# RRB NTPC Previous Year Maths Question & Answers PDF Set-2

0
2574

## RRB NTPC Previous Year Maths Question & Answers PDF Set-2

Download RRB NTPC  Previous Year Maths Questions and Answers PDF. Top 15 RRB NTPC Maths questions based on asked questions in previous exam papers very important for the Railway NTPC exam.

Question 1: Find the ratio in which a dealer should mix sugar of 12/- per kg with another sugar of 18/- per kg so that he can sell the mixture at 20/- to earn 25% profit ?

a) 2 : 1

b) 1 : 2

c) 2 : 3

d) 3 : 2

Question 2: Pipe A can fill a tank in 2 hrs and pipe B can empty the tank in 2.5 hrs, then find the time in which the tank would be filled if both pipes are opened at the same time ?

a) 10 hrs

b) 12 hrs

c) 8 hrs

d) 6 hrs

Question 3: Find the value of $\dfrac{1}{sin A} – \dfrac{sin A}{cos^2 A}$.

a) 0

b) 1

c) 2cot 2A sec A

d) 2 tan 2A sec A

Question 4: If cos x + sec x = 3, find the value of $cos^3 x + sec^3 x$.

a) 12

b) 18

c) 15

d) 21

Question 5: If sec x = cosec 5x ( 0 < x < $90^\circ$), then find the value of x.

a) 12

b) 14

c) 16

d) 15

Question 6: If a = 6, b = 2 and c = -8, then what is the value of $a^3 + b^3 + c^3$?

a) 0

b) -2146

c) -286

d) -288

Question 7: If $x + \dfrac{1}{x} = 3$, find the value of $x^3 + \dfrac{1}{x^3}$.

a) 15

b) 18

c) 12

d) 9

Question 8: Find $(a+b)(a^2-ab+b^2+3ab)$ = ?

a) $(a-b)^3$

b) $(b+a)^3$

c) $(a+b)^2$

d) $(b-a)^3$

Question 9: Find the value of $x$ (from the given options), if $5x^2-13x-6 = 0$ ?

a) -2

b) 3/5

c) -3

d) -2/5

Question 10: If p, q are the sum and product of the roots of $3x^3-4x^2+5x-6=0$, then find p/q ?

a) 3

b) 1/3

c) 2/3

d) 3/2

Question 11: Two numbers A and B are in the ratio 2:5. If the sum of squares of numbers is 2349, then find the smallest number.

a) 14

b) 18

c) 20

d) 12

Question 12: The ratio of two numbers is 2:5. If the difference between the squares of the numbers is 1029, then find the sum of the two numbers.

a) 35

b) 56

c) 49

d) 28

Question 13: The average weight of 6 employees increases by 3.5 kg when a new employee comes in place of one of them weighing 57 kg. What might be the weight of the new employee?

a) 82 kg

b) 72 kg

c) 88 kg

d) 78 kg

Question 14: What is the value of (361.223-34.567$\times$2+123.345)

a) 413.137

b) 412.267

c) 415.434

d) 414.367

Question 15: Find the HCF of two numbers if LCM and product of those two numbers are 45 and 675 respectively ?

a) 25

b) 20

c) 15

d) 35

Selling price of the mixture = 20/-

Profit % = 25%

1.25(CP) = 20

CP = 16/-

Let the ratio = m:n

12(m)+18(n) = 16(m+n)

12m + 18n = 16m + 16n

4m = 2n

m/n = 2/4 = 1/2

So the answer is option B.

Let the capacity of tank = LCM of 2 and 2.5 = 10 units

Filling efficiency of pipe A = 10/2 = 5 units/hr

Emptying efficiency of pipe B = 10/2.5 = 4 units/hr

If both pipes are opened,

The tank will be filled in 10/(5-4) = 10/(1) = 10 hrs

So the answer is option A.

$1/sinA – SinA/Cos^2A$
= $(cos^2A-sin^2A)/(sinA.cos^2A)$
= $2(Cos2A)/(sin2A.CosA)$
= $2Cot2A.secA$
So the answer is option A

Given, cos x + sec x = 3
Cubing on both sides,
$(cos x + sec x)^3 = 27$

⇒ $cos^3 x + sec^3 x + 3 \times cos x \times sec x \times (cos x + sec x) = 27$
⇒ $cos^3 x + sec^3 x + 3 \times 3 = 27$
Therefore, $cos^3 x + sec^3 x = 27 – 9 = 18$

sec x = cosec 5x
⇒ sec x = sec (90 – 5x)
⇒ x = 90 – 5x
⇒ 6x = 90
⇒ x = 15

Given, a = 6, b = 2, c = -8
Here, a+b+c = 0.
We know that if a+b+c = 0, then $a^3+b^3+c^3 = 3abc$
Therefore, $a^3 + b^3 + c^3 = 3 \times 6 \times 2 \times (-8) = -288$

Given, $x + \dfrac{1}{x} = 3$
Cubing on both sides,
$(x + \dfrac{1}{x})^3 = 27$
$x^3 + \dfrac{1}{x^3} + 3 \times x \times \dfrac{1}{x} (x + \dfrac{1}{x}) = 27$
$x^3 + \dfrac{1}{x^3} + 3 \times 3 = 27$
Therefore, $x^3 + \dfrac{1}{x^3} = 27-9 = 18$

$(a+b)(a^2-ab+b^2+3ab)$ = $(a+b)(a^2+b^2+2ab)$ = $(a+b)(a+b)^2$ = $(a+b)^3$

So the answer is option B.

$5x^2-13x-6 = 0$

$5x^2-15x+2x-6 = 0$

$5x(x-3)+2(x-3) = 0$

$(x-3)(5x+2) = 0$

$x = 3 (or) x = -2/5$

So the answer is option D.

Sum of roots = p = -b/a = 4/3

Product of roots = -d/a = 6/3  = 2

p/q = (4/3)/2 = 2/3

So the answer is option C.

Let the numbers be 2x and 5x
Given, $(2x)^2 + (5x)^2 = 2349$
⇒ $29x^2 = 2349$
⇒ $x^2 = 81$
⇒ $x = 9$
Hence, Smallest number = 2x = 2*9 = 18

Let the two numbers be 2x and 5x.
Given, $(5x)^2 – (2x)^2 = 1029 ⇒$25x^2 – 4x^2 = 1029
⇒ \$21x^2 = 1029
⇒ x^2 = 49
⇒ x = 7.
Then, the two numbers will be,
2x = 2*7 = 14
5x = 5*7 = 35
Then, Sum of two numbers = 14+35 = 49.

Given that the average weight increased by 3.5 Kg when a new employee replaced an older one
So the total increase in average weight = (6 x 3.5) kg = 21 kg.
As, the new employee is replacing an older employee, the Weight of new employee = (57 + 21) kg = 78 kg.

By simplifying we get
(292.089+123.345)=415.434