Algebra Questions for RRB NTPC: Download Free PDF & Practice Now

Dreaming of a job in the Indian Railways? Whether you want to be a clerk or a Station Master, the RRB NTPC exam is your golden ticket. But to get that ticket, you have to cross the hurdle of Mathematics. Many students get scared when they see Algebra questions with x, y, and z. They think they need a lot of practice, but Algebra in RRB NTPC is actually very simple. It is not as complex as other exams. It is purely based on a few fixed formulas. If you memorize just 5 or 6 standard identities, you can solve these questions in seconds without any confusion. To help you prepare smart, we have analyzed previous Railway papers and created a PDF in which we have provided the most important Algebra questions for RRB NTPC.

Why is Algebra Important for RRB NTPC?

In both CBT-1 and CBT-2, Advanced Math plays a huge role, and Algebra is a major part of it.

• High Weightage: You can expect 2 to 3 questions in CBT-1 and around 3 to 4 questions in CBT-2.
• Time Saver: Algebra questions often use short tricks. If you know the trick for x + 1/x, you can solve it in 5 seconds while others are still calculating.
• Accuracy: There is no ambiguity. If your formula is right, your answer is right.

Important Formulas You Must Remember

You don’t need to study the whole book. RRB mostly asks questions from these specific areas:

1. Cubic Identities: (a+b)^3 and a^3 + b^3. RRB mostly asks questions where these identities are used most.
2. The “Zero” Condition: If a+b+c = 0, then a^3+b^3+c^3 = 3abc.
3. Polynomials: Finding roots of a quadratic equation (ax^2 + bx + c = 0).

Download Free PDF of Algebra Questions for RRB NTPC

We have prepared a comprehensive PDF containing exam-level questions. We have chosen questions that match the exact difficulty level of RRB NTPC—tricky but logical. Download it, save it, and practice these questions to remove your fear of variables.

Q1. If x + 1/x = 5, find the value of x^3 + 1/x^3.

(a) 125
(b) 110
(c) 115
(d) 140

Answer: (b) 110
Logic: Formula is k^3 − 3k. Here k = 5.
5^3 − 3(5) = 125 − 15 = 110.

Q2. If a + b + c = 0, find the value of a^2/bc + b^2/ca + c^2/ab.

(a) 0
(b) 1
(c) 3
(d) −1

Answer: (c) 3
Logic: Taking LCM as abc, the numerator becomes a^3 + b^3 + c^3.
Since a + b + c = 0, a^3 + b^3 + c^3 = 3abc.
So value = 3abc / abc = 3.

Q3. If x = 7 − 4√3, find the value of x + 1/x.

(a) 14
(b) 8
(c) 8√3
(d) 7

Answer: (a) 14
Logic: 1/x = 7 + 4√3 (conjugate).
Adding: (7 − 4√3) + (7 + 4√3) = 14.

Q4. Find the roots of the quadratic equation x^2 − 7x + 12 = 0.

(a) 3, 4
(b) −3, −4
(c) 2, 5
(d) 6, 1

Answer: (a) 3, 4
Logic: Numbers multiplying to 12 and adding to −7 are −3 and −4.
Roots are x = 3 and x = 4.

Q5. If a^2 + b^2 + 1/a^2 + 1/b^2 = 4, find the value of a^2 + b^2.

(a) 1
(b) 2
(c) 4
(d) 0

Answer: (b) 2
Logic: This is possible only when a^2 = 1 and b^2 = 1.
So a^2 + b^2 = 1 + 1 = 2.

Q6. If x/y = 3/4, find the value of (2x + 3y) / (3y − 2x).

(a) 3
(b) 2
(c) 1
(d) 4

Answer: (a) 3
Logic: Take x = 3 and y = 4.
Numerator = 2(3) + 3(4) = 18
Denominator = 3(4) − 2(3) = 6
Value = 18/6 = 3.

Q7. If x + y = 4 and x − y = 2, find the value of x^2 − y^2.

(a) 6
(b) 8
(c) 12
(d) 16

Answer: (b) 8
Logic: x^2 − y^2 = (x + y)(x − y)
= 4 × 2 = 8.

Q8. If (x − 3)^2 + (y − 5)^2 + (z − 4)^2 = 0, find (x + y) / z.

(a) 1
(b) 2
(c) 3
(d) 4

Answer: (b) 2
Logic: Each square must be zero.
x = 3, y = 5, z = 4
(x + y)/z = 8/4 = 2.

Q9. If x + 1/x = 2, find x^17 + 1/x^19.

(a) 2
(b) 0
(c) 1
(d) −2

Answer: (a) 2
Logic: x + 1/x = 2 implies x = 1.
1^17 + 1/1^19 = 2.

Q10. The factors of x^2 + x − 20 are:

(a) (x + 5)(x − 4)
(b) (x − 5)(x + 4)
(c) (x + 2)(x − 10)
(d) (x − 2)(x + 10)

Answer: (a) (x + 5)(x − 4)
Logic: Numbers multiplying to −20 and adding to +1 are +5 and −4.

How to Prepare for Algebra Easily?

Don’t calculate everything. Use smart tricks to save time.

• Value Putting Method: This is the best trick for RRB NTPC. If a question has variables (a, b, c) and options are numbers, just assume a=1, b=1, c=1 (or other small numbers) and solve. It works 90% of the time!
• Memorize Cubes: Learn cubes up to 15. It helps in solving a^3+b^3 questions quickly.
• Use Options: For finding roots of quadratic equations, don’t solve the equation. Just put the option values in the equation to see which one makes it zero.
• Attempt Topic Tests: Reading formulas is not enough. You must apply them. Attempt our Free Topic Tests to increase your speed and accuracy.

FAQs: Algebra Questions for RRB NTPC

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