 33 1/3%

44. A took two loans altogether of Rs.1200 from B and C. B claimed 14% simple interest per annum, while C claimed 15% per annum. The total interest paid by A in one year was Rs.172. Then, A borrowed-

a. Rs.800 from C

b. Rs.625 from C

c. Rs.400 from B

d. Rs.800 from B

Ans : If A borrowed Rs. x from B. and A borrowed Rs. Rs. (1200 – x) from C.

∵ (1200 – x)*15*1/100 + x*14*1/100

⇒ 18000 – 15x + 14x = 172*100

x = Rs. 800

45. If a regular polygon has each of its angles equal to 3/5 times of two right angles, then the number of side is-

a. 3

b. 5

c. 6

d. 8

Ans : If the number of sides a regular polygon be n.

Then (2n-4)/n = 2*3/5

⇒ (2n – 4)*5 = 6n

∴ n = 5

46. A square is of area 200 sq. m. A new square is formed in such a way that the length of its diagonal is √2 times of the diagonal of the given square. The the area of the new square formed is-

a. 200√2 sq.m

b. 400√2 sq.m

c. 400 sq.m

d. 800 sq.m

Ans : Length of the diagonal of Ist square

= √2*200

= 20 m

∴ Length of the diagonal of new square = 20√2m

∴ Area of the new square = ½*(20.√2)2 = 400 sq. m

47. The heights of a cone, cylinder and hemisphere are equal. If their radii are in the ratio 2 : 3 : 1, then the ratio of their volumes is-

a. 2 : 9 : 2

b. 4 : 9 : 1

c. 4 : 27 : 2

d. 2 : 3 : 1

Ans : Ratio of their volumes [cone : cylinder : hemisphere]

= 1/3(2)2h : (3)2*h : 2/3(1)2.h

= 4/3 : 9 : 2/3 = 4 : 27 : 2

48. A motor-boat can travel at 10 km/hr in still water. It travelled 91 km downstream in a river and then returned to the same place, taking altogether 2 hours. Find the rate of flow of river-

a. 3 km/hr

b. 4 km/hr

c. 2 km/hr

d. 5 km/hr

Ans : Let the rate of flow of river be x km/hr.

∵ 91/(10 + x) + 91/(10 – x) = 20

⇒ 91(10 – x + 10 + x)(10 + x) (10 – x) = 20

⇒ 91*20 = 20(100 – x2)

⇒ x2 = 9 = (3)2

∴ x = 3 km/hr

49. A man driving at 3/4th of his original speed reaches his destination 20 minutes later than the usual time. Then the usual time is-

a. 45 minutes

b. 60 minutes

c. 75 minutes

d. 120 minutes

Ans : Let the original speed be x km/hr and the usual time be y hours.

∵ x * y = ¾ x(y+1/3)

∴ 4y = 3y + 1

∴ y = 1 hr = 60 minutes

50. A motor-boat, travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 hours. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 hours. The speed of the stream is –

a. 2 km/hr

b. 3 km/hr

c. 4 km/hr

d. 5 km/hr

Ans : Let the speeds of motor boat and the stream be x and y km/hr respectively.

∵ 39/x + y + 25/x – y = 8 …(1)

and 52/x + y + 35/x – y = 11 …(2)

Solving equations (1) and (2), we get-

∴ 100 – 105/x – y = 32 – 33

∴ x – y = 5

and x + y = 13

∴ y = 4 km/hr

51. If a sum of money placed at compound interest, compounded annually, doubles itself in 5 years, then the same amount of money will be 8 times of itself in-

a. 25 years

b. 20 years

c. 15 years

d. 10 years

Ans : Required time = 5log 8/log 2

= 5*3log 2/log 2

= 15 years

52. A person has left an amount of Rs.1,20,000 to be divided between his 2 son aged 14 years and 12 years such that they get equal amounts when each attains 18 years of age. If the amount gets a simple interest of 5% per annum, the younger son’s share at present is-

a. Rs.48,800

b. Rs.57,600

c. Rs.62,400

d. Rs.84,400

Ans : Let the present share of the younger son be Rs. x.

∴ The share of the elder son = Rs. (120000 – x)

∵ x + x*6*5/100

= (120000 – x) + (120000 – x)*4*5/100

⇒ 130x/100 = (120000 –x)*120/100

⇒ 13x = 1440000 – 12x

⇒ 25x = 1440000

∴ x = Rs. 57600

53. If the simple interest on Rs.x at a rate of a% for m years is same as that on Rs. y at a rate of a2% for m2 years, then x : y is equal to-

a. m : a

b. am : 1

c. 1/m : 1/a

d. 1/am : 1

∵ x*a*m/100 = y*a2*m2/100

⇒ x/y = am/1

∴ x : y = am : 1

54. Base of a right prism is an equilateral triangle of side 6 cm. If the volume of the prism is 108√3 cc, its height is-

a. 9 cm

b. 10 cm

c. 11 cm

d. 12 cm

Ans : Height of the prism = 108√3*4/√3*(6)2 = 12cm

55. If a + 1/a + 2 = 0, then the value of (a37 – 1/a100) is-

a. 0

b. -2

c. 1

d. 2

Ans : ∵ a + 1/a + 2 = 0

⇒ a2 + 1 +2a = 0

⇒ (a + 1)2 = 0

⇒ a +1 = 0

∴ a = -1

∴ a37 -1/a100 = (-1) – (1) = -2

56. The value of k for which the graphs of (k-1) x+y-2 = 0 and (2-k) x -3y + 1 = 0 are parallel is-

a. ½

b. -1/2

c. 2

d. -2

Ans : (k – 1) x + y – 2 = 0

∴ y = (1 – k) x + 2 ….(1)

and (2 –k) x – 3y – 1 = 0

3y = (2 – k) x +1

Y = 2 – k/3 x + 1/3 ….(2)

∵ m1 = m2

⇒ 1 – k = 2 – k/3

⇒ 3 – 3k = 2 – k

∴ k = 1/2

57. If a2 + b2 + c2 = 2 (a-b-c) – 3, then the value of (a – b + c) is-

a. -1

b. 3

c. 1

d. -2

Ans : a2 + b2 + c2 = 2(a – b – c) – 3

⇒ a2 – 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0

⇒ (a – 1)2 + (b + 1)2 + (c + 1)2 = 0

⇒ a – 1 = 0, b + 1 = 0, c + 1 = 0

⇒ a = 1, b = -1, c = -1

∴ a + b – c = 1 – 1 + 1 =1

58. If x2 + 3x + 1 = 0, then the value of x3 + 1/x3 is-

a. -18

b. 18

c. 36

d. -36

Ans : ∵ x2 + 3x + 1 = 0

⇒ x + 3 + 1/x = 0

⇒ x + 1/x = -3

⇒ (x + 1/x)3 = (-3)3

⇒ x3 + 1/x3 + 3 (-3) = -27

∴ x3 + 1/ x3 = -18

59. If xa, xb, xc = 1, then the value of a3 + b3 + c3 is –

a. 9

b. abc

c. a + b + c

d. 3abc

Ans : ∵ xa. xb. xc = 1

⇒ xa + b + c = x0

⇒ a +b + c =0

∴ a3 + b3 + c3 = 3abc

60. Base of a right pyramid is a square, length of diagonal of the base is 24√2 m. If the volume of the pyramid is 1728 cu.m, its height is-

a. 7 m

b. 8 m

c. 9 m

d. 10 m

Ans : Area of the base of the pyramid

= ½ (24√2)2 = 576m2

∴ Height of pyramid + 1728*3/576 = 9m

61. The height of a right circular cone and the radius of its circular base are respectively 9 cm and 3 cm. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e., the lower part) of the cone is 44 cubic cm. The radius of the upper circular surface of the frustum (taking = 22-7) is-

a. 3√12 cm

b. 3√13 cm

c. 3√6 cm

d. 3√20 cm

Ans : Let the radius of the upper circular part of the frustum be r cm.

(Picture)

Then r/3 = x/9 = AC/AD

∴ x = 3r (where AC = x cm)

⇒ /3h(r12 + r1r2+r22 = 44

⇒ /3(9 – x)*(9 + 3r + r2) = 44

⇒ (9 – x)*(9 + 3r + r2) = 44*3*7/22 = 42

⇒ 81 + 27r + 9r2 – 9x – 3rx – r2x = 42 On putting x = 3r,

⇒ 81 + 27r + 9r2 – 9r2 – 3r3 – 27r = 42

⇒ 3r3 = 39

∴ r = 3√13 cm

62. The ratio of radii of two right circular cylinder is 2 : 3 and their heights are in the ratio 5 : 4. The ratio of their curved surface area is-

a. 5 : 6

b. 3 : 4

c. 4 : 5

d. 2 : 3

Ans : Required ratio = 2*2r*5h/2*3r*4h = 5 : 6

63. A solid cylinder has total surface area of 462 sq.cm. Curved surface area is 1/3rd of its total surface area. The volume of the cylinder is-

a. 530 cm3

b. 536 cm3

c. 539 cm3

d. 545 cm3

Ans : ∵ 2r(r + h) = 462

and 2rh = 1/3*462 = 154

∴ r + h/h = 462/154 =3

∴ r + h = 3h

∴ r = 2h

∴ 2*2h2 = 154

∴ h2 = 154*7/22*4 = 49/4

= (7/2)2

∴ h = 7/2 cm

and r = 7 cm

∴ Volume of the cylinder

= 22/7*49*7/2

= 539 cm3

64. A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, the ratio of their radius and height is-

a. 1 : 2

b. 1 : 3

c. 2 : 3

d. 3 : 4

Ans : Let the radius and height of each are r and h respectively.

∵ 2rh/r√h2 + r2 = 8/5

∴ 10h = 8√r2 + h2

⇒ 100h2 =64r2 + 64h2

∴ h2 = 64 r2/36 = (4/3 r)2

⇒ h = 4/3r

∴ r : h = 3 : 4

65. A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of radius and height of its conical part is-

a. 1 : 3

b. 1 :1

c. √3 : 1

d. 1 : √3

∵ rl = 2r2

⇒ l = 2r

⇒ √h2 + r2 = 2r

⇒ h2 = 3r2

∴ r : h = r/h

= 1 : √3

66. If O is the circumcentre of ∆ ABC and ∠OBC = 350, then the ∠BAC is equal to-

a. 550

b. 1100

c. 700

d. 350

Ans : ∴ ∠BOC = 1800 – (350 + 350) = 1100

∴ ∠BAC = 1/2 * 1100 = 550

67. If I is the incentre of ∆ ABC and ∠ BIC = 1350, then ∆ ABC is-

a. Acute angled

b. Equilateral

c. Right angled

d. Obtuse angled

Ans :

∠BIC = 1350

⇒ B/2 + C/2 = 1800 – 1350 = 450

⇒ ∠B + ∠C = 900

∴ ∠A = 1800 – (∠B + ∠C) = 900

i.e., ∆ ABC is a right angled.

68. If sin2 (∝ + β/2) is-

a. 1

b. -1

c. 0

d. 0.5

∵ sin2 ∝ + sin2 β = 2

⇒ 1 – cos2 ∝ 1 – cos2 β = 2

⇒ cos2 ∝ cos2 β = 0

⇒ cos ∝ = 0

and cos β = 0

⇒ ∝ = /2 and β = /2

∴ cos (∝ + β/2) = cos [/2 + /2 / 2]

= cos /2 = 0

69. The length of a shadow of a vertical tower is 1/√3 times its height. The angle of elevation of the Sun is-

a. 300

b. 450

c. 600

d. 900

Ans :

∵ tan θ = h/1√3 h = √3 = tan 600

70. The graphs of x +2y =3 and 3x-2y = 1 meet the Y-axis at two points having distance-

a. 8/3 units

b. 4/3 units

c. 1 unit

d. 2 units

Ans : When the graphs meet the Y-axis at two points.

Then, [x + 2y = 3] at x = 0 ⇒ [0, y1 =3/2]

[3x – 2y = 1] at x = 0

and i.e., [0, y2 = -1/2]

Required distance = (y1 – y2)

= 3/2 – (- ½) = 2 units

71. If x+1/16x = 1, then the value of 64×3 + 1/64×3 is-

a. 4

b. 52

c. 64

d. 76

∵ x + 1/16x = 1

⇒ 16×2 – 16x + 1 =0

⇒ 16×2 – 16x + 4 = 3

⇒ (4x – 2)2 = 3

⇒ 4x = 2 + √3

⇒ 64×3 = (2±√3)3

=8 + 3√3 + 6√3 (2 + √3)

= 26 + 15√3

∴ 64×3 + 1/64×3 = (26 + 15√3) + 1/ (26 + 15√3)

= (26 + 15√3) + 26 – 15√3/676 -675

=52

72. If a, b, c, are three non-zero real numbers such that a + b + c = 0, and b2 ≠ ca, then the value of a2 + b2 + c2/ b2 –ca is-

a. 3

b. 2

c. 0

d. 1

∵ a + b + c = 0

⇒ a + c = -b

⇒ a2 + c2 = b2 -2ac

⇒ a2 + b2 + c2 = 2b2 – 2ac

∴ a2 + b2 + c2/ b2 ac = 2

73. If a4 + a2 b2 + b4 = 8 and a2 + ab + b2 = 4, then the value of ab is-

a. -1

b. 0

c. 2

d. 1

∵ a4 + a2 b2 + b4/ a2 + ab + b2 = 8/4

⇒ (a2 + b2)2 – (ab) 2/ (a2 + b2 + ab) = 2

⇒ a2 – ab + b2 = 2 ….(1)

and a2 + ab + b2 = 4 …..(2)

⇒ 2ab = 2

⇒ ab = 1

74. If a = 25, b = 15, c = -10, then the value of a3 + b3 + c3 – 3abc/ (a-b)2 + (b-c)2 + (c-a)2 is-

a. 30

b. -15

c. -30

d. 15

∵ a3 + b3 + c3 – 3abc

= (25)3 + (15)3 + (-10)3 – 3*25*15*(-10)

=15625 + 3375 – 1000 + 11250 = 29250

and (a – b)2 + (b – c)2 + (c – a)2

= (10)2 + (25)2 + (-35)2

= (10)2 + 625 + 1225

= 1950

∴ Required value = 29250/1950 =15

75. A, B, C are three points on a circle. The tangent at A meets BC produced at T, ∠BTA = 400, ∠CAT = 440. The angle subtended by BC at the centre of the circle is-

a. 840

b. 920

c. 960

d. 1040

Ans : (Picture)

∠ACB = 400 + 440 = 840

∴ ∠ACO = 900 – 440 = 460 = ∠OAC

⇒ ∠OCB = ∠ACB – ∠ACO

= 840 – 460 = 380 = ∠OBC

∴ ∠BOC = 1800 – (∠OCB + ∠OBC)

= 1800 – (380 + 380) = 1040

76. If the length of a chord of a circle at a distance of 12 cm from the Centre is 10 cm, then the diameter of the circle is-

a. 13 cm

b. 15 cm

c. 26 cm

d. 30 cm

Ans : (Picture)

∵ OA = √OM2 + AM2

= √122 + 52 = 13

∴ Diameter of the circle = 2*OA

= 2*13 = 26cm

77. In ∆ ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR = 2 cm, then BC =

a. 4 cm

b. 2 cm

c. 12 cm

d. 6 cm

∵ PR/RQ = ½

But, PR = 2cm

RQ = 2*PR

= 4cm

(Picture)

∴ PQ = PR + RQ

= 2 + 4 = 6 cm

∴ BC = 2*PQ = 12CM

78. If tan θ tan 2θ = 1, then the value of sin2 2θ + tan2 is equal to –

a. ¾

b. 10/3

c. 3 ¾

d. 3

∵ tan θ * tan 2θ = 1

⇒ tan θ * 2 tan θ/1 – tan2 θ = 1

⇒ 2 tan2 θ = 1 – tan2 θ

⇒ 3 tan2 θ = 1

⇒ tan θ = 1/√3 = tan 300

∴ θ = 300

∴ sin2 2θ + tan2 2θ = sin2 600 + tan2 600

= ¾ + 3

=3 ¾

79. The value of cot /20 cot 3/20 cot 5/20 cot 7/20 cot 9/20 is-

a. -1

b. ½

c. 0

d. 1

Ans : Given Exp.

= cot /20. cot 3/20. cot 5/20. cot 7/20. cot 9/20

= cot 90. cot 270. cot 450. cot 630. cot 810

= cot 90. cot 270*1*tan 270. tan 90.

= cot 90. cot 270*1*1/ cot 270*1/ cot 90

=1

80. If sin θ+ cos θ = 17/13, 0<θ<900, then the value of sin θ- cos θ is-

a. 5/17

b. 3/19

c. 7/10

d. 7/13

∵ sin θ + cos θ = 17/13

⇒ sin2 θ + cos2 θ + 2sin θ.cos θ = 289/169

∴ 2sin θ.cos θ = 289 /169 -1

= 289 -169/169 = 120/169

∴ sin2 θ + cos2 θ – 2 sin2 θ.cos θ = 1 – 120/169

= 49/169

⇒ (sin θ – cos θ)2 = (7/13)2

∴ sin θ – cos θ = 7/13