Number Series, Quadratic Equations, Simplification, Approximation - One Line Questions
1.
If the roots of the quadratic equation 2x^2 + kx + 6 = 0 are 2 and 3, what is the value of k? —
-10
2.
If the roots of the quadratic equation ax^2 + bx + c = 0 are real and equal, then the discriminant is: —
= 0
3.
Simplify: (7/3) * (9/14) + (5/6) —
1
4.
Simplify: (4/7) / (16/21) * (7/3) —
3/4
5.
What is the next term in the series: 1, 8, 27, 64, ? —
125
6.
Approximate the value of (125.05)^2 - (24.95)^2 —
16000
7.
What is the next term in the series: 1, 1, 2, 3, 5, 8, ? —
13
8.
Approximate the value of sqrt(81.05) + sqrt(16.02) —
13
9.
Simplify: 6 * (15 - 7) / 4 + 5 —
14
10.
What is the result of simplifying 15% of 200? —
30
11.
For the quadratic equation 3x^2 - 4x + 5 = 0, the discriminant is: —
-16
12.
If one root of the quadratic equation x^2 - 5x + c = 0 is 2, what is the other root? —
3
13.
Consider the quadratic equation x^2 + 4x + 4 = 0. What are its roots? —
-2 and -2
14.
What are the roots of the quadratic equation x^2 - 5x + 6 = 0? —
2 and 3
15.
Approximate the value of sqrt(100.15) * 3.98 —
40
16.
Find the missing term in the series: 11, 13, 17, 19, ? —
23
17.
What is the next number in the series: 5, 15, 45, 135, ? —
405
18.
What is the missing term in the series: 10, 12, 16, 22, ? —
30
19.
What is the product of the roots of the quadratic equation 3x^2 + 6x - 9 = 0? —
-3
20.
Solve for x: 2x^2 - 18 = 0 —
3 and -3
21.
Find the roots of the quadratic equation x^2 - 9 = 0. —
3 and -3
22.
Identify the pattern in the series: 1, 4, 9, 16, 25. What is the next term? —
36
23.
If a number series is 2, 5, 10, 17, 26, what is the next term? —
37
24.
Approximate the value of 36.01 * 10.98 —
396
25.
If the quadratic equation x^2 + px + 8 = 0 has equal roots, what is the value of p? —
-8
26.
Simplify: 25% of 80 + 50% of 60 —
60
27.
What is the next number in the series: 10, 20, 30, 40, ? —
50
28.
For the quadratic equation 2x^2 - 5x + 2 = 0, what is the sum of its roots? —
5/2
29.
Approximate the value of 19.98% of 500.12 —
100
30.
Approximate the value of (7.99)^3 —
512
31.
If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k? —
10
32.
What is the missing term in the series: 3, 7, 15, 31, ? —
63
33.
Simplify: (2/3 + 1/2) * (4/5) —
14/15
34.
Simplify: 18/5 of 25 + 12/3 of 15 —
120
35.
Find the missing term in the series: 4, 16, 36, 64, ? —
100
36.
Approximate the value of 49.87 * 19.95 + 10.12 —
1000
37.
The series 5, 10, 20, 40, 80 follows which pattern? —
Multiplying by 2 each time
38.
Consider the series 2, 8, 18, 32, 50. What is the pattern? —
2 * n^2 where n = 1, 2, 3...
39.
Which operation should be performed first in the expression 10 + (6 * 2) - 12 / 3? —
Multiplication
40.
In a number series, if the pattern involves adding a progressively increasing number, what is this type of progression called? —
Increasing Difference Series
41.
What type of series is 8, 4, 2, 1, 0.5? —
Geometric Progression (decreasing)
42.
Which of the following is the characteristic of a geometric progression in a number series? —
Constant ratio between consecutive terms
43.
Approximation is used in quantitative aptitude to: —
Estimate a value close to the exact value
44.
The series 100, 95, 90, 85, 80 is an example of: —
Arithmetic Progression
45.
The series 7, 14, 21, 28, 35 is an example of: —
Arithmetic Progression
46.
When simplifying the expression (5 + 3) * 4 / 2, what is the correct order of operations? —
Addition, Multiplication, Division
47.
Consider the quadratic equation ax^2 + bx + c = 0. If the discriminant (b^2 - 4ac) is positive, how many real roots does the equation have? —
Two distinct real roots
48.
The quadratic equation x^2 - (sum of roots)x + (product of roots) = 0 is a standard form. What are the sum and product of roots for x^2 - 7x + 12 = 0? —
Sum = 7, Product = 12
49.
If the discriminant (b^2 - 4ac) of a quadratic equation is zero, what can be said about its roots? —
Two equal real roots
50.
If the discriminant of a quadratic equation is negative, what are its roots? —
No real roots (complex roots)