Disha Maths book for SSC PDF Download

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Disha Maths book PDF Download:-

SC CGL Maths Formulas:-

a2 – b2 = (a – b)(a + b)
(a+b)2 = a2 + 2ab + b2
a2 + b2 = (a – b)2 + 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
1.(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
1.-(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
1.(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
1(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
a4 – b4 = (a – b)(a + b)(a2 + b2)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

Number System Quick Maths Formulas

No.-1. 1 + 2 + 3 + 4 + 5 + … + n = n (n + 1)/2
No.-2. (12 + 22 + 32 + …. + n2) = n (n + 1) (2n + 1) / 6
No.-3. (13 + 23 + 33 + …. + n3) = (n (n + 1)/ 2)2
No.-4. Sum of first n odd numbers = n2
No.-5. Sum of first n even numbers = n (n + 1)
No.-6. (a + b) * (a – b) = (a2 – b2)
No.-7. a + b)*2 = (a2 + b2 + 2ab)
No.-8. (a – b)*2 = (a2 + b2 – 2ab)
No.-9. (a + b + c)*2 = a2 + b2 + c2 + 2(ab + bc + ca)
No.-10. (a3 + b3) = (a + b) * (a2 – ab + b2)
No.-11. (a3 – b3) = (a – b) * (a2 + ab + b2)
No.-12. (a3 + b3 + c3 – 3abc) = (a + b + c) * (a2 + b2 + c2 – ab – bc – ac)
No.-13. When a + b + c = 0, then a3 + b3 + c3 = 3abc

A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job?
(A) 80/13
(B) 70/13
(C) 75/13
(D) 60/13
Answer : D

A large cube is formed from the material obtained by melting of three cubes 3cm, 4cm and 5cm respectively. Find the ratio of the total surface area of the smaller cubes to the larger cube?
(A) 2:1
(B) 3:2
(C) 25:18
(D) 27:20
Answer : C

Geometry Formulas for SSC CGL.

Formulas –

No.-1. If the current age is x, then n times the age is nx.
No.-2. If the current age is x, then age n years later/hence = x + n.
No.-3. If the current age is x, then age n years ago = x – n.
No.-4. The ages in a ratio a : b will be ax and bx.
No.-5. If the current age is x, then 1/n times the age is x/n.

Quicker Methods – To find out son’s age, use this formula
No.-1. If t1 years earlier the father’s age was x times that of his son. At present the father’s age is y times that of his son. Then the present age of son will be?Son’s Age = t1 (x-1) / (x-y)

No.-2. If present age of the father is y times the age of his son. After t2 years the father’s age become z times the age of his son. Then the present age of son will be?
Son’s Age = (z-1)t1 / (y-z)

No.-3. t1 years earlier, the age of the father was x times the age of his son. After t2 years, the father’s age becomes x times the age of his son. Then the present age of son will be?
Son’s Age = [(z-1)t2 + (x-1)t1] / (x-z)

No.-4. Son’s or Daughter’s Age = [Total ages + No. of years ago (Times – 1)] / (Times+1)

No.-5. Son’s or Daughter’s Age = [Total ages – No. of years ago (Times – 1)] / (Times+1)
Father : Son
Present Age = x : y
T years before = a : b
Then, Son’s age = y * [ T(a-b) / Difference of cross product ] And Father’s age = x * [ T(a-b) / Difference of cross product ]

Some Important Maths Questions:-

1. The value of log 10000 is-
(A) 4 (B) 8 (C) 5 (D) 1 (Ans : a)
Hint: log 10000 = log10 104=4

2. A boy takes 20 minutes to reach the school at an average speed of 12 km/h. If he has to reach the school in 15 minutes, then the average speed should be…..
(A) 14 km/h (b) 15 km/h (c) 16 km/h (d) 18 km/h (Ans: c)
Hint: Distance of school =12×20/60=4 km
Now his speed=distance/time=4/15/60
=16 km/h

3. If the side of a square is doubled, then the area-
(A) doubles (B) 4 times (C) 8 times (D) 16 times (Ans : b)
Hint: According to the question, A1=a2
A2=(2a)2=4a2
So obviously it will be four times.

4. 15% of 220 =?
(A) 33 (B) 22 (C) 24 (D) 26 (Ans : a)
Hint: 220×15/100=33

5. 8888 + 888 + 88 + 8 = ?
(A) 9784 (B) 9792 (C) 9072 (D) None of these (Ans : d)

6. Out of 450 apples, 30% are rotten. How many apples are fine?
(A) 135 (B) 140 (C) 125 (D) 315 (Ans : a)
Hint: Number of rotten apples = 30% of 450
= 450×30/100=135

7. A star is about 8.1×1013 km away from the earth. Suppose light travels at a speed of 3.0×105 km/s. Find the time taken by the light from the star to reach the earth.
(A) 2.7×108 (B) 2.7×1011 (C) 7.5×104 (D) 7.5×103 (Ans : a)

Hint: Time taken from star to type to reach Earth 1
= distance/speed = 8.1×1013/3.0×105 = 2.7×108 seconds

8. An article worth Rs. By selling it for 220, Neeta made a profit of 10%. Accordingly for how much should he sell it so that the profit becomes 30%?
(a) Rs. 220 (b) Rs. 230 (c) Rs. 260 (d) Rs. 280 (Ans : c)
Hint: Cost price of article =200 × 100/110 = Rs. 200
Selling price of article to make 30% profit
= 130% of 200 = Rs. 260

9. 100 × 10 – 100 + 2000 » 100 is equal to?
(a) 20 (b) 920 (c) 980 (d) 1000 (Ans : b)
Hint: 100 × 10 – 100 + 2000 » 100
= 1000 – 100 + 20 = 900 + 20 = 920

10. A man gave 1/4th of his property to his daughter, to his sons and 1/5 to charity. Accordingly, how much did he give in total?
(a) 1/20 (b) 19/20 (c) 1/10 (d) 9/10 (Ans : b)
Hint: Total part given by the person
=1/4+½+1/5=5+10+4/20=19/20

11. If each interior angle of a regular octagon is 135°, then the exterior angle of the octagon will be-
(A) 65° (B) 75° (C) 45° (D) 70° (Ans: c)
Hint: Each exterior angle of an octagon is 180° – interior angle
= 180° – 135° = 45°

12. In a school, 85 boys and 35 girls took a public examination. If the mean marks obtained for boys was 40% and that of girls was 60%, then tell the average marks obtained in the school in percentage.
(A) 50.60 (B) 54.16 (C) 45.83 (D) 48.53 (Ans : c)
Hint: School’s average score in percentage
= 85×40+35×60/(85+35)
= 3400+2100/120
= 550/12=45.83

13. A sum of money doubles itself in 20 years at simple interest. In how many years will it be four times?
(A) 40 (B) 50 (C) 60 (D) 80 (Ans: c)
Hint: If an amount doubles in 20 years at simple interest, it will be thrice in 40 years and four times in 60 years.

14. By what should that number be multiplied to get 35% of a number?
(a) 7/20 (b) 3.5 (c) 7/20 (d) 5/20 (Ans : c)
Hint: 35%= 35/100=7/20

15. 36% of 4800 × 0.2% of 1320 is equal to-
(A) 4535.52 (B) 4551.36 (C) 4561.92 (D) 4572.48 (Ans : c)
Signal: ? = 4800 of 36/100×1320 of 0.2/100
= 1728 × 2.64
= 4561.92

16. 741560 + 935416 + 1143 + 17364 is equal to-
(A) 1694583 (B) 1695438 (C) 1695483 (D) 1659483 (Ans : c)
Hint: = 741560 + 935416 + 1143 + 17364
= 1695483

17. (7857 + 3596 + 4123) » 96 is equal to-
(A) 155.06 (B) 162.25 (C) 151.83 (D) 165.70 (Ans : b)
Signal: ? = 7857 + 3596 + 4123/96
= 15576/96 = 162.25

18. If a person goes from place A to B at a speed of 5 km/h and comes back at a speed of 4 km/h, what will be his average speed?
(A) 35/9 km/h (b) 40/9 km/h (c) 46/9 km/h (d) 50/9 km/h (Ans: b)
Hint: Average Speed = 2xy/x+y
= 2×5×4/5+4
=40/9 km/h

19. The multiples of 13 between 100 and 300 are-
(a) 18 (b) 16 (c) 21 (d) 13 (Ans : b)
Hint: There are multiples of 13 between 100 and 300
104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299
= 16

20. Four bells are rang together first and then at intervals of 6 sec, 7 sec, 8 sec and 9 sec respectively. How many times will the bells ring together in each hour and in what interval (seconds)?
(a) 14; 480 (b) 12; 504(c) 7; 504(d) 16; 580 (Ans : c)
6, 7, 8, 9 S. = 504
Hint: plus the number of rings in the hour
= 60×60/504=7.1428
So 7 times in an hour, all will ring together at an interval of 504 seconds.

Some Important Maths Questions:-

21. A monkey tries to climb a pole 30 m high. He climbs 15m in the first minute but slips 12m in the second minute. In how much time will he climb to the top of the pole at this rate?
(A) 10 minutes (B) 12 minutes (C) 11 minutes (D) 15 minutes (Ans: d)
Hint: Part Cracked in 2 Minutes
= 15 – 12 = 3 m
2×85=10 min = 3×5=15 m
In the 11th minute he will climb another 15m and climb 30m.

22. The rate of annual growth of population is 5%. If the present population of a city is 140000, then after three years the population of that city will be approximately?
(A) 164000 (B) 153000 (C) 162000 (D) 157000 (Ans : c)
Hint: Population after three years
= 140000(1+5/10)3
= 140000(21/20)3
= 140000×21×21×21/20×20×20
= 162067.5 = 162000

23. After three years at the rate of 6% per annum Rs. What will be the amount of simple interest on an amount of 5760?
(a) Rs. 1042.50 (b) Rs. 1036.80 (c) Rs. 1024.70 (d) Rs. 1060.20 (Ans : b)
Hint: Simple Interest = Principal × Rate × Time / 100
=5760×6×3/100 = Rs. 1036.80

24. Among 22 people Rs. If the amount of 41910 is divided equally, then how much will each person get?
(a) Rs. 1905 (b) Rs. 1720 (c) Rs. 1908 (d) Rs. 1910 (Ans: a)
Hint: Required amount to be received by each person
= 41910/22 = Rs. 1905

25. A train 108 m long crosses an electric pole in 20 seconds. What is the speed of the train?
(A) 36.5 km/h (b) 32.4 km/h (c) 60 km/h (d) 28.6 km/h (Ans: b)
Hint: Speed of train = 180/20 = 9 m/s
= 9×18/5 =162/5 km/h
= 32.4 km/h

26. Find the least number which when divided by 27, 42, 63 and 84 leaves a remainder of 21 in each case.
(A) 760 (B) 745 (C) 777 (D) 767 (Ans : c)
Hint: L of 27, 42, 63 and 84. S. = 756
So required number = 756 + 21 = 777

27. How many numbers up to 200 are there which are divisible by both 2 and 3?
(A) 35 (B) 27 (C) 29 (D) 33 (Ans : d)
Hint: 2nd and 3rd L. S. = 6
When 200 is divided by 6, the divisor is 33, so there are 33 numbers that are divisible by 2 and 3.

28. There are 850 students in a school. Out of these 44% are Muslim, 28% Hindu, 10% are Sikh and the rest are from other communities, then how many students are there in the number of other communities?
(A) 173 (B) 143 (C) 153 (D) 163 (Ans : c)
Hint: Percentage of students from other communities
= 100 – (44+28+10)
= 100 – 82 = 18
Number of students from other communities
= 850×18/100 = 153

29. A table costing Rs. 750 was sold at 4% loss. What was his selling price?
(a) Rs. 746 (b) Rs. 730 (c) Rs. 780 (d) Rs. 720 (Ans : d)
Hint: Required selling price = 750×(100 – 4)/100
=750×96/100 = Rs. 720

30. The average age of 15 boys in a class is 11 years. If 5 more boys of 9 years old join the class, then their average age now will be-
(A) 20 years (b) 10 years (c) 10.5 years (d) 10.33 years (Ans: c)
Hint: Required average age = 15×11+5×9/(15+5)
= 165+45/20 = 10.5 years

31. Find the greatest number which when divided by 1050, 1250 and 1650 leaves remainder 43, 31 and 7 respectively.
(A) 63 (B) 53 (C) 73 (D) 59 (Ans : b)
Hint: 1050 – 43 = 1007
1250 – 31 = 1219
1650 – 7 = 1643
Required number = M of 1007, 1219 and 1643. S. = 53

32. How many bricks of size 25 cm × 12.5 cm × 7.5 cm are required to build a wall 5 m long, 3 m high and 20 cm wide?
(a) 1200 (b) 1350 (c) 1280 (d) 1400 (Ans : c)
Hint: Number of Bricks Required
=500×300×20/25×12.5×7.5 = 1280

33. If the cost price of 18 articles is equal to the selling price of 15 articles, then find the percentage profit.
(a) 20 (b) 16 2/3 (c) 25 (d) 15 (Ans : a)
Hint: Required profit percentage
= 18 – 15/15 ×100
= 3/15×100 = 20%

34. The value of (11.6 » 0.8) (13.5 » 2) will be-
(A) 98 (B) 99 (C) 100 (D) None of these (Ans : d)
(11.6 » 0.8) (13.5 » 2)
(14.5)×(6.75) = 97.875
35. If A = ‘»’, B = ‘–’, C = ‘×’, D = ‘+’, then the value of 15 D 5 C 16 B 20 A 2 is-
(A) 85 (B) 65 (C) 75 (D) 72 (Ans : a)
Hint: After changing the sign
, = 15 + 5 × 16 – 20 » 2
= 15 + 80 – 10 = 85

36. In what time will a sum of money double itself at the rate of 20% per annum?
(a) 5 years (b) 6 years (c) 10 years (d) 80 years (Ans: a)
Hint: Required time = (2 – 1) × 100/20 = 100/20 = 5 years

37. What will be the average of first eight natural numbers?
(a) 3½ (b) 4½ (c) 5½ (d) 6½ (Ans : b)
Hint: Required average = 1+2+3+4+5+6+7+8/8
= 36/8 = 4½

38. Ram is 14th from the top and 18th from the bottom in his row, then how many students are there in the row?
(A) 31 (b) 30 (c) 32 (d) 29 (Ans : a)
Hint: Total number of students in the queue
= (14+18) – 1
= 32 – 1 = 31

39. A chair costs Rs. There is a profit of 20% on selling it for 720, then what will be the cost price of the chair?
(a) Rs. 660 (b) Rs. 580 (c) Rs. 600 (d) Rs. 560 (Ans : c)
Hint: Required purchase price
= Selling Price × 100/100 + Percentage Profit
= 720 × 100/100+20
= 720 × 100/120 × Rs. 600

40. If the successive discounts on an article are 20% and 30%, then what will be its equivalent discount?
(A) 40% (B) 56% (C) 44% (D) 62% (Ans : c)
Hint: Required Equivalent Discount
= 20 + 30 – 20 × 30/100
= 50 – 6 = 44%

maths gk questions and answers

1. Who is the father of mathematics?
Answer: Archimedes

2. Who discovered Zero (0)?
Answer: Aryabhata, 458 AD
Explanation: Aryabhatta invented zero but he did not give any symbol for zero, Brahmagupta was the first to give the symbol of zero and the rules for counting with zero.

3. What is the average of the first 50 natural numbers?
Answer: 25.5

4. When is Pi Day celebrated across the world?
Answer: 14 March

5. The value of pi?
Answer: 3.14159

6. The value of cos is 360°?
Answer 1

7. What is an angle greater than 180 degrees but less than 360 degrees called?
Answer: Reversible angle

8. Who discovered the laws of lever and pulley?
Answer: Archimedes

9. Scientist who was born on Pi Day?
Answer: Albert Einstein

10. Who discovered the Pythagorean theorem?
Answer: Pythagoras of Samosas

11. Who discovered the symbol infinity “∞”?
Answer: John Wallis

12. Father of Algebra?
Answer: Muhammad ibn Musa al-Khwarizmi (Persian mathematician)

13. Who discovered the Fibonacci sequence?
Answer: Leonardo Pisano Bigolo

14. The first person to use the Greek letter pi (π) to denote a constant?
Answer: William Jones in 1706

15. Who discovered logarithm and decimal point?
Answer: John Napier

16. Who invented the equal sign (=)?
Answer: Robert Ricarde

17. Who invented the slide rule?
Answer: William Otrade

18. Who invented the moon?
Answer: Joseph Huddart

19. Who discovered the center of gravity?
Answer: Archimedes

20. Where was the abacus invented?
Answer: China

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