0
2269

# Algebra Questions PDF For RRB Group D

Download Top 20 RRB Group-D Algebra Questions and Answers PDF. RRB Group-D Algebra questions based on asked questions in previous exam papers very important for the Railway Group-D exam.

Question 1: If (a+b)*(b+c)*(c+a) = 0, what is the value of $(a+b+c)^3$?

a) 0

b) $a^3+b^3+c^3$

c) $3a^2bc + 3b^2ca + 3c^2ab$

d) 3abc

Question 2: Given: a < b, c $\geq$ b and d > c. Which of the following option best describes the relationship between a and d?

a) a is less than d

b) a is less than or equal to d

c) a is equal to d

d) No relationship can be established between a and d.

Question 3: If $x^y + y^x$ = 1 for any value of x,what is the value of y?

a) -1

b) 0

c) 1

d) 2

Question 4: If 25%x + 40 % y is more than 40% x + 25% y by 15, what is the value of x – y?

a) 100

b) 0

c) -100

d) 50

Question 5: Which of the following is not a factor of $6x^3+ 23x^2+ 17x+6$?

a) x+3

b) 2x+1

c) 3x+2

d) 4x+4

Question 6: What is the value of $\frac{4.1^3 + 2.1^3}{4.1^2 + 2.1^2 – 8.61}$

a) 2

b) 6.2

c) 8.61

d) 0

Question 7: What is the value of x if $2^{2x} * 2^{2^{x}} * 2^{x}$ = 32?

a) 0

b) 1

c) 2

d) 4

Question 8: If x$\leq$y, y < z and z$\geq$w, which of the following inequalities is implied?

a) x < z

b) y$\geq$w

c) x$\leq$w

d) y>w

Question 9: Given a = 3, b =4 and c = 6, which of the following statements is true?
3a+ 4b -c = 20
ab + bc – ca = 18
abc – $c^2$ + ca – b = 52
$a^2c > b^2a$

a) Only 2

b) Only 4

c) Only 1 and 3

d) Only 2 and 4

Question 10: If $3^{y+1} – 3^{y-1}$ = 72, then what is the value of $y^2+ 2y+2$?

a) 17

b) 27

c) 37

d) 47

Question 11: The smallest positive integer n with 24 divisors considering 1 and n as divisors is

a) 420

b) 240

c) 360

d) 480

Question 12: 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 13: 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 14: The length of a rectangular hall is 8/5th of its breadth. If the perimeter of the hall is 260 feet, what is the length of the hall?

a) 60 feet

b) 70 feet

c) 80 feet

d) 90 feet

Question 15: For which of the following values of ‘m’ does the equation 3x + mx = 15 have exactly one solution?

a) 0

b) -3

c) -2

d) More than one of the above

Question 16: A number is such that when 76 is subtracted from 5 times that number, the result equals that number. What is that number?

a) 19

b) 20

c) 18

d) 21

Question 17: Find the value of the expression:$\frac{114^3+7^3}{114^2+7^2-(114*7)}$

a) 118

b) 124

c) 125

d) 121

Question 18: Find the value of the following expression:$\frac{124^3+1^3+7^3-(3*124*1*7)}{124^2+1^2+7^2-(124*1)-(124*7)-(7*1)}$

a) 125

b) 132

c) 116

d) 119

Question 19: The smallest positive integer n with 24 divisors considering 1 and n as divisors is

a) 420

b) 240

c) 360

d) 480

Question 20: The HCF of x and y is 15 such that both x and y are greater than 15 and x > y. Find the minimum sum of x and y.

a) 60

b) 45

c) 75

d) 30

The formula we use here is $(a+b+c)^3$ = $a^3 + b^3+c^3$ + 3(a+b)(b+c)(c+a)

Given: a < b, c $\geq$ b and d > c.
So, a < b $\leq$ c < d
Let’s consider the two cases:
b is less than c
So, a < b < c < d
Hence a is less than d

2) b is equal to c
So, a < b = c < d
Hence a is less than d

So, in both the possible scenarios, a is less than d

We can substitute each of the values of y in the equation and easily determine that y = 0 is the only possible solution for this equation.

Given: (25%x + 40 % y) – (40% x + 25% y) = 15
So, 0.15y – 0.15 x = 15
y – x = 100
So, x – y = -100

We can multiply (x+3)*(2x+1)*(3x+2) to get $6x^3+ 23x^2+ 17x+6$. So, other than (d), all others are factors of expression.

We use the formula $a^3 + b^3$ = (a+b) * $(a^2+b^2-ab)$
So, the answer = 4.1 + 2.1 = 6.2

Given $2^{2x} * 2^{2^{x}} * 2^{x}$ = $2^5$
So, $2x + 2^x + x$ = 5
We can observe that for x = 1, we can get required value.
So, option (b) is the correct answer.

Since y is less than z and x is less than or equal to y, x is less than z. So, option (a) is implied.
For options (b), (c) and (d), we have the inequality y

Substituting the values in (1), we get 3 * 3 + 4 * 4 – 6 = 19
So, (1) is false.

Substituting the values in (2), we get 3 * 4 + 4 * 6 – 6 *3 = 18
So, (2) is true

Substituting the values in (3), we get 3 * 4 * 6 – 4 * 4 + 6 * 3 – 4 = 50
So, (3) is false.

Substituting the values in (4), we get 3 * 3 * 6 > 4 * 4 * 3
So, (4) is true
Hence the correct option is (d)

Given: $3^{y+1} – 3^{y-1}$ = 72
Let y – 1 = x
So, y + 1 = x + 2
Hence, $3^{x+2} – 3^{x}$ = 72
So, $3^x$ (9-1) = 72
So, $3 ^ x = 3 ^ 2$
Hence x = 2.
Y = 3.
The required value = $3^2+2*3+2$ = 9 + 6 + 2 = 17

Let’s use the options to solve, starting with the option having the smallest number

240=2$^{4}$ x 3 x 5

the no of factors of 240=(4+1)(1+1)(1+1)=20

So B is incorrect.

360=2$^{3}$ x 3$^{2}$ x 5

no of factors=4 x 3 x 2=24

Thus, option C is the right choice.

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.

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

So, length = 8b/5
Perimeter = 2*(b+8b/5) = 26b/5 = 260
So, b = 260*5/26 = 50 feet
So, the length of the hall is 8*50/5 = 80 feet.

3x + mx = 15
=> (3+m)x = 15
=> x = 15/(3+m)

So, for all real values of m except -3, the equation has exactly one solution.

Let the number be x. 5 times that number = 5x
So, 5x – 76 = x => 4x = 76
=> x = 19

$\frac{114^3+7^3}{114^2+7^2-(114*7)} = \frac{(114+7)(114^2+7^2-(114*7))}{114^2+7^2-(114*7)}$ = 121

$\frac{124^3+1^3+7^3-(3*124*1*7)}{124^2+1^2+7^2-(124*1)-(124*7)-(7*1)} =$\frac{(124+1+7)(124^2+1^2+7^2-(124*1)-(124*7)-(7*1))}{124^2+1^2+7^2-(124*1)-(124*7)-(7*1)}$= 124+1+7 = 132 19) Answer (C) Let’s use the options to solve, starting with the option having the smallest number 240=2$^{4} $x 3 x 5 the no of factors of 240=(4+1)(1+1)(1+1)=20 So B is incorrect. 360=2$^{3}$x 3$^{2}\$ x 5

no of factors=4 x 3 x 2=24

Thus, option C is the right choice.