The CAT QA section requires speed and accuracy, along with a thorough understanding of the Linear & Quadratic Equations. This article provides a set of MCQs on Linear & Quadratic Equations 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 2025 exam 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 Linear & Quadratic Equations
1. If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is
A
0
B
1
C
\(\frac{-4}{3}\)
D
\(\frac{8}{3}\)
2. If \(f(x)=x^2−7x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))−3x\) is
A
-20
B
-15
C
-12
D
-16
3. If x and y are real numbers such that x2 + (x-2y-1)2 = 4y(x+y), here the value x-2y is?
A
1
B
2
C
0
D
-1
4. The equation \(x^3+(2r+1)x^2+(4r-1)x+2=0\) has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of \(r\) is
A
2
B
-2
C
3
D
0
5. A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is
A
15
B
17
C
19
D
23
6. Let \(k\) be the largest integer such that the equation \((x-1)^2+2kx+11=0\) has no real roots. If \(y\) is a positive real number, then the least possible value of \(\frac{k}{4y}+9y\) is
A
4
B
6
C
8
D
10
7. The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
A
1620000
B
1296000
C
1944000
D
972000
8. Let \(k\) be a constant. The equations \(kx + y = 3\) and \(4x + ky = 4\) have a unique solution if and only if
A
\(|k|≠2\)
B
\(|k|=2\)
C
\(k≠2\)
D
\(k=2\)
9. Let \(m\) and \(n\) be positive integers, If \(x^2+mx+2n=0\) and \(x^2+2nx+m=0\) have real roots, then the smallest possible value of \(m+n\) is
A
7
B
8
C
5
D
6
10. Let \(\alpha\) and \(\beta\) be the two distinct roots of the equation of 2x2-6x+k=0, such that (\(\alpha+\beta\)) and \(\alpha\beta\) are the distinct roots of the equation x2+px+p=0, then, the value of 8(k-p) ?
A
1
B
4
C
6
D
3
11. Given below are 3 equations I, II and III where 'a' and 'b' are the roots of equation I where (a < b) and 'c' and’d’ are roots of equation II where (c < d). On this basis, solve for equation III and find the relationship between 'z' and 'k' given that k = 11
I. 3x(x - 12) + 72 = x2 - 11x - 5
II. 5y(y - 3) - 64 = y(3y - 2) – 19
III. (z + 2a - d)2 = 169
I. 3x(x - 12) + 72 = x2 - 11x - 5
II. 5y(y - 3) - 64 = y(3y - 2) – 19
III. (z + 2a - d)2 = 169
A
z > k
B
z < k
C
z = k or the relationship cannot be established
D
z ≤ k
12. If x2 - 5x + 6 = 0, what is the value of x3 - 3x2 + 2x?
A
6
B
12
C
18
D
24
13. If \(3x + 4y = 12\) and \(x - y = 1\), what is the value of \(x + y\)?
A
\(\dfrac{25}{7}\)
B
\(\dfrac{16}{7}\)
C
\(\dfrac{9}{7}\)
D
\(\dfrac{7}{2}\)
14. If the roots of the equation x2 - kx + 16 = 0 are integers, what is the sum of the roots?
A
4
B
6
C
8
D
10
15. A shop sells two types of pens at Rs. 10 and Rs. 15 each. If 50 pens are sold for Rs. 650, how many pens of Rs. 10 were sold?
A
20
B
25
C
30
D
35
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