The CAT QA section requires speed and accuracy, along with a thorough understanding of the Algebra. This article provides a set of MCQs on Algebra to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT preparation.
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Algebra
1. If \(5^x-3^y=13438\) and \(5^{x-1}+3^{y+1}=9686,\) then \(x+y\) equals?
A
11
B
14
C
15
D
13
2. If (x - 1)3 + (y - 2)3 + (z - 3)3 + 3(x + y - 3)(y + z - 5)(x + z - 4) = 0, then what is the value of (x + y + z) ?
A
3
B
8
C
6
D
9
3. What is the value of 'x' in the expression given below ?
\(\frac{x^4-16}{x^2-6x+9}\times\frac{x^3-27}{(x^2+4)(x+2)}\div\frac{x^2+3x+9}{x-3}=\frac{3}{2}\)
\(\frac{x^4-16}{x^2-6x+9}\times\frac{x^3-27}{(x^2+4)(x+2)}\div\frac{x^2+3x+9}{x-3}=\frac{3}{2}\)
A
2.5\r
B
3.5
C
1.5
D
4.5
4. What is the value of \((x^4+y^4+x^2y^2)\frac{x^2-2xy+y^2}{x^2-xy+y^2}\div(x^3-y^3)\) ?
A
(x - y)/(x + y)
B
(x + y)/(x - y)
C
x + y
D
x - y
5. If a3 + b3 + c3 = 62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac ?
A
3
B
4
C
5
D
6
6. If a, b and c are integers such that a2 + b2 + c2 = 228, a + b + c = 26 and b = c, then what is the value of a ?
A
8
B
10
C
12\r
D
6
7. If \((4x^2+\frac{1}{4x^2})=2\), then what is the value of \((8x^3+\frac{1}{8x^3})\) ?
A) +2
B) -2
C) +4
D) -4
A) +2
B) -2
C) +4
D) -4
A
Only A
B
Only C
C
Both C and D
D
Both A and B
8. If a + b + c = 4, (a + b)2 + (b + c)2 + (c + a)2 = 20. Find the value of (a2 + b2 + c2).
A
4
B
8
C
6
D
2
9. If f(x)=x-5, and f2(x)=f(f(x)), f3(x)=f(f(f(x))) and so on, then find the value of f8(9).
A
-39
B
-26
C
-36
D
-31
10. If x and y are integers and – 5 ≤ x ≤ 6 and 4 ≤ y ≤ 9, then the minimum value of \(\frac{2x-y}{x} \) is____.
A
-7
B
-2
C
1
D
\(\frac{19}{5}\)
11. Nitish booked movie tickets online which collects the same internet handling charges for normal movies and 3D movies, whereas the cost price of each normal movie ticket is 80% of the 3D movie ticket. Nitish paid Rs. 1030 for two 3D movie tickets and 3 normal tickets and Rs. 610 for one 3D movie ticket and 2 normal tickets. Find the internet handling charges per ticket.
A
10
B
30
C
40
D
50
12. Nitin raised a fund for the national environmental day. The amount (in thousands) on any given day after the start of fundraising event is given by a quadratic function f(x) = ax2 + bx + c , where f(x) is the money in thousand and x is the given day. If the amount collected on the first 3 days is 9, 10, and 13, then find the amount raised on the 10th day.
A
70 thousand
B
80 thousand
C
90 thousand
D
100 thousand
13. α and β are the roots of the equation x2+9x+18=0, where α>β. Then for the equation x2-ax+b=0 with its roots as (α+β) and (-3α), find the value of (a+b).
A
0
B
-81
C
189
D
63
14. Find the range of x that satisfies the equation: || 3x-6| +4|<10.
A
(–4, 4)
B
(–4, 4)
C
(–4, 4)
D
(–4, 4)
15. If \(x + 1 = x^2\) and \(x > 0\), then \(2x^4\) is
A
\(6+4\sqrt{5}\)
B
\(3+5\sqrt{5}\)
C
\(5+3\sqrt{5}\)
D
\(7+3\sqrt{5}\)
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