Analogy Questions for SSC

Analogy Questions for SSC 

Analogy Questions for SSC 

in Analogy Questions for SSC , a particular relationship is given and we have to identified another similar relationship from the given alternatives provided. Analogy means correspondence and partial similarity. There are so many types of questions of Analogy.

Type I:

Q1. Doctor : Nurse :: ? : Follower (Bank PO 1996)

1) Employer     2) Leader            3) Worker               4) Manager           5) Union

Q2. Tumbler : Empty :: Seat : ?                                                                               (Syndicate Bank PO 2010)

1) Occupied      2) Person           3) Chair                  4) Sitting                5) vacant

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Q3. Nail is related to Nail Cutter in the same way as ‘Hair’ is related to _ .                  (CBI PO 2010)

1) Oil                 2) Comb              3) Scissors             4) Haircut               5) Color

Q4. Army is related to ‘Land’  in the same way as ‘Navy’ is related to ? (Syndicate Bank PO 2010)

1) Ships            2) Battle               3) Water              4) Admiral               5) Defense

Q5. Which of the following has the same relationship as that of Money: Wealth?

(RBI Grade-B Officer 2011)

  1. Pity : Kindness
  2. Cruel : Anger
  3. Wise : Education
  4. Pride : Humility
  5. None of these

Q6. Gram is related to Mass in the same way as ‘Centimeter is related to _?

(Andhra Bank PO 2009)

1) Area                2) Volume               3) Length                  4) Sound                     5) Energy

Q7. Island is related to ‘Sea’ in the same way as an ‘Oasis’ is related to _?                       (BOM 2010)

1) Water              2) Illusion              3) Pond                       4) Trees                       5) Desert

Q8. Hematology : Blood :: Physiology : ?                                                                                (SSC CGL 2015)

1) Diseases         2) Fungi                  3) Fishes                     4) Algae

Q9. Garbage : House :: Gangue : ?                                                                                (SSC CGL Tier-I 2015)

1) Ore                  2) Drugs                 3) Factory                   4) Office

Analogy Questions for SSC CGL/ IBPS SO

Q10. Waitress : Restaurant :: ?                                                                                     (SSC CGL Tier-1 2014)

  1. Doctor : Nurse
  2. Driver : School
  3. Teacher : School
  4. Actor : Role

Q11. Book : Paper :: Bread : ?                                                                                           (SSC CGL Tier-I 2015)

  1. Flour
  2. Biscuit
  3. Cake
  4. Butter

Q12. Voyage : Sea Sickness : Heights : ? (SSC CGL Tier -I 2014)

1) Ship                        2) Travel                            3) Giddiness                   4) Motion

Type II:

Q13. The set which resembles the given set 1,5,12 is-                                            (SSC CGL Tier-I 2014)

1) 7, 11, 35                  2) 4, 8, 24                        3) 10,14, 44                    4) 9, 13, 42

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Q14. Given Set: (4, 9, 25)                                                                                                 (SSC CML (Pre) 2000)

1) 4, 25, 36                2) 9, 16, 25                        3) 4, 16, 36                     4) 9, 25, 49

Q15. Given Set: (8, 56, 72)                                                                                                (SSC CGL Tier-1 2011)

1) 7,56,63                   2) 3,15,24                         3) 6,42,54                       4) 5,30,35

Q16.  Given Set: (246, 257, 358)                                                                      (Oriental Insurance AO 2010)

1) 233,343,345           2) 273, 365, 367             3) 143,226,237              4) 145,235,325

Q17. Given Set (91, 77,143)

1) 109,99,119             2) 117,63,187               3) 119,99,187                   4) 167,121,127

Type III:

Q18. 12 : 5  ::  ? : 27                                                                                   (Oriental Insurance Company 2012)

1) 78                      2) 81                       3) 83                   4) 87

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Q19. 12 : 72 :: 8 : ?                                                                                                                 (SSC CGL Tier-1 2015)

1) 36                      2) 38                      3) 40                    4) 32

Q 20. 8: 256 :: ?                                                                                                                                  (SSC CGL 2014)

1) 7 : 343               2) 9: 243               3) 10: 500            4) 5:75

Type IV:

Q21. JOKE : GLHB  ::  RISK : ?                                                                                       (SSC CGL Tier -1 2015)

1) OFPH                2) SJTL                3) ULVN               4) QHRJ

Q22. TRAVEL : UDKUSB

        CORNER : MDQDPS

‘SURVEY’ is related to _?                                                                                                                (IBPS SO 2013)

1) UDXSTV                   2) UXDTSV                3) TVSUDX               4) UDXTVS                 5) UDXVTS

Q23.  TRAVEL : UDKUSB

        CORNER : MDQDPS

‘GROUPS’ is related to _?                                                                                                               (IBPS SO 2013)

1) TORHSP                 2) TOHRSP             3) TORPHS               4) ROTHSP                              5) ROTPHS

Q24. ‘FLOP’ is related to ‘OPFL’ and ‘SECOND’ is related to ‘ONDSEC’. Then find who is related to ‘MIXTURE’?                                                                                                                                      (BOI PO 2010)

1) TUREMIX             2) UREMIXT           3) URETMIX           4)cannot be determined          5) none of these

Q25. EARN is related to RANE and BOND is related to NODB in the same way as TEAR is related ?                                                                                                                                                 (SBI PO (Tier-I) 2008)

1) AERT            2) ATRE          3) ARET           4) REAT                      5) None of these

TYPE V :

Q26.  Prides of Lions :: ___ of Cats                                                                              (SSC CGL Tier-I 2015)

1) Bunch           2) Herd          3) School            4) Clowder

Q27. F : 216 :: L : ?                                                                                                                (SSC CGL Tier-1 2013)

1) 1723             2) 1728           3)1700                  4)1600

Q28. IC : 6 :: DP : ?                                                                                                                (SSC CGL Tier-I 2011)

1) 14           2) 10         3) 12              4) 16

Answer Key-

 

1. Leader               2. Vacant              3. Scissors              4. Water              5. 1                6. 3             7. Desert                8. Algae                9.Ore                        10. 3                      11. 1               12. 3                             13. 2                         14. 1                       15. 3                           16. 2                      17. 3              18. 1                             19. 4                         20.4                      21. 1                            22. 4                     23. 1              24. 3                           25. 1                         26. 4                      27. 2                          28. 3

Ratio and Proportion Questions for SSC

Ratio and Proportion Questions for SSC

Ratio and Proportion Questions for SSC CGL BANK POO SO and other government exam.

Ratio : The ratio of a to b is a fraction a/b and is written as a:b

Note: the value of ratio remains same if we multiply or divide  the numerator and denominator of a fraction by the same number.

a : b = a/b = am/bm = a : b  or

A : b = a/b = a/mb/m = a/m

Compounded ratio : If two or more ratios are multiplied term by term i.e the numerator to numerator and denominator to denominator, the ratio thus obtained is called their compounded ratio

Example the compounded ratio of a : b and c : d is ac : bd

Duplicate ratio : the duplicate ratio of a : b is a^2 :  b^2

Example the duplicate ratio of 2 : 3 = 4 : 9

Triplicate ratio : the triplicate ratio of a : b is a^3 : b^3

Sub-duplicate ratio : the sub-duplicate ratio of a : b is a^½ : b^½

Sub triplicate ratio : the sub triplicate ratio of a : b is a^⅓ : b^⅓

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Reciprocal or inverse ratio : the inverse ratio of a : b is 1/a : 1/b which is same as     b : a

Proportion : if two ratios are equal, then they are said to be in proportion

Example : consider 2 : 5 and 4 : 10 , since  2/5  = 4/10 , hence 2,5,4 and 10

are in proportion and can be  written as 2 : 5 : : 4 : 10

In the proportion 2 : 5 : : 4 : 10, the end terms 2 and 10 are called extremes and the middle terms  5 and 4 are called means.

Product of extremes = product of means

Continued proportion and third proportion : If a/b = b/c , then  a, b, and c are said to be in continued proportion  and c is called the third proportion. The third proportion of a and b is b^2 / a.

Fourth proportion : if a, b, c and d are in proportion then d is called the fourth proportion. The fourth proportion of a, b and c is bc / a .

Mean proportion : mean proportion of two numbers a and b is √ab

Short tricks

1. If A : B : C = a : b : c

Then A/B : B/C : C/A = ac : b2 a : ca

2. If A : B = a : b, B : C = b : c, C : D = c :d

Then A : C = a : c, A : D = a : d and B : D = b : d

3. If a sum of money R is divided in A and B in the ratio  m : n, then

  • Share of A = R/m  + n × m
  • Share of B = R/m  + n × n
  • Difference between the share of A and B = R/m  + n × (m – n)

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4. If a bag contain the coins of Rs. x, Rs. y and Rs. z in the ratio of m : n : r and the total value of the coins is Rs. R, then

  • Numbers of coin x = m/xm + yn + zr × R
  • Numbers of coin y = n/xm + yn + zr × R
  • Numbers of coin z = r/xm + yn + zr × R
5. In a glass, the ratio of the mixture of milk and water is m : n and in another glass of same quantity of mixture is p : q. If the mixture of these two glasses mix up in a third glass, then the ratio of milk and water  will be

                                       = (m/m + n  p/p + q) : (n/m + n q/p + q)

6. In X lite mixture, the ratio of water and milk is p : q. How many liters of water should be added to this mixture so that the ratio will become r : s.

                 = X(ps – qr)r/(p + q)

                           Allegation and mixture

Allegation rule : The two ingredients should be mixed in the inverse ratio of the differences of the two given prices and the mean price i.e.

(Quantity of cheaper product / quantity of dearer product ) = (Cost price of dearer – mean price) /    

                                                                        (mean price – cost price of cheaper)       

Note : C.P. of unit quantity of the mixture is called the mean price.

We represent it as

capture

     Cheaper quantity  : dearer quantity = (d – m) : (m – c)

Short tricks on allegation and mixture

  • If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of milk should be added to the mixture such that the quantity of milk increase to n % = X(n – m)/100 – n
  • If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of water should be decreased or vaporized from the mixture such that the quantity of milk increase to n % = X(m – n)/100 – n
  • A container contains X liters of water. If m liters of water is replaced by m liters of milk and this process is repeated n times , then the quantity of water in the new mixture is

                  X (1 – m/x)n

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  • If by selling mixture of milk and water on the cost price of milk there is a profit of m%, then the ratio of milk and water = 100 : r  

                                    Partnership

Partnership : To solve the problems involving partnership , use this trick

(A’s capital × A’s time in partnership)/(B’s capital ×  B’s time in partnership) = A’s profit/B’s profit

For three persons A, B and C

(A’s capital × A’s time) : (B’s capital × B’s time ) : (C’s capital × C’s time ) =

A’s profit : B’s profit : C’s profit       

For Practice Question                                               

Practice Questions on Ratios and Proportions

 

Practice Questions

Practice Questions on Ratios and Proportions

Practice Questions on Ratios and Proportions for SSC CGL,Bank IBPS SO and government examination Preparing.

1. Seats for maths, physics and biology are in the ratio 5 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats ?

      1. 2 :3 :4
      2. 6 : 7 : 8
      3. 6 : 8 : 9
      4. Cannot be determined
      5. None of these                                                                              Canara Bank PO exam. 09.02.2003

2. If a : b = 7 : 9 and b : c = 15 : 7, then what is a : c

      1. 5 :3
      2. 3 :5
      3. 7 : 21
      4. 7 : 15                                                                                        (SSC CGL Prelim Exam. 04.07.1999)

3. If A : B : C = 2 : 3 : 4, then A/B : B/C : C/A is equal to

      1. 8 : 9 : 16
      2. 8 : 9 : 12
      3. 8 : 9 : 24
      4. 4 : 9 : 16                                                                                     (SSC CGL Prelim Exam. 13.11.2005)
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4. A starts a business with an initial investments of Rs. 18000. After 4 months, B enters into the partnership with an investment of Rs. 24000. Again after two months C enters with an investment of Rs. 30000. If C receives Rs. 1845 in the profit at the end of the year , what is the total annual profit ?

      1. 6027
      2. 6327
      3. 6527
      4. 6080
      5. None of these                                                                     (Bank Of Baroda PO Exam. 14.08.2014)

Practice Questions on Ratios and Proportions

5. Tanvi started a business investing Rs. 45,000. After 8 months Jitesh joined her with a capital of Rs. 52,000. At the end of the year the total profit was Rs. 56,165. What is the share of profits of Jitesh ?

    1. 21,450
    2. 24,440
    3. 27,635
    4. 31,765
    5. None of these

                                                                   (Oriental Bank Of Commerce PO Exam. 21.12.2008)

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6. A man has divided his total money in his will in such a way that half of it goes to his wife, 2/3rd of the remaining among his three sons equally and the rest among his four daughter equally. If each daughter gets Rs. 20,000, how much money will each son get ?

      1. 50,333.33
      2. 48,233.33
      3. 53,333.33
      4. Data inadequate
      5. None of these                                                                                (SBI Banks PO Exam. 20.08.2000)

7. In a mixture of two liquids A1 and A2 the proportion of A2 by weight was 60%. If in the 60 gms mixture 15 gms A2 was added, what would be the percentage of A2 in the new mixture ?

      1. 75%
      2. 88%
      3. 68%
      4. 70%
      5. None of these

8. When one litre of water is added to a mixture of acid and water, the new mixture contains 20% acid. When one litre of acid is added to the new mixture, then the resulting mixture contains 33 1/3 % acid. The percentage of acid in the original mixture was

      1. 20%
      2. 22%
      3. 24%
      4. 25%                                                                                                            (insurance exam 22.05.2011)

9. P, Q and R started a business with investment Rs 5000, 6000 and 8000 respectively. After one year R withdrew 50% of his capital and P increased his capital by 80% of his investment. After two years in what ratio should the profit of P,Q and R be distributed ?

      1. 7 : 6 : 6
      2. 2 : 3 : 3
      3. 13 : 12 : 12
      4. 4 : 3 : 2
      5. None of these
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10. Mahesh started a business investing Rs. 42000. After 2 months Ramesh joined him with a capital of Rs. 63000 and another one month later Shyam joined with them with Rs. 56000. If the profit of Mahesh was Rs. 2403 after 6 months, then what was the profit of Shyam ?

      1. 3204
      2. 2403
      3. 1602
      4. 2060
      5. None of these

11. If A : B = 3 : 14, B : C = 4 : 3, C : D = 7 : 5 and D : E = 15 : 4, then A : E = ?

      1. 2 : 3
      2. 3 : 2
      3. 4 : 3
      4. 3 : 4

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12. The ratio of the ages of two persons is 4 : 7. If one person is older to the other by 9 years. What is the sum of their ages ?

      1. 95 years
      2. 86 years
      3. 99 years
      4. 97 years
      5. None of these

13. In an innings of a cricket match, three players A,B and C scored a total of 361 runs. If the ratio of the number of runs scored by B  to that scored by C be 3 : 2, the number of runs scored by A was

      1. 171
      2. 181
      3. 185
      4. Cannot be determined
      5. None of these                                                                      (SSC CGL Prelim Exam. 04.02.2007)

14. Ramesh bought 30 kg of apples at Rs. 150/ kg and another 20 kg of apples at Rs. 140 / kg. He mixed them together.  At what rate should he sell the mixture to earn 5 % profit ?

  1. 150.25 /kg
  2. 153.3 /kg
  3. 152 / kg
  4. 152.6 / kg
  5. None of these

15. In a school the ratio of the number of boys to the number of girls is 4:5. If the number of boys is increased by 30% and number of girls is decreased by 20%, what will be the new ratio of number of boys to that of girls ?

      1. 14 : 5
      2. 7 : 15
      3. 7 :3
      4. 13 :10
      5. None of these

16. The ratio of A and B in Rs. 58812 are 6 : 7. What is the difference between thrice of share A and thrice of share B ?

      1. Rs. 13572
      2. Rs. 4524
      3. Rs. 8425
      4. Rs. 12560
      5. None of these

17. Two persons Mahesh and Ramesh start a business with investments of Rs.27100 and Rs. 23900 respectively. After 3 months shyam joined them. Total profit at the end of the year was Rs. 14794 and shyam’s profit was 3744. What was the shyam’s investments ?

      1. Rs. 25064
      2. Rs. 23040
      3. RS. 45230
      4. Rs. 25080
      5. None of these

18. If A : B = 4 : 3, B : C = 4 : 5 and C : D = 6 : 7, then A : B : C : D = ?

      1. 8 : 9 : 30 : 35
      2. 8 : 9 : 15 : 21
      3. 32 : 24 : 30 : 35
      4. 32 : 24 : 35 : 30
      5. None of these

19. Mr. x invested a certain amount in Debit and Equity funds in the ratio of 4 : 5 respectively. At the end of one year, he earned a total dividend of 30% on his investments. After one year he reinvested the amount including dividend in the ratio of 6 : 7 in Debit and equity funds. If the amount reinvested in equity funds was Rs. 94,500, what was the original amount invested in equity funds ?

      1. 75000
      2. 81007
      3. 60000
      4. 65007
      5. None of these                                                      (SBI Associate Banks PO Exam. 07.08.2011)

20. The ratio of present ages of P and Q is 8 : 5. After 4 years their ages will be in the ratio 4 : 3 respectively. What will be the ratio of P’s age after 7 years from now and Q’s age now ?

    1. 3 :2
    2. 1 : 2
    3. 2 : 1
    4. 3 : 1
    5. None of these                                                                          (IBPS BANK PO/MT CWE_IV 18.10.2014)

Answers key

1. 1 7. 3 13. 4 19. 1
2. 1 8. 4 14. 2 20. 4
3. 3 9. 1 15. 4
4. 1 10. 3 16. 1
5. 5 11. 2 17. 2
6. 3 12. 5 18. 3

Practice Question on Geometry for SSC Exam

Practice Question on Geometry for SSC Exam 

  Practice Question on Geometry for SSC Exam, SSC CGL, BANK, RBI and other government exams.

1. ABCD is a cyclic parallelogram. The angle B is equal to

a. 30°            b. 60°          c. 45°               d. 90°

2. A quadrilateral ABCD circumscribes a circle and AB = 6 cm, CD = 5 cm and AD = 7 cm. The length of side BC is

a. 4 cm         b. 5 cm      c. 3 cm          d. 6 cm

3. The three successive angles of a cyclic quadrilateral are in the ratio 1 : 3 : 4, find the measure of the fourth angle

a. 72             b. 108       c. 36                d.30

4. Two chords of length a unit and b unit of a circle make angles 60 degree and 90 degree at the centre of a circle respectively, then the correct relation is

a. b = 3/2 a           b. b = √2a                c. b = 2a                   d. b = √3a

5. ABC is a cyclic triangle and the bisectors of angle BAC, angle ABC and angle BCA meet the circle at P, Q  and R respectively. Then the angle RQP is

a. 90 – B/2            b. 90 + B/2              c. 90 +            d. 90  – A/2

Practice Question on Geometry for SSC Exam

6. Ashok has drawn an angle of measure 4527’ when he was asked to draw an angle of 45. the percentage error in his drawing is

a. 0.5                       b. 1.0                         c.1.5                  d. 2.0

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7. The angle between the external bisectors of two angles of a triangle is 60. Then the third angle of the triangle is

a. 40                       b. 50                          c. 60                 d. 80

8. The measure of an angle whose supplement is three times as large as its complement, is

a. 75                       b. 30                         c. 45                   d. 60

9. If the complement of an angle is one- fourth of its supplementary angle, then the angle is

a. 60                      b. 30                         c. 90                   d. 120

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10. If D, E and F are the mid_ points of  BC, CA and AB respectively of the triangle ABC then the ratio of area of the parallelogram DEFB and area of the trapezium CAFD is

a. 2:3                    b. 3:4                         c. 1:2                   d. 1:3

11. If the ratio of the angles of a quadrilateral is 2 : 7 : 2 : 7, then it is a

a. Trapezium      b. Parallelogram    c. square              d. Rhombus

12. In the given figure angle ONY = 50° and OMY = 15°. then the value of the angle MON is

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a.30          b. 40              c. 20               d. 70

13. Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to  the circle. The relation of PT and PQ is

a. PT = 2PQ                   b. PT < PQ                 c. PT > PQ                   d. PT = PQ

14. AB is a chord of a circle with center O. DC is a line passing through O starting from D (on a circle) end on ( C is a point on the produced line AB). If angle BCO = 30, then angle AOD is

a. 90                              b. 120                              c. 100                         d. 80

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15. If the ratio of the angles of a quadrilateral is 2 : 2 : 2 : 2 , then it is a

a. Trapezium               b.rectangle                     c. square                    d. Rhombus

16. If O is the cir-cum center of a triangle ABC lying inside the triangle, then angle OBC – angle BAC is equal to

a.90                             b. 60                                  c. 110                           d. 120

17. Two circles of radii 5 cm and 3 cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line joining the centers of the circles is :

a. 5 : 3                        b. 3 : 5                                c. 2.5 : 1.5                   d. 1.5 : 2.5

18. The distance between the centers of two circles having radii 8 cm and 3 cm, is 13 cm. The length (in cm ) of the direct common tangent of the two circles is

a. 15                            b. 16                                   c. 18                              d. 12

19. For a triangle cir-cum center lies on one of its sides. The triangle is

a. Right angled          b. Obtused angled          c. isosceles                  d. Equilateral

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20. ABCD is a rhombus whose side AB = 4 cm and angle ABC = 120, then the length of diagonal BD is equal to

a. 1 cm                         b. 2 cm                              c. 3 cm                           d. 4 cm

21. A square ABCD is inscribed in a circle of unit radius. Semi circles are described on each sides as a diameter. The area of the region bounded by the four semicircles and the circle is

a. 1 sq. unit                b. 2 sq. unit                      c. 1.5 sq. unit                d. 2.5 sq. unit

22. A, B, C, D are four points on a circle . AC and BD intersect at a point E such that angle BEC = 130 and angle ECD = 20, angle BAC is

a. 120                         b. 90                                 c. 100                           d. 110

23. Three circles of radius 6 cm each touches each other externally. Then the distance of the center of one circle from the line joining the centers of other two circles is equal to

a. 6√5 cm                    b. 6√3 cm                          c. 6√2 cm                        d. 6√7 cm

24. The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is

a. Acute angled              b. Right angled                         c. Obtuse angled                         d. Either acute angled or right angled

25. AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm ) is

a. 4                      b. 5                   c. 6                    d. 8

                                          

                                                 Answer keys

1. d 7. c 13. d 19. a 25. b
2. a 8. c 14. a 20. d 26.
3. a 9. a 15. b 21. 27.
4. b 10. a 16. b 22. d 28.
5. a 11. b 17. 23. b 29.
6. b 12. d 18. d 24. a 30.

Geometry for SSC Exam

Geometry for SSC CGL Exam

Geometry for SSC Exam, IBPS SO, RRB and government exam preparation.

Angles  An angle is a measurement of rotation of a line about a fixed point

The fixed point is called the vertex of an angle.

Angle is generally measured in degree

We read it as angle AOB

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Types of angles

Acute angle If an angle is less than 90°, then it is called an acute angle

Right angle if an angle is equal to 90°, then it is called right angle

Obtuse angle If an angle is greater than 90° but smaller than 180°, then it is called an obtuse angle

Straight angle If an angle is equal to 180°, then it is called a straight angle

Reflexive angle If an angle is greater than 180° and smaller than 360°, then it is called reflexive angle

Complete angle If an angle is equal to 360°, then it is called complete angle

Complementary angles  Two angles are called complementary if their sum is equal to 90°

Supplementary angles Two angles are called supplementary if their sum is equal to 180° or equal to two right angles.

Transverse lines when two lines intersected by a third line then the third line is called transverse line

Corresponding angles If the lines are parallel then their corresponding angles are equal and if the corresponding angles are equal then the lines are parallel 

Corresponding angles is in the form of F

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Alternate angle if the lines are parallel then their alternate angles are equal and its converse is also true

Alternate angle is in the form of Z

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Vertically opposite angles when two lines intersect each other then the angles made at their intersection point are called vertically opposite angles.

These angles are in the form of X

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Triangle A plane figure bounded by three straight lines is called a triangle

  • A triangle has 3 angles
  • The sum of angles of a triangle is 180°

Scalene triangle A triangle whose all sides are of different length

Geometry for SSC Exam

Isosceles triangle A triangle whose at least two sides are equal

Equilateral triangle a triangle whose all sides are equal

In equilateral triangle all angles are 60°

Right angled triangle A triangle in which an angle is equal to 90°

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Pythagoras theorem In a right angled triangle AB2 + BC2 = AC2

Its converse is also true i.e. AB2 + BC2 = AC2, then the triangle is right angled triangle.

Acute angled triangle If all the angles of a triangle are acute angle, Then there is acute angled triangle.

Obtuse angled triangle If one angle of a triangle is obtuse, then there is obtuse angled triangle.

Median The median is a line segment joining a vertex to the mid_point of opposite sides.

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Centroid The intersection point of medians is called centroid.

All the medians are concurrent i.e. they intersect each other at same point

Centroid divides the median into 2:1.

Orthocentre the intersection of  altitudes drawn from vertex to its opposite sides is called orthocentre.

All the altitudes are concurrent.

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Incentre The intersection point of angle bisector is called the incentre.

All the angle bisectors are concurrent.

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Incircle is the centre of largest circle that can be inscribed in a triangle.

Circumcenter The intersection point of perpendicular bisector of any two sides of a triangle is called the circumcentre.

  • All the perpendiculars bisectors are concurrent
  • Circumcenter is the radius of largest circle that is outside the triangle and touch the vertices of triangle

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Some important results on triangle

  • If a side of a triangle is produced then the angle so formed is called  exterior angle and is equal to the sum of opposite interior angles

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  • The sum of exterior angles of a triangle is equal to 360
  • The sum of two sides of a triangle is always greater than the third side
  • The angle opposite to greater side of a triangle is greater i.e. if AB > BC > CA, then angle C > angle A > angle B and conversely
  • If any two sides of a triangle are equal, then the angles opposite to them are also equal and conversely
  • Centroid divides the median of a triangle in 2:1
  • In equilateral triangle centroid, orthocentre, incentre and circumcentre coincides i.e. they lie on the same point
  • The line joining the mid_ points of two sides of a triangle is parallel to the third side
  • Let ABC is a right angled triangle, right angle at B and D is the mid_ point of AC . then BD = ½ AC

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  • Let the bisector of angle B and angle C intersect each other at a point O.

           Then angle BOC = 90 + ½ A

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If ABC is a triangle and line BC is produced to D and AL is the bisector of angle A, then Angle ABC + angle ACD = 2 ( angle ALC)

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Congruent triangles Two triangles are said to be congruent if they are the same triangle with different rotation i.e. they are of same size (all angles and all sides are equal)

If ABC is congruent to DEF  we written this as  ABCDEF

Every triangle is congruent to itself

Some important triangle

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Sufficient condition for congruence of two triangles

  • SAS (side angle side) If two sides and angle between them of one triangle is equal to the corresponding sides and angle between them of the other triangle
  • ASA (angle side angle) If two angles and included side of one triangle is equal to the corresponding angle and included side of the other triangle
  • SSS (side side side) If three sides of one triangle is equal to the corresponding sides of the other triangle
  • RHS (right angle – hypotenuse side ) If the hypotenuse and other side of one triangle is equal to hypotenuse and the corresponding side of the other triangle

Similar triangles Two triangles are said to be similar if they have same shape but their size can be different i.e. their corresponding sides are in proportion and their corresponding angles are equal

If ΔABC is similar to ΔDEF  we written this as  ΔABC∼ΔDEF

A/B D/E = B/C E/F = AC/DF

  • Every triangle is similar to itself
  • If ΔABC∼ΔDEF then area ΔABC/area ΔDEF = (AB/DE)2= (BC/EF)2 = (AC/DF)2

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Quadrilaterals A plane figure bounded by 4 line segments is called quadrilateral

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Sum of all the angles of a quadrilateral is 360°

AC and BD are the diagonals of a quadrilateral

Types of quadrilateral

Parallelogram  A quadrilateral whose opposite sides are parallel  is called a parallelogram

  • Opposite sides of a parallelogram are equal
  • Opposite angles of a parallelogram are equal
  • Diagonals of a parallelogram bisect each other
  • Sum of consecutive angles of a parallelogram is 180°

Rectangle A quadrilateral whose opposite sides are parallel and interior angles is equal to 90°

  • Opposite sides of a rectangle are equal
  • All the angles of a rectangle are equal to 90°
  • Diagonals of a rectangle are equal and bisect each other

Rhombus A parallelogram whose all sides are equal is called a rhombus

  • Diagonals bisects each other at  90°
  • Sum of the squares of the side is equal to the squares of the diagonals

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Square A parallelogram whose all sides are equal and interior angles are equal to 90°

  • Diagonals of a square bisect each other at 90°
  • Diagonals of a square are equal

Polygons A polygon is a plane figure bounded by n straight lines

Example triangle, quadrilateral

Number of sides                                          polygon

3                                                                    triangle

4                                                                    quadrilateral

5                                                                    pentagon

6                                                                    hexagon

7                                                                    heptagon

8                                                                    octagon

9                                                                    nonagon

10                                                                 decagon

Regular polygons If all sides and all angles of a polygon are equal, then it is called a regular polygon

Properties of a polygon

  • Sum of all interior angles of a polygon of sides n is (n – 2) × 180°
  • Each exterior angle of a regular polygon of n sides is (360/n)°
  • Each interior angle of a regular polygon is (n – 2) × 180°/n
  • number of diagonals of a polygon of n sides is n × (n – 3)/2
  • Sum of all exterior angle of a regular polygon is 360°

Circle A circle is the set of all points in a plane which are equidistant from the fixed point

This fixed point is called the center of the circle and the distance of the centre to the circle is called radius

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In the above figure O is the center of circle

OD is the radius of a circle

Chord The line segment joining the two points on a circle is called a chord. In the above figure AB is the chord and CD is also a chord

Diameter the chord passing through the center is called a diameter. CD is a diameter

Tangent A line segment which touch the circle at only one point is called a tangent. EF is a tangent in the above figure

Secant A line which intersect the circle at two points is called a secant. GH is a secant in the above figure

Some important results on circle

  • The perpendicular from the center of a circle to a chord bisects the chord.
  • The line joining the center of circle to the mid_ point of the chord is perpendicular to the chord.
  • The perpendicular bisectors of two chords of a circle intersect at the center of a circle.
  • The angle subtended by an arc of the circle at the center is double the angle subtended by it at the circle.
  • Chords which are equidistant from the center of a circle are equal.
  • Equal chords are equidistant from the center of a circle.
  • Angle in a same segment of the circle are equal.
  • Tangent is perpendicular to the line joining the center of the circle to the point of contact.
  • Angle in a semi_circle is 90°.
  • Through a single point, an infinite number of circle can be drawn.
  • Through two points , an infinite number of circles can be drawn.
  • Through three-col-linear points, a unique circle can be drawn.

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Direct and Indirect Speech 2 English section

Direct and Indirect Speech 2 English section

Let us discuss important Grammar concepts from Direct and Indirect Speech 2 English section

images-29

 

Indispensable changes to keep in mind while changing the Direct Speech into Indirect speech-

  1. Says to” changes to “tells”.
  2. Said to” changes to “told”              (Note :- Never use “tells to” or “told to” while converting speech)
  3. Simple Present tense” changes to “Simple past tense.”
  4. Simple past tense ” changes to “ Past Perfect tense .”
  5. For past perfect – there will be no change
  6. Present continuous” changes to “past continuous.”
  7. Past continuous” changes  “past perfect continuous.”
  8. For past perfect continuous– No change
  9. Present perfect/Present perfect continuous” changes to “past perfect continuous.
  10. For Past perfect/ past perfect continuous– No change  
  11. shall/will  changes to should/ would
  12. May changes to might.
  13. Can changes to could.
  14. Today changes to that day.
  15. Tomorrow changes to the next day.
  16. Yesterday changes to the previous day/ the day before.
  17. Tonight changes to that night.
  18. This changes to that.
  19. These changes to those.
  20. Now changes to then.
  21. Ago changes to before.

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Interrogative Sentences-

Those sentences which are in the form of questions and carries question mark are called interrogative sentences. The interrogative sentences are of two types i.e in two form. In one form the Sentence is just a simple question whose answer is in the form of Yes/No.

In another form the sentence is in form of an inquiry.

Direct and Indirect Speech 2 English section

Changes-

  1. “Said to” changes to “asked”, “questioned”, “enquired”, interrogated.
  2. With “Wh” family sentences , no conjunction is used.
  3. Change the pronoun accordingly.
  4. If the sentence is a simple question then use conjunction ‘If’ and “whether”.
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For Instance-

Direct Speech – He said to me, “ Do you study eight hours a day.”

Indirect Speech – He asked me if I studied eight hours a day.

Direct Speech – He said to him, “ What are you doing now?”

Indirect Speech – He asked him  what he was doing then.

Direct Speech  – She said to her, “ When will the Bus arrive?”

Indirect Speech – She enquirer of her when the bus would arrive.

 

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Imperative Sentences-

Those Sentences which are in the form of “suggestions”, “advice”, “commands”, “orders” etc are called imperative sentences.

Changes-

  1. Said to” , “says to” changes to ordered /advised/ requested/ suggested etc.
  2. Change the pronoun accordingly.
  3. Conjunction “To” will be added.

For Instance-

Direct Speech   – The Captain said to the team members, “Play Hard ”

Indirect Speech – The Captain commanded the team members to play hard.

Direct Speech  – My father said to me, “Help others but do not expect anything in return.”

Indirect Speech – My Father advised me to help others but not to expect anything in return.

 

 

Optative Sentences-

Those sentences which involve blessings and wishes are called Optative sentences.

Changes-

  1. “Said” changes to “wished” or “prayed”.
  2. Use of conjunction ‘that’
  3. Change of Pronouns.

For instance-

Direct Speech – She said, “ May God bless you”

Indirect Speech –  She prayed that God might bless me.

 

Exclamatory Sentences-

Those sentence which includes excitement or emotions” are called the exclamatory sentences.

Changes-

  1. Said +Alas! Changes to Exclaimed with sorrow.
  2. Said+Hurray ! changes to exclaimed with Joy.
  3. Conjunction that is used.
  4. Change the Pronoun  accordingly

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Direct and Indirect Speech 1 English section

Direct and Indirect Speech 1

Important Grammar rules from Direct and Indirect Speech 1

images-29

 

NARRATION

  • Narration refers to description of connected events or a story.
  • Narration comprises of Direct and Indirect Speech.

 

Direct Speech

  • When the words are reported in “actual way”, it is called direct speech.
  • In direct speech the actual words are quoted in inverted commas.

For instance- Tushar says, “I play Table Tennis. ”

Here, ‘says’ is a reporting verb whereas  ‘I play Table Tennis’ is a reported speech.

Hence, in Direct Speech original words are quoted.

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Indirect Speech

  • When the words are modified and reported according to pronoun and with respect to the narrator, It is called Indirect speech.
  • The inverted commas are not used in Indirect speech.
  • For instance- Tushar says that he plays Table Tennis.

 

 

Let us observe the use of Narration in different kind of sentences. The First case will be of Assertive sentences-

 

Assertive sentences or Simple statement sentences –

Those sentences which are in the form of “simple statements” or “facts” are called assertive sentences.

  • Direct Speech   – Tushar says, “ I  work hard.”
  • Indirect Speech – Tushar says that he works hard.
  • Direct Speech – Virat Kohli says, “ I play according to the ball.”
  • Indirect Speech– Virat Kohli says that he plays according to the ball.
  • Direct Speech – She says to me, “ You Work hard.”
  • Indirect Speech – She tells me that I work hard.
  • Direct Speech – Jitesh Says to me , “ She works hard.”
  • Indirect Speech– Jitesh tells me that she works hard.
  • Direct Speech – Shalu said , “ There are eight planets in solar system.”
  • Indirect Speech– Shalu Said that there are eight planets in solar system.
  • Direct Speech – Sumit said to me , “ I am a  good dancer.”
  • Indirect Speech– Sumit told me that he was a good dancer.
  • Direct Speech – Deepak said, “ I came here yesterday.”
  • Indirect Speech – Deepak Said that he had come there the previous day.
  • Direct Speech – Tushar said, “ Only three persons are running academy”
  • Indirect Speech – Tushar said that only three persons were running academy.
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Furthermore , the remaining rules are discussed in in the next post- Direct and Indirect speech 2.

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Reading Comprehension Questions

Reading Comprehension Questions

Reading Comprehension Questions for SSC exam.

Indispensable Questions from Reading Comprehension 5 aiming Govt. Exams

 

Passage-5

Directions (1-10) : Read the following passage carefully and answer the questions given below it. Certain words have been printed in bold to help you locate  them while answering some of the questions-

Peacemaking may well have been the intent behind Samajwadi Party patriarch Mulayam Singh Yadav’s summons to his warring son and brother at a party meet in Lucknow on Monday. But the gathering soon lapsed into a tawdry spectacle of blame-calling and weepy confessional, with all three airing their grievances petulantly in full view of the assembled party faithful. Since September 13, when Mr. Yadav replaced son Akhilesh Yadav, the Chief Minister of Uttar Pradesh, with his brother Shivpal Yadav as the SP’s State unit chief, the party has been hurtling inexorably towards a split, in a blaze of sackings and accusations.

The occasional restoration of one or the other of the dramatis personae to a lost post has failed to check the feud. Monday’s developments have all but foreclosed the possibility of any resolution that could put the SP back together again in time for the Assembly elections in a dangerously polarised landscape. Ever since he became Chief Minister in 2012, Akhilesh Yadav has functioned in the shadow of his father and “uncles” — relatives and party stalwarts.

This has cut both ways for the young Chief Minister. He has had to field questions about his authority with charges that U.P. in effect had “four and a half CMs” — but it also allowed him to separate himself from the SP’s worst instincts. Their overbearing presence allowed his government an alibi for failing to maintain law and order. Their continuance served as a reminder of the generational shift he effected, from their traditional resistance to English education and computers, and their “boys will be boys” excuse-making for the politics of patronage and rent-seeking.Till the meltdown over the last couple of months, it seemed that all that the SP was headed towards was a final transition from the old guard towards a more aspirational politics.

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A convincing transition is now all but impossible, and the timing of Akhilesh Yadav’s next steps could determine his future in public life. It is ironic that Mulayam Singh Yadav, a most pragmatic politician who left no bridge unbuilt across the ideological spectrum, is presiding over nothing more than a power grab among his family and friends. Mr. Yadav’s legacy includes the deepening of the Mandal politics of social justice, being a guarantor of the safety of minorities and getting a grip on the agrarian economy in the State.

Reading Comprehension Questions

It is unfortunate to see him publicly value a fellow-traveler primarily for keeping him out of prison, and not make any effort to transform a feud into a constructive contest of ideas. At a time when he has decided to openly take stock of his inner circle’s loyalty, he has let himself down the most.

Q-1 Which of the following is most opposite in meaning to the word given in Bold warring  –

  1. Opposite                b) conflicting                c)  Matching                  d) Favoring                      e) None of these

Q-2 Which of the following is most similar in meaning to the word given in Bold tawdry –

  1. Gaudy                   b) nice                c) sophisticated                   d) tasteful                e) None of these

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Q-3 Which of the following is most similar in meaning to the word given in Bold inexorably-

  1. Sympathetic         b) lenient             c) remorseful                 d) yielding              e) None of these

Q-4 Which of the following is most similar in meaning to the word given in Bold pragmatic-

  1. Excited              b)  inefficient              c) unrealistic           d) idealistic              e) down to earth

Q-5 Which of the following is most opposite in meaning to the word given in Bold feud  –

  1. Altercation         b) disagreement              c) fracas               d) squabble              e)  harmony

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Q-6 With respect to the passage the phrase “dramatics personae” means-

1. The characters in a situation                   2.  Drama Artist                      3. Person who exacerbates drama     4. Personal drama                                          5.None of these

Q-7 The agrarian economy here refers to which region –

  1. India                      2. Uttar Pradesh                       3. Lucknow                      4. Kanpur                       5. Delhi

Q-8 In the passage a phrase “generational shift” has come which means-

  1. A communication gap   
  2. Difference in attitudes of two people of different generations.
  3. The people belonging to two different generations.
  4. None of these
  5. Leaders lacking understanding

Q-9 “The gathering soon lapsed into a tawdry spectacle of blame-calling and weepy confessional” this here refers to –

  1. The meeting had no conclusion but a drama.
  2. The meeting merged into a weepy confession.
  3. A virtual meeting.
  4. A successful meeting
  5. None of these

Q-10 The Irony about Mulayam Singh is that –

  1. He is experienced enough to handle politics
  2. His priority is still to “ power grab” among family and friends.
  3. His son  opposes  his decisions.
  4. Both b and c
  5. None of these

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