Rukmini Railway Group-D Mathematics Vol-1

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Rukmini Railway Group-D Mathematics Vol-1

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Today we are sharing important notes pdf Rukmini Railway Group-D Mathematics Vol-1 SSC NOTES like SSC CGL, BANK, RAILWAYS,  RRB NTPC, LIC AAO, and many other exams.BA all Subjects list and Syllabus for all Semesters 2022   is very important for any competitive exam and this Rukmini Railway Group-D Mathematics Vol-1 for SSC, BANK, AND RAILWAYS is very useful for it. this FREE PDF will be very helpful for your examination.

 

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Rukmini Railway Group-D Mathematics Vol-1  for SSC, BANK, AND RAILWAYS is very Simple and Easy. We also Cover Basic Topics like math, Geography, History, Polity, etc, and study materials including Previous Year Question Papers, Current Affairs, Important Formulas, etc for upcoming Banking, UPSC, SSC CGL Exams. Our PDF will help you to upgrade your marks in any competitive exam.

 

Topic Related posts 

    MATH TOPICS

  1. Algebra.
  2. Arithmetic.
  3. Calculus.
  4. Geometry.
  5. Probability and Statistics.
  6. Number System.
  7. Set Theory.
  8. Trigonometry.
  9. Number System
  10. H.C.F & L.C.M
  11. Decimal Fraction
  12. Simplification
  13. Square Root & Cube Root
  14. Average
  15. Problem on Numbers
  16. Problem on Ages
  17. Surds & Indices
  18. Percentage
  19. Profit & Loss
  20. Ratio & Proportion
  21. Partnership
  22. Compound Proportion
  23. Time & Work
  24. Pipes & Cistern
  25. Time And Distance
  26. Problem on train
  27. Boats & Streams
  28. Allegation & Mixture
  29. Simple Interest
  30. Compound Interest
  31. Area
  32. Volume of Solids
  33. Races
  34. Calendar
  35. Clock
  36. Stock & Shares
  37. True Discount
  38. Algebra
  39. Banker’s Discount
  40. Linear Education in Two Variables
  41. Quadratic Equation
  42. Trigonometry
  43. Line & Angles
  44. Triangles
  45. Quadrilaterals
  46. Circle
  47. Polygons
  48.  Number Series

 

   MATH QUESTION AND ANSWER

Q1 A right circular cone is cut by 3 planes parallel to its base. The planes cut the altitude of the cone in four equal parts. Find out the ratio of volume of each part.
A
1 : 7 : 19: 37
B
1 : 8 : 27: 64
C
1: 9 : 16: 25
D
1 : 2 : 3 : 4
» Explain it
Correct Option: A

Volume of cone, V ∝r3 ∝h3

The volume of 1st part, an ∝ h3

Volume of 2nd part, b ∝ 8h3– h3 = 7h3

Volume of 3rd part, c∝ 27h3– 8h3 =19h3

Volume of 4th part, d ∝ 64h3– 27h3 = 37h3

Therefore, required ratio = h3 ∶ 7h3 ∶ 19h3 ∶ 37h3 = 1 ∶ 7 ∶ 19 ∶ 37

Hence, option A is correct.

Q2 -A merchant uses a weight of 125 grams instead of 100 grams while buying an article. He used 80 grams instead of 100 grams while selling. He marked up the price by 20% and then offers 20% discount. Find the overall profit or loss percentage.
A
20%
B
30%
C
40%
D
50%
» Explain it
Correct Option: D
Effective ratio of SP to CP

= 125 × 100 × 120 × 80 = 3
100 80 100 100 2
Therefore Profit Percentage = 1 ×100 = 50 %
2
Thus , D is the correct answer.

3 -If x =
√5 + 1 ,
√5 – 1
then the value of 5×2 – 5x – 1 will be
A
0
B
3
C
4
D
5
» Explain it
Correct Option: C
According to the given question

we have,

x =
√5 + 1 =
√5 + 1
√5 – 1
√5 – 1
Now, Numerator and denominator multiplied by (√5 + 1)

x =
(√5 + 1) × (√5 + 1)
(√5 – 1) (√5 + 1) =
(√5 + 1)2
5 – 1 = √5 + 1
2
Now we also have, 5×2 – 5x – 1

put value of x in above equation

⇒ 5 ( √5 + 1 ) 2 – 5 ( √5 + 1 ) – 1
2 2
⇒ 5 (6 + 2√5) – 5√5 – 5 – 1
4 2
⇒ 5 (3 + √5) – 5√5 – 5 – 2
2 2
⇒ 15 + 5√5 – 5√5 – 7 = 8 = 4
2 2
Hence, option C is correct.

Q4 The ratio of the work done by 50 women to the work done by 25 men, in the same time is 4 : 3. If 18 women and 12 men can finish a piece of work in 5 days, then how many women can finish the same work in 20/3 days?
A
18
B
27
C
33
D
30
» Explain it
Correct Option: B
Given that,

The ratio of the work done by 50 women and 25 men is

1 : 1
3 4
The ratio of the work done by one man and one woman
= 1 : 1
150 100
Let the time taken by one woman and one man to complete the work be 150x and 100x respectively.
18 × 5 + 12 × 5 = 1
150x 100x
x = 6
Q5 Time taken by one woman and one man to complete the work be 180 days and 120 days respectively.

The number of women worked for 20/3 days to complete the work
= 3 × 180 = 27
20
Hence, option B is correct.

 

Rukmini Railway Group-D Mathematics Vol-1

 

Q6 Two varieties of sugar are mixed in the ratio 3 : 2 and sold for ₹80 per kg to make a profit of 25%. If the cost of the variety of sugar whose quantity is more is ₹40 per kg, what is the cost of the other variety of sugar?
A
Rs. 50
B
Rs. 48
C
Rs. 75
D
Rs. 100
» Explain it
Correct Option: D
Sale price of the mixture = Rs.80

Cost price of mixture = 80 × 100 = Rs. 64
125
Rs. 40 Rs. x
\ /
Rs. 64
/ \
x – 64 24
⇒ x – 64 = 3 ⇒ x = Rs. 100
24 2
Hence, option D is correct.

In math questions answers each question are solved with an explanation. The questions are based on different topics. Care has been taken to solve the questions in such a way that students can understand each and every step.

1. Which is greater than 4?

(a) 5,

(b) -5,

(c) -1/2,

(d) -25.
Solution: 5 greater than 4.

Answer: (a)

 

 

2. Which is the smallest?

(a) -1,

(b) -1/2,

(c) 0,

(d) 3.

Solution:

The smallest number is -1.

Answer: (a)

Q 3. Combine terms: 12a + 26b -4b – 16a.

(a) 4a + 22b,

(b) -28a + 30b,

(c) -4a + 22b,

(d) 28a + 30b.
Solution:

12a + 26b -4b – 16a.

= 12a – 16a + 26b – 4b.

= -4a + 22b.
Answer: (c)

Q4. Simplify: (4 – 5) – (13 – 18 + 2).

(a) -1,

(b) –2,

(c) 1,

(d) 2.
Solution:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.
Answer: (d)

Q5. What is |-26|?

(a) -26,

(b) 26,

(c) 0,

(d) 1
Solution:

|-26|

= 26.
Answer: (b)

 

Q6. Multiply: (x – 4)(x + 5)

(a) x2 + 5x – 20,

(b) x2 – 4x – 20,

(c) x2 – x – 20,

(d) x2 + x – 20.
Solution:

(x – 4)(x + 5).

= x(x + 5) -4(x + 5).

= x2 + 5x – 4x – 20.

= x2 + x – 20.

Answer: (d)

Q7. Factor: 5x2 – 15x – 20.

(a) 5(x-4)(x+1),

(b) -2(x-4)(x+5),

(c) -5(x+4)(x-1),

(d) 5(x+4)(x+1).
Solution:

5x2 – 15x – 20.

= 5(x2 – 3x – 4).

= 5(x2 – 4x + x – 4).

= 5{x(x – 4) +1(x – 4)}.

= 5(x-4)(x+1).

Answer: (a).

Q8. Factor: 3y(x – 3) -2(x – 3).

(a) (x – 3)(x – 3),

(b) (x – 3)2,

(c) (x – 3)(3y – 2),

(d) 3y(x – 3).

 

Solution:

3y(x – 3) -2(x – 3).

= (x – 3)(3y – 2).

Answer: (c).

Q9. Solve for x: 2x – y = (3/4)x + 6.

(a) (y + 6)/5,

(b) 4(y + 6)/5,

(c) (y + 6),

(d) 4(y – 6)/5.
Solution:

2x – y = (3/4)x + 6.

or, 2x – (3/4)x = y + 6.

or, (8x -3x)/4 = y + 6.

or, 5x/4 = y + 6.

or, 5x = 4(y + 6).

or, 5x = 4y + 24.

or, x = (4y + 24)/5.

Therefore, x = 4(y + 6)/5.
Answer: (b).

Q10. Simplify:(4x2 – 2x) – (-5x2 – 8x).
Solution:

(4x2 – 2x) – (-5x2 – 8x)

= 4x2 – 2x + 5x2 + 8x.

= 4x2 + 5x2 – 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)

 

Q11. Find the value of 3 + 2 • (8 – 3)

(a) 25,

(b) 13,

(c) 17,

(d) 24,

(e) 15.
Solution:

3 + 2 • (8 – 3)

= 3 + 2 (5)

= 3 + 2 × 5

= 3 + 10

= 13

Answer: (d)

Q12. Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Solution:

33/4 ÷ 4 pounds.

= (4 × 3 + 3)/4 ÷ 4 pounds.

= 15/4 ÷ 4 pounds.

= 15/4 × 1/4 pounds.

= 15/16 pounds.

Now we know that, 1 pound = 16 ounces.

Therefore, 15/16 pounds = 15/16 × 16 ounces.

= 15 ounces.

Answer: 15 ounces.

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