# Maths Practice set for RRB NTPC PDF

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## Maths Practice set for RRB NTPC PDF

Download RRB NTPC Top-20 Maths Practice set PDF. Top 20 RRB NTPC questions based on asked questions in previous exam papers very important for the Railway NTPC exam.

Question 1: The smallest positive integer n with 24 divisors considering 1 and n as divisors is

a) 420

b) 240

c) 360

d) 480

Question 2: In an election a candidate gets 40% of votes polled and is defeated by the winning candidate by 298 votes. Find the total number of votes polled.

a) 1360

b) 1490

c) 1520

d) 1602

Question 3: Two numbers are less than the third number by 30% and 37% respectively. By what percent is the second number less than the first number?

a) 15%

b) 10%

c) 25%

d) 20%

Question 4: What is the median of the following list of numbers: 55. 53, 56, 59. 61, 69, and 31?

a) 55

b) 56

c) 59

d) 61

Question 5: If the arithmetic mean of 10 numbers is 35 and each number is increased by 2, find the mean of the new set of numbers.

a) 28

b) 34

c) 40

d) 37

Question 6: A train ‘A’ of 180 metres is running at the rate of 72 km/hr. Another train ‘B’ of 120 metres is coming from opposite direction is the rate of 108 km/hr. How long will they take to cross one another ?

a) 24 sec

b) 12 sec

c) 6 sec

d) 30 sec

Question 7: A man went to his office on cycle at the rate of 10 km/hr and reached late by 6 minutes. When he increased the speed by 2 km/hr, he reached 6 minutes before time. What is the distance between his office and his departure point ?

a) 6 km

b) 7 km

c) 12 km

d) 16 km

Question 8: 10 persons can build a wall in 8 days. How many persons can build this wall in half day ?

a) 80

b) 100

c) 120

d) 160

Question 9: A train of 150 metres crosses a railway bridge in 26 seconds at a speed of 90 km/hr. What is the length of this bridge ?

a) 500 metres

b) 60 metres

c) 650 metres

d) 550 metres

Question 10: If the length of a rectangle is decreased by 5 metres and breadth increased by 3 metres, its area decreases by 9 $m^{2}$. If its length is increased by 3 m and breadth by 2 m,its area increases by 67 $m^{2}$. What is the length of a rectangle ?

a) 8 m

b) 15.6 m

c) 17 m

d) 18.5 m

Question 11: There is a path 1 m wide outside a rectangular field of 16 m length and 11m breadth then the total area of the path is

a) 58 sq.m

b) 68 sq.m

c) 36 sq.m

d) 28 sq.m

Question 12: The value of $cos^{2}$90°- $sin^{2}$90° is

a) 1

b) $\frac{1}{2}$

c) -1

d) None of these

Question 13: A triangle has a perimeter of 200. If two of its sides are equal and the third side is 20 more than the equal sides, what is the length of the third side?

a) 60

b) 50

c) 80

d) 70

Question 14: A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30° with the ground. How high on the wall does the ladder reach?

a) 10 m

b) 17.32 m

c) 34.64 m

d) 30 m

Question 15: A invested Rs 10,000 for 9 months and B invested Rs 18,000 for some times in a business If the profits of A and B are equal then the period of time for which B’s capital was invested is

a) 6 months

b) 5 months

c) 4 months

d) 3 months

For any given number, that can be represented as $A^{x} \times B ^ {y}$, etc

The number of factors is denoted by (x+1) x ( y+1), etc

360 = $2 ^ {3} \times 3 ^ {2} \times 5^ {1}$

So the number of factors = (3 +1) x (2+ 1) (1+ 1) = 4x3x2 = 24

For 240, it is $2 ^ {4} \times 3 ^ {1} \times 5^ {1}$

Number of factors = 5 x 2 x 2 = 20 only

There is an assumption in the question that there are only two candidates participating in the election. One candidate got 40% votes and the other candidate got 60% votes. The difference is 20% votes which are 298. If 298 votes are 20%, 100% is how much.

= 298/20% = 1490

Let the third number be x. So, the first number is .7x

The second number is .63x

So, the second number is less than the first number by .7 ie 10% of the first number.

If we organise above numbers in ascending order then we will get following sequence:

31,55.53,56,59.61,69.

There are total 5 numbers present in the series.

So,for an odd number of series median would be the middle term of the series.

Here middle term in the series is 56.

So,median would be 56.

B is correct choice.

It is the property of arithmetic mean

If we increase variable by same no. that is any constant k then the mean will also be increase by k

For eg.

X x+2

1 3

2 4

3 5

4 6

5 7

— —

15 25

— —

Mean = $15\div 5$=3

Mean for x+2= $25\div 5$=5

so in this question

Mean =35

Increased no. =2

Then increased mean = 37

Speed of the train A = 72 * 5 /18 = 20 m/s

Speed of train B = 108 * 5/18 = 30 m/s

Total time to cross each other = total distance / total speed

= 300/50 = 6 seconds

Let the distance be d.

D/10 = T+ 1/10

D/12 = T – 1/10

So, D = 12 kilometers.

10 people can build a wall in 8 days

80 people can build a wall in 1 day

160 people can build a wall in half day.

90 kmph = 90 * 5 /18 = 25 m/s

(150 + x ) / 26 = 25

So, x = 500 mts

(l – 5)(b+3) = lb – 9 …. (1)

(l+ 3)(b+2) = lb + 67 …… (2)

(1) => lb – 5b + 3l -15 = lb – 9

or 3l – 5b = 6

(2) = > lb + 3b + 2l + 6 = lb + 67

or 2l + 3b = 61

from these equations, l = 17 m

The area of the bigger rectangle is 18 x 13

The are of the smaller rectangle is 16 x 11

The required value is 18 x 13 – 16 x 11 = 58 sq.m

Cos 90 = 0

sin 90 = 1

So, the given expression is 0 – 1 = -1

Let the equal side be x.

x + x + x + 20 = 200

x = 60

Length of third side = 80

So, the answer would be option c)80.

From the given information, Below is the figure formed.

From the figure,We can say $Sin 30 = \frac{height of wall}{height of ladder}$

=> $\frac{1}{2}=\frac{height of wall}{20}$

=> height of wall = 10m